Class and Level Geekery XIV - We are the Geek Pantheon

[Reboot]

But your question does actually deserve a serious answer. When we are dealing with a roll of one or two dice, maybe three, then taking the minimum or maximum as appropriate is entirely sensible. But more dice than that makes it sensible for the purposes of this thread to assume the average. It's nearly 30 years since I studied statistics seriously, but I still remember the binomial distribution.

Averages, standard deviations, etc are irrelevant: God does not roll dice. Nor does he work based on the most statistically probable rolls.

[Emanick]

Averages, standard deviations, etc are irrelevant: God does not roll dice. Nor does he work based on the most statistically probable rolls.

Yes, but for the purposes of this thread, we ignore dramatic effect and treat OOTS as if it operated as a normal game, except for the caveats that we know exist or have strong evidence that they exist (e.g. flight encumbrance rules, teleportation not requiring touch, Medium-sized goblins, etc.).

This thread would quickly become impossible to maintain if we acted as though the Rule of Plot, rather than RAW, predominated. The Giant specifically pointed that out in this thread a couple years ago, if you recall.

I should also note that, in the comic you linked, an in-universe explanation for why Qarr was able to summon a pit fiend (or w/e that thing was) was provided in one of the following strips, rather than one relying on the Rule of Drama.

[zimmerwald1915]

This thread would quickly become impossible to maintain if we acted as though the Rule of Plot, rather than RAW, predominated. The Giant specifically pointed that out in this thread a couple years ago, if you recall.

Good thing nobody's suggesting that. What is being pointed out is that we have no reason to privilege the statistically likely over the statistically-unlikely but rules-permitted outcomes. Specifically, we don't need to invoke special circumstances to explain why a fireball dealt enough damage to a bunch of frost giants that Haley could kill them with sneak attacks.

[Reboot]

Good thing nobody's suggesting that. What is being pointed out is that we have no reason to privilege the statistically likely over the statistically-unlikely but rules-permitted outcomes. Specifically, we don't need to invoke special circumstances to explain why a fireball dealt enough damage to a bunch of frost giants that Haley could kill them with sneak attacks.

What he said. ↑

[Emanick]

Good thing nobody's suggesting that. What is being pointed out is that we have no reason to privilege the statistically likely over the statistically-unlikely but rules-permitted outcomes. Specifically, we don't need to invoke special circumstances to explain why a fireball dealt enough damage to a bunch of frost giants that Haley could kill them with sneak attacks.

Assuming that Haley and V both rolled max damage would be tantamount to assuming Rule of Plot, IMO - by RAW the odds of that occurring would be, at minimum, one in quadrillions, i.e. functionally impossible. If it was a question of whether that happened, or if something unlikely but many orders of magnitude more probable was happening - Haley having gained a level and getting more sneak attack damage, V having an ability that increased hir fire damage, etc. - then it would make much less sense to privilege the status quo. Whether we could come up with a single plausible alternative explanation for the scene is, of course, another question entirely.

Now, I don't think we need special circumstances to explain why the frost giants died so easily, so this is a hypothetical. But it's an artificial distinction to try and differentiate between "Rule of Plot" and "oh, they just happened to roll a damage total that they had a 1 in 1 trillion chance of producing." If we assume that the latter is plausible, then we also need to consider that Elan may well be a closet lammasu.

[Reboot]

Not just in that direction. A Frost Giant has (14d8+70)hp. Now, that's generally treated as 133hp, assuming an average roll of 4.5 (in the middle of the bell curve).

But an average roll of 4 is 126hp.
An average roll of 3.5 is 119hp
An average roll of 3 is 112hp
An average roll of 2.5 is 105hp.

It is entirely possible to roll very badly (or very well). That's the whole POINT of having XdY+Z numbers rather than just a straight figure, after all! At what point does a giant's HP get ludicrously low, IYO?

[And, of course, flip the whole thing for damage rolls]

[Jasdoif]

Now, I don't think we need special circumstances to explain why the frost giants died so easily, so this is a hypothetical. But it's an artificial distinction to try and differentiate between "Rule of Plot" and "oh, they just happened to roll a damage total that they had a 1 in 1 trillion chance of producing." If we assume that the latter is plausible, then we also need to consider that Elan may well be a closet lammasu.

What matters is that the latter is possible under the existing writeup we have for Haley, meaning there's no way to guarantee a modification for that writeup would be more accurate (or equally accurate).


But since I'm curious now....OK, let's see how the average results go.

A frost giant has an average of 133 hp. Vaarsuvius didn't declare any metamagic modifiers, so the spell isn't modified by metamagic (mode average for spells cast without metamagic modifiers declared). That's 10d6 fire damage because of the cap, which averages 35; since frost giants are vulnerable to fire, that's increased by 50% for 52.5 .

Haley's base bow damage against the frost giants would be 1d8+5(enhancement); for an average of 9.5. So Haley's sneak attack damage would have to come up with the remaining (133-52.5-9.5) 71 points of damage.

Since sneak attack is measures in d6s, and the average on a d6 is 3.5, that requires 20 and two-sevenths d6s...since sneak attack comes in d6 increments, that means we'd have to take the ceiling to get enough damage. That's 21d6.

OK...If Haley was a level 30 rogue, she'd have 15d6 base sneak attack damage, and could have taken Improved Sneak Attack six times (the standard feats at 21, 24, 27, 30; and the rogue epic bonus feats at 24 and 28) to get 21d6.


So, totally average rolls require Haley to be level 30. I'm...actually not sure if that's worse odds than the Elanmasu.

[Seto]

Wouldn't it be easier to assume that V rolled very well? Unless I'm mistaken, V rolls once for Fireball's damage and it applies to all affected creatures, whereas Haley rolls separate damage for every sneak attack. Therefore, it find it really unlikely that Haley rolled max damage or close to max for every one of the four giants... but the possibility of V rolling max damage or close to max, on the other hand, is entirely acceptable.

If that's the case, the math gives us max 90 damage coming from the Fireball (which is a lot better than 52.5), and Haley has to fill the rest... which is still really unlikely. Oh well. She probably was very lucky. (Or, to put it that way, I find that "Haley was really lucky" is still more credible than "Haley is 30th level").

[Jasdoif]

(Or, to put it that way, I find that "Haley was really lucky" is still more credible than "Haley is 30th level").

Exactly my point: Allowing for Haley (and Vaarsuvius) to roll really high works with average-sounding levels; whereas assuming Haley and Vaarsuvius each rolled the statistically most likely roll needs beyond-outlandishly-high levels.

There's no inherent stabilization with operating on average rolls throughout, it simply shifts the unusually-high-number-ness onto the builds. And "I guess Haley and Vaarsuvius rolled really good this time! Oh well..." is far more tenable than "Haley must be the highest, or one of the highest, level characters in the comic!" The former can be isolated to the one comic, while the latter would need to be reflected in following comics (and raise questions about earlier comics).

[Quild]

I thought the standard approach here was "is what we see possible with what we know?". If answer is yes, then we can't add anything. Sadly.

V's Fireball probably does 15-90 damage each target.
Haley's attacks do 14-61 damage each target.
That's 29-151 damage for each target.

Frost Giants have 84-182 HP.

So Haley and V were lucky, no Giant had high HP and they rolled rather well.

[Tobtor]

Assuming that Haley and V both rolled max damage would be tantamount to assuming Rule of Plot, IMO - by RAW the odds of that occurring would be, at minimum, one in quadrillions, i.e. functionally impossible.

Please show your math. Is it really one in quadrillions? Also they don't need max (which is granted probably unlikely), but just "very high", or the frost giants below average. If the frost giants are average (133HP seem the accepted value) Haley and V needs to roll between 133 and their max, which is 151 (per Quild), thats a lot of non-6s rolled (152-133 is 19 short of max). As some of the damage is fixed (+5 for the bow etc).

Thus if V maxed the damge, Haley can roll 19 below her max of 56 (from the roll without modifiers by 1d8 and 8d6), which is 37. What is the chance of rolling 37 or above with 1d8 and 8d6 four times in a row? I don't know, but my guess is that its better than one-in-quadrillions.

If you want to do the math, you need to figure out how likely each roll is (for both the giants HP, and V and Haleys attacks), and then evaluate these against eachother.

Thus if the giants rolled below average, and only had, lets say 126HP then Haley should just roll 30 or above on 1d8 and 8d6 four times in a row to kill them.

Quilds numbers suggest that Haley+V do 29-151 damage, and the giants have 84-182 HP. So Haley and V might not need maximum, but I cannot be bothered to calculate the exact % for every fight in the comic. But the chance that every creature have average HP, and every attack does average damage, sound MORE unlikely to me than Haley and V rolling high enough to kill the frost giants

Using just the average is stupid, as sometimes we would end up with creatures with 1/2 a hit point (the problem is that as 10.5 is the average of 3d6, but clearly not a likely result of 3d6).

As calculating the likely outcomes of the batlle gets very tricky, it is better to use min-max.

[Dr.Zero]

As calculating the likely outcomes of the batlle gets very tricky, it is better to use min-max.

Luckily we can simulate it.
The results after 30000 simulations is shown here (I didn't do more in librecalc, because so much were already making my cpu's fan scream for air)



Please, notice that I subdivided the simulation in groups of 4 giants (for the effect of the fireball)

Anyway, we have approximately 13/10000 giants killed. Not in a single case a group of 4 was killed.

But knowing the average probability to kill a giant is enough, even if 13/10000 on a simulation of only 30000 can give a high error.

So let's be very generous and say that the real probability to kill 1 (one) FG is instead 20/10000=1/500.

Killing 4 of them requires (1/500)^4=1/62.500.000.000.
So no more than 1 chance on 62.5 billions, even being quite generous with the errors.

Edit: I correct myself. The probability is not exactly computed in that way, because, since the damage of V's fireball is the same for all the giants in the same group, the events are not independent (translating this in common: since the damage of the fireball is the same for all the 4 of them, if coupled with Haley's damage it's enough to kill one of them, then there's a greater chance that the coupled damages can kill the others).

If I came with some way to compute this, without a simulation requiring 1 million examples, I'd inform you.

[5a Violista]

You can calculate this with statistics-math without having to run tons of experiments.

Anyway, I just thought of something that could possibly severely complicate this: what are the chances all of the Frost Giants started the battle at full HP? If they all have regeneration or natural healing powers or an abundance of healers, then it seems pretty likely, but hundreds of combat-ready Frost Giants gathered together in a place with falling rocs with little notice aren't guaranteed to always be at 100% optimal strength (unless there was little-to-no thought put into what they were doing before appearing in front of the PCs). If they had been previously cliff-jumping or defending their villages from rocs or rocks or dwarves, or whatever else and don't have access to easy healing, then many of them will be at lower-than-full HP.

If they weren't at full HP, would there be some visual cue?

[Crusher]

This is a can of worms, but how do we know characters *always* state invoked meta-magic? I mean, sure, they usually do just like they usually say spell names when casting. But they don't always do it. We simply dont know that casters arent occasionally Maximizing their spells and not stating it.

Of course; the downside is that it would cast uncertainty on all our existing spell slot math.

[Black Egg]

While I agree that we shouldn't change the writeup for Haley and Vaarsuvius over this panel, I also think we shouldn't lean too much on the explanation of "lucky roll". There's a fairly good chance that we'll see similarly destructive effects multiple times in the near future, and the odds of "lucky roll" being the explanation for this event multiple times over might get pretty faint.

I don't think that we have to assume that these frost giants are standard 133 HP warriors, though. There are a LOT of these guys which, to me, means that they are mooks to our heroes. It seems reasonable to say that at least some of these frost giants aren't fully trained warriors and don't have the typical stats.

As a humorous side note, one of the groups I GM for seems convinced (and not without some evidence) that my d6 rolls average somewhere around 4.75.

[Phoniex]

If they weren't at full HP, would there be some visual cue?

There "should" be some visual cue if a character is damaged, at least the giant has been putting damage marks in since the start of the comic. So since the frost giants did not have any marks showing damage prior to getting fireballed, I think we can say they were effectively at full HP for them. I think the biggest thing we should concentrate on is the fact that the fireball "boom" is BIG. V has used fireball MANY times (I'm sure someone will link to them) but I have never seen a boom that big.. is it possible the giant is using a critical hit system and somehow V rolled the 20? Or is there a feat or something that unlocks criticals for spells? Because while the frost giants being weak against fire does explain a little bit of them taking more damage, it does not explain why this fireball goes BOOM compared to the many other FB's that V has thrown.

[Dr.Zero]

You can calculate this with statistics-math without having to run tons of experiments.

Anyway, I just thought of something that could possibly severely complicate this: what are the chances all of the Frost Giants started the battle at full HP? If they all have regeneration or natural healing powers or an abundance of healers, then it seems pretty likely, but hundreds of combat-ready Frost Giants gathered together in a place with falling rocs with little notice aren't guaranteed to always be at 100% optimal strength (unless there was little-to-no thought put into what they were doing before appearing in front of the PCs). If they had been previously cliff-jumping or defending their villages from rocs or rocks or dwarves, or whatever else and don't have access to easy healing, then many of them will be at lower-than-full HP.

If they weren't at full HP, would there be some visual cue?

Usually yes, everytime someone is hurt or not at full HP, there are clearly visible cuts and bruises.

About the numbers, there are two ways that I can think of.
First one: I write some lines of codes in C and let them run for a while.
Probably in a couple of hours I can get some tens of millions of simulations.
The other one is using the data of the 120.000 simulations (yes, I managed to go so far in librecalc, still no group of 4 killed) to get average and standard deviation of the MAX residual HP of a group of 4 giants (since that is the value that must be 0 to kill them all) and then SUPPOSING that the normal distribution is a good approximation... do nothing, because I think the table of values in my old books don't go so far to probabilities near 1/1.000.000 or worse. :D

If there is another good (and fast) solution, feel free to write your results. :)

Or we can just agree that it was practically impossible to see such an event and it happened because rule of plot and move on, more of less as for Familicide (this maybe is the best solution :D).

[Quartz]

I've re-read my post and I've spotted that I missed a very important point: since I'm assuming average HP for the giants, assuming averages elsewhere is entirely appropriate.

[Quild]

Luckily we can simulate it.
The results after 30000 simulations is shown here (I didn't do more in librecalc, because so much were already making my cpu's fan scream for air)
[...]
If I came with some way to compute this, without a simulation requiring 1 million examples, I'd inform you.

Maybe consider this approach.

V rolled very well. Like 54 or more on 10d6 (not sure about my calculation but I think there's like a 0,0045% chance of that), then you can make your simulations with Haley's damage.
So V did 80 damages to each Giant.

Now don't forget that Haley still can crit (with 1/19 chances since we know she didn't fumble)

You should have easier time for 2 or 3 giants to be dead at the same time and... even 4!
Chances are still low for the 4 to be dead even considering these unlikely high damages from V but still, it can happen.


Also these Frost Giant all have white hair instead of "light blue or dirty yellow" in SRD. Maybe these are only the older of their clan. Maybe they are from this very Frost Giant's clan with moderately lower CON than usual.

[Dr.Zero]

Maybe consider this approach.

V rolled very well. Like 54 or more on 10d6 (not sure about my calculation but I think there's like a 0,0045% chance of that), then you can make your simulations with Haley's damage.
So V did 80 damages to each Giant.

Now don't forget that Haley still can crit (with 1/19 chances since we know she didn't fumble)

You should have easier time for 2 or 3 giants to be dead at the same time and... even 4!
Chances are still low for the 4 to be dead even considering these unlikely high damages from V but still, it can happen.


Also these Frost Giant all have white hair instead of "light blue or dirty yellow" in SRD. Maybe these are only the older of their clan. Maybe they are from this very Frost Giant's clan with moderately lower CON than usual.

About the fumbling, technically a simulation cannot work in that way. :)
If we work taking in account what happens in the strip, then the probability of them killing 4 giants (and doing the relative high damage) is 100%, since it is exactly what happens.
A simulation tries all the outcomes and then check the chances to get what we see.
Anyway, I made it run 10 millions of time with and without fumbling.
This is without fumbling

Spoiler: 10 blocks, up to 10.000.000 runs, without fumbling for Haley

Show

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After 1e+06 runs:
Average HP Giant0: Starting=132.987 Ending=39.0096
Average HP Giant1: Starting=132.989 Ending=39.0214
Average HP Giant2: Starting=133.002 Ending=39.0254
Average HP Giant3: Starting=132.999 Ending=39.0291
Average Fireball damage=52.4972
Average Haley's crits=0.0500063 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97723 Sneak damage=31.4985 Total damage=41.4757
Average Total damage=93.9729
Probability at least 1 Giants killed=0.007217 (Absolutes = 7217)
Probability at least 2 Giants killed=0.000259 (Absolutes = 259)
Probability at least 3 Giants killed=1.1e-05 (Absolutes = 11)
Probability at least 4 Giants killed=1e-06 (Absolutes = 1)
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After 2e+06 runs:
Average HP Giant0: Starting=132.994 Ending=39.0213
Average HP Giant1: Starting=132.999 Ending=39.0304
Average HP Giant2: Starting=132.995 Ending=39.0242
Average HP Giant3: Starting=132.999 Ending=39.0232
Average Fireball damage=52.497
Average Haley's crits=0.0499801 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97613 Sneak damage=31.4989 Total damage=41.475
Average Total damage=93.9721
Probability at least 1 Giants killed=0.0071665 (Absolutes = 14333)
Probability at least 2 Giants killed=0.0002465 (Absolutes = 493)
Probability at least 3 Giants killed=1.15e-05 (Absolutes = 23)
Probability at least 4 Giants killed=5e-07 (Absolutes = 1)
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After 3e+06 runs:
Average HP Giant0: Starting=132.989 Ending=39.0146
Average HP Giant1: Starting=132.999 Ending=39.0279
Average HP Giant2: Starting=132.989 Ending=39.0162
Average HP Giant3: Starting=133.001 Ending=39.028
Average Fireball damage=52.4993
Average Haley's crits=0.0499354 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97466 Sneak damage=31.4989 Total damage=41.4735
Average Total damage=93.9729
Probability at least 1 Giants killed=0.007197 (Absolutes = 21591)
Probability at least 2 Giants killed=0.000246333 (Absolutes = 739)
Probability at least 3 Giants killed=1.33333e-05 (Absolutes = 40)
Probability at least 4 Giants killed=1e-06 (Absolutes = 3)
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After 4e+06 runs:
Average HP Giant0: Starting=132.991 Ending=39.0157
Average HP Giant1: Starting=132.997 Ending=39.0229
Average HP Giant2: Starting=132.993 Ending=39.0171
Average HP Giant3: Starting=133 Ending=39.0239
Average Fireball damage=52.5028
Average Haley's crits=0.0499337 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97465 Sneak damage=31.4979 Total damage=41.4725
Average Total damage=93.9753
Probability at least 1 Giants killed=0.007195 (Absolutes = 28780)
Probability at least 2 Giants killed=0.0002425 (Absolutes = 970)
Probability at least 3 Giants killed=1.25e-05 (Absolutes = 50)
Probability at least 4 Giants killed=7.5e-07 (Absolutes = 3)
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---------------------------------------
After 5e+06 runs:
Average HP Giant0: Starting=132.993 Ending=39.017
Average HP Giant1: Starting=132.996 Ending=39.0186
Average HP Giant2: Starting=132.993 Ending=39.0165
Average HP Giant3: Starting=133 Ending=39.0233
Average Fireball damage=52.5041
Average Haley's crits=0.049943 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.9746 Sneak damage=31.4979 Total damage=41.4725
Average Total damage=93.9766
Probability at least 1 Giants killed=0.0071914 (Absolutes = 35957)
Probability at least 2 Giants killed=0.0002434 (Absolutes = 1217)
Probability at least 3 Giants killed=1.26e-05 (Absolutes = 63)
Probability at least 4 Giants killed=8e-07 (Absolutes = 4)
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After 6e+06 runs:
Average HP Giant0: Starting=132.997 Ending=39.0204
Average HP Giant1: Starting=132.997 Ending=39.0194
Average HP Giant2: Starting=132.993 Ending=39.0177
Average HP Giant3: Starting=132.999 Ending=39.0233
Average Fireball damage=52.5033
Average Haley's crits=0.0499609 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97459 Sneak damage=31.4985 Total damage=41.473
Average Total damage=93.9763
Probability at least 1 Giants killed=0.00718583 (Absolutes = 43115)
Probability at least 2 Giants killed=0.000242333 (Absolutes = 1454)
Probability at least 3 Giants killed=1.18333e-05 (Absolutes = 71)
Probability at least 4 Giants killed=6.66667e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 7e+06 runs:
Average HP Giant0: Starting=132.997 Ending=39.0245
Average HP Giant1: Starting=132.998 Ending=39.0232
Average HP Giant2: Starting=132.995 Ending=39.0205
Average HP Giant3: Starting=132.999 Ending=39.026
Average Fireball damage=52.5005
Average Haley's crits=0.0499421 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97432 Sneak damage=31.4987 Total damage=41.473
Average Total damage=93.9736
Probability at least 1 Giants killed=0.00719129 (Absolutes = 50339)
Probability at least 2 Giants killed=0.000241143 (Absolutes = 1688)
Probability at least 3 Giants killed=1.21429e-05 (Absolutes = 85)
Probability at least 4 Giants killed=5.71429e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 8e+06 runs:
Average HP Giant0: Starting=132.996 Ending=39.0217
Average HP Giant1: Starting=132.998 Ending=39.0227
Average HP Giant2: Starting=132.995 Ending=39.02
Average HP Giant3: Starting=132.998 Ending=39.0248
Average Fireball damage=52.5012
Average Haley's crits=0.0499641 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97464 Sneak damage=31.4989 Total damage=41.4735
Average Total damage=93.9747
Probability at least 1 Giants killed=0.00719925 (Absolutes = 57594)
Probability at least 2 Giants killed=0.000245375 (Absolutes = 1963)
Probability at least 3 Giants killed=1.1875e-05 (Absolutes = 95)
Probability at least 4 Giants killed=5e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 9e+06 runs:
Average HP Giant0: Starting=132.997 Ending=39.021
Average HP Giant1: Starting=132.999 Ending=39.0233
Average HP Giant2: Starting=132.997 Ending=39.0202
Average HP Giant3: Starting=132.998 Ending=39.0224
Average Fireball damage=52.5018
Average Haley's crits=0.0499691 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97477 Sneak damage=31.4992 Total damage=41.474
Average Total damage=93.9758
Probability at least 1 Giants killed=0.00720244 (Absolutes = 64822)
Probability at least 2 Giants killed=0.000245556 (Absolutes = 2210)
Probability at least 3 Giants killed=1.2e-05 (Absolutes = 108)
Probability at least 4 Giants killed=4.44444e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 1e+07 runs:
Average HP Giant0: Starting=132.997 Ending=39.0208
Average HP Giant1: Starting=132.999 Ending=39.0234
Average HP Giant2: Starting=132.997 Ending=39.0199
Average HP Giant3: Starting=132.999 Ending=39.0237
Average Fireball damage=52.5021
Average Haley's crits=0.049974 Fumblings(ignored, will be 0)=0
Average Haley's base damage=9.97481 Sneak damage=31.4991 Total damage=41.4739
Average Total damage=93.976
Probability at least 1 Giants killed=0.0072066 (Absolutes = 72066)
Probability at least 2 Giants killed=0.0002451 (Absolutes = 2451)
Probability at least 3 Giants killed=1.17e-05 (Absolutes = 117)
Probability at least 4 Giants killed=4e-07 (Absolutes = 4)
---------------------------------------

Spoiler: 10 blocks, up to 10.000.000 runs, with Haley fumbling

Show

---------------------------------------
After 1e+06 runs:
Average HP Giant0: Starting=132.987 Ending=41.0616
Average HP Giant1: Starting=132.989 Ending=41.0679
Average HP Giant2: Starting=133.002 Ending=41.0796
Average HP Giant3: Starting=132.999 Ending=41.0882
Average Fireball damage=52.4972
Average Haley's crits=0.0500063 Fumblings=0.0500628
Average Haley's base damage=9.50139 Sneak damage=29.9214 Total damage=39.4228
Average Total damage=91.9199
Probability at least 1 Giants killed=0.006995 (Absolutes = 6995)
Probability at least 2 Giants killed=0.000241 (Absolutes = 241)
Probability at least 3 Giants killed=9e-06 (Absolutes = 9)
Probability at least 4 Giants killed=1e-06 (Absolutes = 1)
---------------------------------------
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After 2e+06 runs:
Average HP Giant0: Starting=132.994 Ending=41.0762
Average HP Giant1: Starting=132.999 Ending=41.0804
Average HP Giant2: Starting=132.995 Ending=41.0781
Average HP Giant3: Starting=132.999 Ending=41.0784
Average Fireball damage=52.497
Average Haley's crits=0.0499801 Fumblings=0.0500766
Average Haley's base damage=9.50019 Sneak damage=29.9214 Total damage=39.4216
Average Total damage=91.9186
Probability at least 1 Giants killed=0.006934 (Absolutes = 13868)
Probability at least 2 Giants killed=0.000229 (Absolutes = 458)
Probability at least 3 Giants killed=9e-06 (Absolutes = 18)
Probability at least 4 Giants killed=5e-07 (Absolutes = 1)
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After 3e+06 runs:
Average HP Giant0: Starting=132.989 Ending=41.0585
Average HP Giant1: Starting=132.999 Ending=41.0788
Average HP Giant2: Starting=132.989 Ending=41.0664
Average HP Giant3: Starting=133.001 Ending=41.0776
Average Fireball damage=52.4993
Average Haley's crits=0.0499354 Fumblings=0.0499631
Average Haley's base damage=9.49983 Sneak damage=29.9251 Total damage=39.4249
Average Total damage=91.9242
Probability at least 1 Giants killed=0.006964 (Absolutes = 20892)
Probability at least 2 Giants killed=0.000227667 (Absolutes = 683)
Probability at least 3 Giants killed=1.13333e-05 (Absolutes = 34)
Probability at least 4 Giants killed=1e-06 (Absolutes = 3)
---------------------------------------
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After 4e+06 runs:
Average HP Giant0: Starting=132.991 Ending=41.0599
Average HP Giant1: Starting=132.997 Ending=41.0753
Average HP Giant2: Starting=132.993 Ending=41.0697
Average HP Giant3: Starting=133 Ending=41.0743
Average Fireball damage=52.5028
Average Haley's crits=0.0499337 Fumblings=0.0500012
Average Haley's base damage=9.49944 Sneak damage=29.9232 Total damage=39.4226
Average Total damage=91.9254
Probability at least 1 Giants killed=0.00696475 (Absolutes = 27859)
Probability at least 2 Giants killed=0.000225 (Absolutes = 900)
Probability at least 3 Giants killed=1.05e-05 (Absolutes = 42)
Probability at least 4 Giants killed=7.5e-07 (Absolutes = 3)
---------------------------------------
---------------------------------------
After 5e+06 runs:
Average HP Giant0: Starting=132.993 Ending=41.0608
Average HP Giant1: Starting=132.996 Ending=41.068
Average HP Giant2: Starting=132.993 Ending=41.0666
Average HP Giant3: Starting=133 Ending=41.072
Average Fireball damage=52.5041
Average Haley's crits=0.049943 Fumblings=0.0499489
Average Haley's base damage=9.5 Sneak damage=29.9245 Total damage=39.4245
Average Total damage=91.9286
Probability at least 1 Giants killed=0.0069636 (Absolutes = 34818)
Probability at least 2 Giants killed=0.0002266 (Absolutes = 1133)
Probability at least 3 Giants killed=1.08e-05 (Absolutes = 54)
Probability at least 4 Giants killed=8e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 6e+06 runs:
Average HP Giant0: Starting=132.997 Ending=41.0657
Average HP Giant1: Starting=132.997 Ending=41.0722
Average HP Giant2: Starting=132.993 Ending=41.0669
Average HP Giant3: Starting=132.999 Ending=41.0736
Average Fireball damage=52.5033
Average Haley's crits=0.0499609 Fumblings=0.0499819
Average Haley's base damage=9.49966 Sneak damage=29.924 Total damage=39.4237
Average Total damage=91.9269
Probability at least 1 Giants killed=0.00695783 (Absolutes = 41747)
Probability at least 2 Giants killed=0.000226333 (Absolutes = 1358)
Probability at least 3 Giants killed=9.83333e-06 (Absolutes = 59)
Probability at least 4 Giants killed=6.66667e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 7e+06 runs:
Average HP Giant0: Starting=132.997 Ending=41.0702
Average HP Giant1: Starting=132.998 Ending=41.0757
Average HP Giant2: Starting=132.995 Ending=41.0689
Average HP Giant3: Starting=132.999 Ending=41.0758
Average Fireball damage=52.5005
Average Haley's crits=0.0499421 Fumblings=0.0499733
Average Haley's base damage=9.49947 Sneak damage=29.9245 Total damage=39.424
Average Total damage=91.9245
Probability at least 1 Giants killed=0.00696357 (Absolutes = 48745)
Probability at least 2 Giants killed=0.000225571 (Absolutes = 1579)
Probability at least 3 Giants killed=1.02857e-05 (Absolutes = 72)
Probability at least 4 Giants killed=5.71429e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 8e+06 runs:
Average HP Giant0: Starting=132.996 Ending=41.0678
Average HP Giant1: Starting=132.998 Ending=41.0748
Average HP Giant2: Starting=132.995 Ending=41.0673
Average HP Giant3: Starting=132.998 Ending=41.075
Average Fireball damage=52.5012
Average Haley's crits=0.0499641 Fumblings=0.0499701
Average Haley's base damage=9.49983 Sneak damage=29.9247 Total damage=39.4245
Average Total damage=91.9258
Probability at least 1 Giants killed=0.00697225 (Absolutes = 55778)
Probability at least 2 Giants killed=0.000229375 (Absolutes = 1835)
Probability at least 3 Giants killed=1e-05 (Absolutes = 80)
Probability at least 4 Giants killed=5e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 9e+06 runs:
Average HP Giant0: Starting=132.997 Ending=41.0675
Average HP Giant1: Starting=132.999 Ending=41.0764
Average HP Giant2: Starting=132.997 Ending=41.0665
Average HP Giant3: Starting=132.998 Ending=41.0726
Average Fireball damage=52.5018
Average Haley's crits=0.0499691 Fumblings=0.0499705
Average Haley's base damage=9.49997 Sneak damage=29.925 Total damage=39.425
Average Total damage=91.9268
Probability at least 1 Giants killed=0.00697489 (Absolutes = 62774)
Probability at least 2 Giants killed=0.000229222 (Absolutes = 2063)
Probability at least 3 Giants killed=1.02222e-05 (Absolutes = 92)
Probability at least 4 Giants killed=4.44444e-07 (Absolutes = 4)
---------------------------------------
---------------------------------------
After 1e+07 runs:
Average HP Giant0: Starting=132.997 Ending=41.0668
Average HP Giant1: Starting=132.999 Ending=41.0761
Average HP Giant2: Starting=132.997 Ending=41.0653
Average HP Giant3: Starting=132.999 Ending=41.0738
Average Fireball damage=52.5021
Average Haley's crits=0.049974 Fumblings=0.0499582
Average Haley's base damage=9.50009 Sneak damage=29.9253 Total damage=39.4254
Average Total damage=91.9274
Probability at least 1 Giants killed=0.0069782 (Absolutes = 69782)
Probability at least 2 Giants killed=0.0002284 (Absolutes = 2284)
Probability at least 3 Giants killed=1.01e-05 (Absolutes = 101)
Probability at least 4 Giants killed=4e-07 (Absolutes = 4)
---------------------------------------

So anyone can choose his preferred system.
Anyway it doesn't change a lot, it's always 4/10.000.000 the cases where all the 4 of them were killed.

[Ephemera]

If there is another good (and fast) solution, feel free to write your results. :)

Oh, you kids today, who grew up with computers. Back when I was a kid, we had to do these things by hand (after walking uphill to school both ways in the snow, of course). [/geezer]

FWIW, with or without computer help, I think it's still easier to calculate all the possible (equally likely) outcomes than it is to simulate. In fact, given that they're all exactly equally likely, it's slightly more rigorous, too, since for any arbitrarily large number of simulations, there's still a non-zero (if slim) chance that you got an unlikely result in your simulation.

In the age of google, we don't even have to do our own work--there's a spreadsheet here that will do it for us. http://www.wikihow.com/Calculate-Mul...-Probabilities

I am, however, with the consensus that adding in probabilities makes the thread less rigorous, not more. For the purposes of this thread, our assumption is that the stickverse operates under 3.5 rules but we can't make any assumptions about how unlikely anything we see on panel may have been. Which, if you think about it, is kind of how science works, too--that's the whole reason why we have to run experiments lots of times, to make sure that our first result wasn't anomalous...

[Tobtor]

I've re-read my post and I've spotted that I missed a very important point: since I'm assuming average HP for the giants, assuming averages elsewhere is entirely appropriate.

No it doesn't work like that. Lets say a creature have 3d6 hit points (for an average of 10.5), and is hit by a person doing 1d12 (average 6.5)+x damage. If averages are used, we should suggest that x is above 4. Even though 0 is still a likely explenation (if the 3d6 creature had 10 or less (50%), there would be 2/12 for it to be killed by x=0, 3/12 byt X=1 etc).

Now I agree that in the current situation it is less likely than this, however the problem is: where to set the line, at 5%, at 1%, at one in a million (which will always happen), one in ten millions?

It is a good guide to whether or not it is a good idea to engage said creature (or to calculate your ability in a min-max environment), but as we don't KNOW what the creatures score actually was it becomes moot.

Dr.Zero: To understand your mode, I have a question. How did you make V's damage the same for all four giants?
Did it run:
1. test all four giants for health individually (G1-G4)
2. Calculate Vs damage and subtract that damage from each Giant
3 calculate Halyes damage four times and aply it in order

or?

And could you do a set where V had maximised the fireball (for 90damage).

[Dr.Zero]

Oh, you kids today, who grew up with computers. Back when I was a kid, we had to do these things by hand (after walking uphill to school both ways in the snow, of course). [/geezer]

Tsk, that's nothing. To have the milk for my morning breakfast, I had to go to milk the cows, and since we were terribly poor and couldn't afford a bucket, I had to transport the milk keeping it in my cupped hand. This, of course, walking shoeless in the snow. (I remember a line like this from The Cosby's show ).

FWIW, with or without computer help, I think it's still easier to calculate all the possible (equally likely) outcomes than it is to simulate.

Not really, here we have not a bunch of dice of the same kind, which indeed can easily be approximated with the normal distribution even if they are too many, but more complex operations, with a lot of combinations involved.

Dr.Zero: To understand your mode, I have a question. How did you make V's damage the same for all four giants?
Did it run:
1. test all four giants for health individually (G1-G4)
2. Calculate Vs damage and subtract that damage from each Giant
3 calculate Halyes damage four times and aply it in order

or?

And could you do a set where V had maximised the fireball (for 90damage).

Yes, to all three of them.
If you know C++ I can copy here the code, since it's pretty simple and standard (aside for the RNG library which is basically a wrapper around boost randomizer library).
So if someone knows C++ can run some test (and check if I did some mistake, since I've written in on the fly ).

Spoiler: C++ Code. Notice the Fireball damage

Show

#include "RNG.h"

using Integer=double;

class FrostGiant
{
private:
    Integer hp_;
public:
    void starting_values()
        {   hp_=70+RNG::rollN(14,8);}
    FrostGiant()
        { hp_=0; }
    void subtractDamage(const Integer damage)
        { hp_-=damage; }
    void sumHP(const FrostGiant& g)
        { hp_+=g.hp_;}
    bool isDead() const
        { return hp_<=0; }
    Integer HP() const
        { return hp_; }

};
class Haley
{
private:
public:
    static Integer base_damage()
        {   return RNG::roll1(8)+5; }
    static Integer sneak_damage()
        {   return RNG::rollN(9,6); }
    static Integer hit_roll()
        {   return RNG::roll1(20);}
};

class FireBall
{
private:
public:
    static Integer damage()
        {   return RNG::rollN(10,6); }
};

class Sim
{
private:
    const unsigned int num_giants=4;
    Integer runs;
    vector<FrostGiant> tot_starting;
    vector<FrostGiant> tot_ending;
    vector<FrostGiant> giants;
    Integer Tot_Fireball;
    Integer Tot_H_bd, Tot_H_sd, Tot_H, Tot_H_critHits, Tot_H_fumbling, Tot_H_totD;
    vector<Integer> numkills;
public:
    Sim();
    void run_one();
    void print_averages();

};

Sim::Sim()
{    runs=0; giants.resize(num_giants); tot_starting.resize(num_giants); tot_ending.resize(num_giants); numkills.resize(num_giants);}

void Sim::run_one()
{
    ++runs;
    unsigned int num_kills=0;
    Integer fireball=(1.5*FireBall::damage());
    for (unsigned int i=0; i<giants.size(); ++i)
    {
        giants[i].starting_values();
        tot_starting[i].sumHP(giants[i]);
        Tot_Fireball+=fireball;
        Integer haley_hit_roll=Haley::hit_roll();
        Integer haley_bd=Haley::base_damage();
        Integer haley_sd=Haley::sneak_damage();
        if (haley_hit_roll==20) {
            Tot_H_critHits++; haley_bd*=2;
        }

        if (haley_hit_roll==1)  {
            Tot_H_fumbling++; haley_bd=0; haley_sd=0;
        }
        Tot_H_bd+=haley_bd;
        Tot_H_sd+=haley_sd;
        Tot_H+=(haley_bd+haley_sd);
        Integer tot_damage=(fireball+haley_bd+haley_sd);
        Tot_H_totD+=tot_damage;
        giants[i].subtractDamage(tot_damage);
        tot_ending[i].sumHP(giants[i]);
        if (giants[i].isDead()) {
            numkills[num_kills]+=1;
            ++num_kills;
        }
    }
}

void Sim::print_averages()
{
    cout << "---------------------------------------" << endl;
    cout << "After " << runs << " runs:" << endl;
    for (unsigned int i=0; i<num_giants; ++i) {
        cout << "Average HP Giant" << i <<": Starting=" << tot_starting[i].HP()/runs << "    Ending="<< tot_ending[i].HP()/runs << endl;
    }
    cout << "Average Fireball damage=" << Tot_Fireball/(runs*num_giants) << endl;
    cout << "Average Haley's crits=" << Tot_H_critHits/(runs*num_giants) << "    Fumblings=" << Tot_H_fumbling/(runs*num_giants) << endl;
    cout << "Average Haley's base damage=" << Tot_H_bd/(runs*num_giants) << "    Sneak damage=" << Tot_H_sd/(runs*num_giants) << "    Total damage=" << Tot_H/(runs*num_giants) <<endl;
    cout << "Average Total damage=" << Tot_H_totD/(runs*num_giants) << endl;
    for (unsigned int i=0; i< num_giants; ++i) {
        cout <<  "Probability at least " << i+1 << " Giants killed=" << numkills[i] /runs << " (Absolutes = " << numkills[i] << ")" << endl;
    }
    cout << "---------------------------------------" << endl;
}



int main(int argc, char *argv[])
{
    Sim simulator;
    for (Integer i=0; i<10; ++i)
    {
        for (Integer j=0; j<1000000; ++j)
        {
            simulator.run_one();
        }
        simulator.print_averages();
    }
}

For the maximed fireball, sure.

Spoiler: 10.000.000 simulations with maximized fireball

Show

---------------------------------------
After 1e+06 runs:
Average HP Giant0: Starting=132.992 Ending=3.57377
Average HP Giant1: Starting=132.993 Ending=3.56982
Average HP Giant2: Starting=133.012 Ending=3.59707
Average HP Giant3: Starting=132.994 Ending=3.56385
Average Fireball damage=90
Average Haley's crits=0.0498328 Fumblings=0.050067
Average Haley's base damage=9.49727 Sneak damage=29.9241 Total damage=39.4214
Average Total damage=129.421
Probability at least 1 Giants killed=0.898376 (Absolutes = 898376)
Probability at least 2 Giants killed=0.585738 (Absolutes = 585738)
Probability at least 3 Giants killed=0.223701 (Absolutes = 223701)
Probability at least 4 Giants killed=0.036451 (Absolutes = 36451)
---------------------------------------
---------------------------------------
After 2e+06 runs:
Average HP Giant0: Starting=132.991 Ending=3.56325
Average HP Giant1: Starting=132.987 Ending=3.55605
Average HP Giant2: Starting=133.01 Ending=3.59462
Average HP Giant3: Starting=132.991 Ending=3.5701
Average Fireball damage=90
Average Haley's crits=0.0499006 Fumblings=0.0500106
Average Haley's base damage=9.49799 Sneak damage=29.9257 Total damage=39.4237
Average Total damage=129.424
Probability at least 1 Giants killed=0.898802 (Absolutes = 1.7976e+06)
Probability at least 2 Giants killed=0.586232 (Absolutes = 1.17246e+06)
Probability at least 3 Giants killed=0.223581 (Absolutes = 447162)
Probability at least 4 Giants killed=0.0364735 (Absolutes = 72947)
---------------------------------------
---------------------------------------
After 3e+06 runs:
Average HP Giant0: Starting=132.991 Ending=3.56215
Average HP Giant1: Starting=132.991 Ending=3.56325
Average HP Giant2: Starting=133.004 Ending=3.58389
Average HP Giant3: Starting=132.998 Ending=3.58041
Average Fireball damage=90
Average Haley's crits=0.0498813 Fumblings=0.0500064
Average Haley's base damage=9.49839 Sneak damage=29.925 Total damage=39.4234
Average Total damage=129.423
Probability at least 1 Giants killed=0.898926 (Absolutes = 2.69678e+06)
Probability at least 2 Giants killed=0.586354 (Absolutes = 1.75906e+06)
Probability at least 3 Giants killed=0.223367 (Absolutes = 670101)
Probability at least 4 Giants killed=0.0364603 (Absolutes = 109381)
---------------------------------------
---------------------------------------
After 4e+06 runs:
Average HP Giant0: Starting=132.99 Ending=3.56569
Average HP Giant1: Starting=132.991 Ending=3.56183
Average HP Giant2: Starting=133.003 Ending=3.58125
Average HP Giant3: Starting=132.997 Ending=3.58164
Average Fireball damage=90
Average Haley's crits=0.0498922 Fumblings=0.049996
Average Haley's base damage=9.49843 Sneak damage=29.9244 Total damage=39.4228
Average Total damage=129.423
Probability at least 1 Giants killed=0.899004 (Absolutes = 3.59602e+06)
Probability at least 2 Giants killed=0.586305 (Absolutes = 2.34522e+06)
Probability at least 3 Giants killed=0.22329 (Absolutes = 893160)
Probability at least 4 Giants killed=0.036432 (Absolutes = 145728)
---------------------------------------
---------------------------------------
After 5e+06 runs:
Average HP Giant0: Starting=132.993 Ending=3.56895
Average HP Giant1: Starting=132.993 Ending=3.56856
Average HP Giant2: Starting=133.001 Ending=3.57707
Average HP Giant3: Starting=132.997 Ending=3.57733
Average Fireball damage=90
Average Haley's crits=0.0498945 Fumblings=0.0500049
Average Haley's base damage=9.49811 Sneak damage=29.9248 Total damage=39.4229
Average Total damage=129.423
Probability at least 1 Giants killed=0.899034 (Absolutes = 4.49517e+06)
Probability at least 2 Giants killed=0.586266 (Absolutes = 2.93133e+06)
Probability at least 3 Giants killed=0.223275 (Absolutes = 1.11638e+06)
Probability at least 4 Giants killed=0.0363372 (Absolutes = 181686)
---------------------------------------
---------------------------------------
After 6e+06 runs:
Average HP Giant0: Starting=132.993 Ending=3.56978
Average HP Giant1: Starting=132.993 Ending=3.56723
Average HP Giant2: Starting=133 Ending=3.57702
Average HP Giant3: Starting=132.997 Ending=3.57641
Average Fireball damage=90
Average Haley's crits=0.049896 Fumblings=0.0499987
Average Haley's base damage=9.49838 Sneak damage=29.9249 Total damage=39.4233
Average Total damage=129.423
Probability at least 1 Giants killed=0.898968 (Absolutes = 5.39381e+06)
Probability at least 2 Giants killed=0.586225 (Absolutes = 3.51735e+06)
Probability at least 3 Giants killed=0.223369 (Absolutes = 1.34021e+06)
Probability at least 4 Giants killed=0.0363432 (Absolutes = 218059)
---------------------------------------
---------------------------------------
After 7e+06 runs:
Average HP Giant0: Starting=132.994 Ending=3.57033
Average HP Giant1: Starting=132.995 Ending=3.57117
Average HP Giant2: Starting=133.001 Ending=3.58055
Average HP Giant3: Starting=132.997 Ending=3.57484
Average Fireball damage=90
Average Haley's crits=0.0498847 Fumblings=0.0500176
Average Haley's base damage=9.49845 Sneak damage=29.9241 Total damage=39.4226
Average Total damage=129.423
Probability at least 1 Giants killed=0.898971 (Absolutes = 6.29279e+06)
Probability at least 2 Giants killed=0.586252 (Absolutes = 4.10376e+06)
Probability at least 3 Giants killed=0.223334 (Absolutes = 1.56334e+06)
Probability at least 4 Giants killed=0.036299 (Absolutes = 254093)
---------------------------------------
---------------------------------------
After 8e+06 runs:
Average HP Giant0: Starting=132.994 Ending=3.56912
Average HP Giant1: Starting=132.996 Ending=3.57343
Average HP Giant2: Starting=133.001 Ending=3.57908
Average HP Giant3: Starting=132.997 Ending=3.57501
Average Fireball damage=90
Average Haley's crits=0.0499039 Fumblings=0.0500077
Average Haley's base damage=9.49868 Sneak damage=29.9243 Total damage=39.423
Average Total damage=129.423
Probability at least 1 Giants killed=0.898873 (Absolutes = 7.19098e+06)
Probability at least 2 Giants killed=0.58619 (Absolutes = 4.68952e+06)
Probability at least 3 Giants killed=0.223311 (Absolutes = 1.78649e+06)
Probability at least 4 Giants killed=0.0362969 (Absolutes = 290375)
---------------------------------------
---------------------------------------
After 9e+06 runs:
Average HP Giant0: Starting=132.994 Ending=3.56806
Average HP Giant1: Starting=132.996 Ending=3.57263
Average HP Giant2: Starting=133.001 Ending=3.57922
Average HP Giant3: Starting=132.998 Ending=3.5731
Average Fireball damage=90
Average Haley's crits=0.0499135 Fumblings=0.0499952
Average Haley's base damage=9.49908 Sneak damage=29.925 Total damage=39.424
Average Total damage=129.424
Probability at least 1 Giants killed=0.898881 (Absolutes = 8.08993e+06)
Probability at least 2 Giants killed=0.586219 (Absolutes = 5.27597e+06)
Probability at least 3 Giants killed=0.223384 (Absolutes = 2.01045e+06)
Probability at least 4 Giants killed=0.0363111 (Absolutes = 326800)
---------------------------------------
---------------------------------------
After 1e+07 runs:
Average HP Giant0: Starting=132.994 Ending=3.56877
Average HP Giant1: Starting=132.996 Ending=3.57055
Average HP Giant2: Starting=133 Ending=3.57983
Average HP Giant3: Starting=132.999 Ending=3.57368
Average Fireball damage=90
Average Haley's crits=0.0499272 Fumblings=0.0499979
Average Haley's base damage=9.49908 Sneak damage=29.9251 Total damage=39.4242
Average Total damage=129.424
Probability at least 1 Giants killed=0.898941 (Absolutes = 8.98941e+06)
Probability at least 2 Giants killed=0.586233 (Absolutes = 5.86233e+06)
Probability at least 3 Giants killed=0.223377 (Absolutes = 2.23377e+06)
Probability at least 4 Giants killed=0.0363045 (Absolutes = 363045)
---------------------------------------

[Jasdoif]

Not really, here we have not a bunch of dice of the same kind, which indeed can easily be approximated with the normal distribution even if they are too many, but more complex operations, with a lot of combinations involved.

HA! This problem just needs to be outsmarted.

First off, our target number is 133 damage; the DMG does in fact say that a creature's full hit point is "usually average rolls on each Hit Die", so taking the average number listed in the stat block is perfectly valid (and almost certainly why the average is listed in the block in the first place).

Spoiler: ZOMG MATH AND PYTHON

Show

Python's itertools' module has combination_with_replacement, which iterates through...combinations that allow elements to be repeated. So basically there will exactly one list returned with all ten 1s, exactly one with nine 1s and one 6, exactly one with five 3s three 4s and two 5s, etc. etc.

So, we can determine the number actual permutations from that (by discarding things like switching the places of a 1 with another 1), without having to calculate every single permutation. With 10d6, this amounts to getting the counts of all 60,466,176 permutations with only 3,003 steps.


First off, the import and function to do all that:

import collections
import functools
import itertools
import math
import operator

def GenerateProductAggregate(thisIterable=[1,2,3,4,5,6], itemCount=10, aggregateFunction=operator.add, showDebug=False):
    thisAggregationTracker=collections.defaultdict(lambda: 0)
    totalPermutations=math.factorial(itemCount)
    for x in itertools.combinations_with_replacement(thisIterable,itemCount):
        thisAggregate=functools.reduce(aggregateFunction,x)
        # This counts how many times each value occurs in the combination....
        thisCounter=collections.Counter(x)
        # This multiplies the product of the factorials of each count
        # ..telling us how many permutations of this combination are identical
        thisIdenticalPermutationsPerCombinationCount=functools.reduce(operator.mul,map(math.factorial,thisCounter.values()))
        # And this divides the total permutations across the entire range by how many permutations are identical for this combination
        # ...so we're left with how many distinct permutations of this combination exist in the entire range
        thisDistinctPermutationsCount=totalPermutations//thisIdenticalPermutationsPerCombinationCount
        if showDebug:
            print("{0} -> {1}, * {2}".format(x,thisAggregate,thisDistinctPermutationsCount))
        thisAggregationTracker[thisAggregate]+=thisDistinctPermutationsCount
    return thisAggregationTracker

Now because I was lazy I put the 10d6 in the defaults....So first step after assignment, making sure the number of rolls reflected is the actual number of possible rolls.

(Note that ">>>" is the interpreter's prompt for input)

>>> fireballRoll=GenerateProductAggregate()
>>> sum(fireballRoll.values())
60466176
>>> 6**10
60466176

So far so good.

We have a dictionary (or associative array if you don't like the term), with the keys as the roll result and the values as the number of occurrences of that result; I'll be using that type of arrangement throughout.

Spoiler: fireballRoll

Show

fireballRoll
Result	Number of Outcomes
10	1
11	10
12	55
13	220
14	715
15	2,002
16	4,995
17	11,340
18	23,760
19	46,420
20	85,228
21	147,940
22	243,925
23	383,470
24	576,565
25	831,204
26	1,151,370
27	1,535,040
28	1,972,630
29	2,446,300
30	2,930,455
31	3,393,610
32	3,801,535
33	4,121,260
34	4,325,310
35	4,395,456
36	4,325,310
37	4,121,260
38	3,801,535
39	3,393,610
40	2,930,455
41	2,446,300
42	1,972,630
43	1,535,040
44	1,151,370
45	831,204
46	576,565
47	383,470
48	243,925
49	147,940
50	85,228
51	46,420
52	23,760
53	11,340
54	4,995
55	2,002
56	715
57	220
58	55
59	10
60	1
TOTAL	60,466,176

Next, another variable for adding the 50%. Per the rules, fractions are always rounded down...and since we won't have overlaps yet, I can just use a standard dictionary instead of the "default to zero" type I use(d) elsewhere here.

>>> fireballDamage={}
>>> for x in fireballRoll.keys():
	damage=math.floor(x*1.5)
	fireballDamage[damage]=fireballRoll[x]

Spoiler: fireballDamage

Show

fireballDamage
Result	Number of Outcomes
15	1
16	10
18	55
19	220
21	715
22	2,002
24	4,995
25	11,340
27	23,760
28	46,420
30	85,228
31	147,940
33	243,925
34	383,470
36	576,565
37	831,204
39	1,151,370
40	1,535,040
42	1,972,630
43	2,446,300
45	2,930,455
46	3,393,610
48	3,801,535
49	4,121,260
51	4,325,310
52	4,395,456
54	4,325,310
55	4,121,260
57	3,801,535
58	3,393,610
60	2,930,455
61	2,446,300
63	1,972,630
64	1,535,040
66	1,151,370
67	831,204
69	576,565
70	383,470
72	243,925
73	147,940
75	85,228
76	46,420
78	23,760
79	11,340
81	4,995
82	2,002
84	715
85	220
87	55
88	10
90	1
TOTAL	60,466,176

---

Now to figure out Haley's contribution. For 8d6 sneak attack, I can just use the function from before:

>>> sneakAttackRoll=GenerateProductAggregate(itemCount=8)

Spoiler: sneakAttackRoll

Show

sneakAttackRoll
Result	Number of Outcomes
8	1
9	8
10	36
11	120
12	330
13	792
14	1,708
15	3,368
16	6,147
17	10,480
18	16,808
19	25,488
20	36,688
21	50,288
22	65,808
23	82,384
24	98,813
25	113,688
26	125,588
27	133,288
28	135,954
29	133,288
30	125,588
31	113,688
32	98,813
33	82,384
34	65,808
35	50,288
36	36,688
37	25,488
38	16,808
39	10,480
40	6,147
41	3,368
42	1,708
43	792
44	330
45	120
46	36
47	8
48	1
TOTAL	1,679,616

Because I'm still lazy, I'll manually add the arrow's 1d8+5 damage here. I suppose I could account for crits here, but if I modeled the attack roll I'd need to account for critical misses, and we didn't see any. Since the giants all survived the fireball and all were killed by Haley, I think it's close enough to simple ignore the possibility of critical misses and critical hits...especially since a longbow has a x3 crit so this ends up being more conservative.

>>> arrowDamage=collections.defaultdict(lambda: 0)
>>> for x in sneakAttackRoll.keys():
	for y in [1,2,3,4,5,6,7,8]:
		arrowDamage[x+y+5]+=sneakAttackRoll[x]

Spoiler: arrowDamage

Show

arrowDamage
Result	Number of Outcomes
14	1
15	9
16	45
17	165
18	495
19	1,287
20	2,995
21	6,363
22	12,509
23	22,981
24	39,753
25	65,121
26	101,479
27	150,975
28	215,075
29	294,091
30	386,757
31	489,965
32	598,745
33	706,545
34	805,811
35	888,811
36	948,591
37	979,895
38	979,895
39	948,591
40	888,811
41	805,811
42	706,545
43	598,745
44	489,965
45	386,757
46	294,091
47	215,075
48	150,975
49	101,479
50	65,121
51	39,753
52	22,981
53	12,509
54	6,363
55	2,995
56	1,287
57	495
58	165
59	45
60	9
61	1
TOTAL	13,436,928

OK. Now, since we want all four giants dead, we're interested in a lower bound on Haley's attack...that is, we'll take the outcomes for all four arrows and store the lowest of the four. I suppose I could've modified the original function to handle input to multiply for this, but...see also: lazy. It didn't even take a whole minute to do the iteration anyway.

>>> haleyDamage=collections.defaultdict(lambda: 0)
>>> for x in itertools.product(arrowDamage.items(),repeat=4):
	lowestDamage=functools.reduce(lambda x,y: min(x,y), (z[0] for z in x))
	numberOfTries=functools.reduce(operator.mul, (z[1] for z in x))
	haleyDamage[lowestDamage]+=numberOfTries

Spoiler: haleyDamage

Show

haleyDamage
Result	Number of Outcomes
14	9,704,203,897,576,520,687,615
15	87,337,737,580,683,494,734,065
16	436,686,055,477,960,677,287,535
17	1,601,144,667,389,974,296,534,945
18	4,803,080,103,416,456,520,611,535
19	12,485,524,139,620,611,067,287,585
20	29,041,391,922,166,764,817,111,455
21	61,635,178,298,591,382,790,469,745
22	120,913,161,008,878,929,144,420,015
23	221,256,544,228,205,447,698,090,305
24	380,053,483,287,389,727,410,494,431
25	615,286,860,903,527,447,954,789,169
26	940,939,442,553,678,038,357,710,831
27	1,360,229,961,131,309,205,312,890,625
28	1,857,774,769,661,536,141,874,609,375
29	2,393,287,038,011,425,575,011,677,489
30	2,900,787,579,435,495,006,023,134,095
31	3,297,288,805,141,139,510,976,491,105
32	3,501,897,530,401,375,007,115,253,215
33	3,460,962,144,751,406,802,637,442,865
34	3,169,499,452,911,383,387,407,169,215
35	2,677,884,422,724,335,173,854,222,641
36	2,078,206,287,843,842,765,704,969,839
37	1,474,891,131,071,109,819,396,944,545
38	952,955,012,078,869,235,432,582,495
39	558,040,178,587,811,928,587,198,865
40	294,800,928,076,812,006,020,105,935
41	139,821,180,722,256,004,864,354,625
42	59,236,738,361,466,648,704,667,855
43	22,295,435,295,822,386,705,091,105
44	7,410,783,331,796,918,421,074,335
45	2,161,102,618,954,620,465,083,505
46	548,832,550,594,353,383,172,815
47	120,366,079,445,426,513,896,225
48	22,576,124,780,224,510,802,175
49	3,580,389,341,860,111,730,705
50	473,677,132,871,346,982,095
51	51,433,509,360,331,342,881
52	4,493,093,464,112,486,079
53	307,937,517,633,603,921
54	16,030,297,910,699,919
55	607,437,253,396,065
56	15,802,745,063,391
57	259,008,440,625
58	2,333,409,375
59	9,140,625
60	9,999
61	1
TOTAL	32,598,675,906,340,458,022,469,369,856

---

AND NOW! To put it all together: We get the total damage, by multiplying the outcomes of each pair of fireball and Haley damage and adding it into the sum of that damage.

>>> totalDamage=collections.defaultdict(lambda: 0)
>>> for h in haleyDamage.keys():
	for v in fireballDamage.keys():
		totalDamage[h+v]+=haleyDamage[h]*fireballDamage[v]

Spoiler: totalDamage

Show

totalDamage
Result	Number of Outcomes
29	9,704,203,897,576,520,687,615
30	184,379,776,556,448,701,610,215
31	1,310,063,431,284,795,624,628,185
32	6,501,736,436,536,289,707,229,120
33	27,753,027,201,720,626,247,609,860
34	103,748,360,492,823,382,365,711,660
35	344,969,028,016,740,023,094,311,705
36	1,050,344,628,607,095,377,984,368,325
37	2,967,727,074,728,817,041,002,657,995
38	7,842,016,439,471,804,857,673,456,850
39	19,557,651,524,340,185,272,326,169,746
40	46,340,357,693,101,717,319,616,628,974
41	104,804,737,325,302,730,577,187,837,666
42	227,233,004,243,960,475,717,451,426,650
43	474,021,155,035,822,003,290,349,857,830
44	954,141,221,213,573,724,299,783,572,974
45	1,857,869,504,618,318,534,076,168,734,350
46	3,507,188,364,604,461,073,487,296,358,482
47	6,430,757,996,540,603,826,485,654,268,473
48	11,472,096,580,707,076,910,131,270,099,657
49	19,940,652,638,219,113,128,928,625,372,615
50	33,815,894,555,356,815,019,594,380,438,196
51	56,013,883,487,543,523,374,862,633,244,872
52	90,724,057,707,804,657,120,630,353,629,240
53	143,819,479,750,411,344,643,500,122,184,110
54	223,336,067,046,266,745,895,704,179,820,338
55	340,008,405,260,330,390,068,032,707,068,782
56	507,837,388,174,987,321,404,857,422,822,028
57	744,648,991,746,726,550,852,245,453,642,712
58	1,072,590,776,688,272,821,788,929,657,031,208
59	1,518,497,850,666,201,934,886,151,797,301,777
60	2,114,046,559,193,244,813,267,529,905,666,165
61	2,895,608,576,688,081,687,542,169,225,669,979
62	3,903,718,025,933,661,653,351,289,200,676,166
63	5,182,075,197,814,320,246,806,373,866,847,054
64	6,776,030,276,747,941,308,407,308,398,801,810
65	8,730,522,226,099,945,322,073,990,756,838,768
66	11,087,495,790,699,089,085,584,989,509,166,224
67	13,882,870,873,918,302,721,333,227,364,400,384
68	17,143,192,165,945,714,392,659,922,865,746,466
69	20,882,145,059,560,680,223,980,977,348,051,794
70	25,097,184,554,432,876,728,751,346,601,756,030
71	29,766,550,738,876,617,414,917,270,804,315,011
72	34,846,945,387,447,021,097,274,263,034,201,219
73	40,272,177,372,943,633,140,796,822,485,342,093
74	45,953,029,716,685,175,144,991,243,349,502,668
75	51,778,484,948,723,373,749,805,679,777,123,496
76	57,618,444,154,536,717,874,835,401,279,511,640
77	63,327,940,856,940,182,629,703,448,419,797,219
78	68,752,631,699,368,652,126,488,747,865,424,263
79	73,735,361,439,287,958,036,856,358,393,473,065
80	78,123,473,451,010,645,094,776,651,930,587,780
81	81,776,312,080,112,978,189,785,295,089,353,012
82	84,572,469,582,066,425,465,293,902,117,124,460
83	86,416,328,065,188,476,931,993,776,282,408,490
84	87,243,320,593,306,513,337,528,551,027,882,522
85	87,023,546,028,347,829,023,426,808,349,347,270
86	85,763,534,257,738,749,465,212,866,078,963,848
87	83,505,944,985,959,465,873,561,923,294,956,096
88	80,327,207,481,436,516,454,662,514,592,478,528
89	76,333,355,664,830,765,836,927,934,523,673,796
90	71,654,324,967,520,011,522,802,660,264,178,076
91	66,437,081,108,343,776,711,490,199,233,572,548
92	60,838,149,924,743,153,356,567,473,774,692,216
93	55,016,055,387,593,195,993,836,844,942,278,368
94	49,124,093,412,072,631,920,616,673,103,368,640
95	43,303,949,711,321,685,734,465,496,726,035,570
96	37,680,521,397,137,299,795,971,564,908,679,946
97	32,358,104,032,107,220,231,544,110,926,559,766
98	27,418,105,373,256,209,298,620,187,150,576,724
99	22,918,289,642,511,758,049,201,091,776,466,068
100	18,893,371,895,428,277,870,791,774,012,524,012
101	15,356,786,940,159,297,401,679,152,379,683,623
102	12,303,376,244,873,890,003,272,471,061,344,479
103	9,712,655,634,582,338,580,259,281,354,300,897
104	7,552,382,651,268,936,017,938,013,781,964,996
105	5,782,153,845,761,104,366,939,419,510,202,616
106	4,356,778,934,693,868,388,267,441,346,969,016
107	3,229,263,619,717,867,970,381,778,981,538,863
108	2,353,287,193,545,286,868,053,272,787,713,003
109	1,685,110,326,899,084,247,442,973,624,582,405
110	1,184,913,460,178,066,618,450,018,082,845,818
111	817,606,168,226,843,879,951,164,597,511,330
112	553,175,774,686,716,635,472,306,417,751,134
113	366,665,120,284,741,617,448,478,506,086,496
114	237,874,871,595,642,023,888,970,929,242,576
115	150,882,445,472,967,725,164,461,046,063,024
116	93,460,046,153,381,490,811,879,460,682,126
117	56,459,404,327,877,145,716,198,759,530,942
118	33,214,437,979,769,777,776,359,724,935,682
119	18,996,648,988,686,119,882,453,907,794,525
120	10,543,308,894,211,711,227,755,593,080,669
121	5,666,523,021,485,148,561,284,897,747,571
122	2,942,210,614,464,039,676,427,375,069,140
123	1,471,979,836,106,639,655,178,340,168,584
124	707,488,736,691,763,796,217,994,931,640
125	325,610,965,458,893,051,607,133,723,726
126	142,973,770,936,251,845,322,353,899,442
127	59,654,464,977,012,184,413,501,805,838
128	23,546,917,504,837,517,988,764,317,772
129	8,750,183,157,525,880,335,424,222,552
130	3,045,047,357,212,121,268,504,882,760
131	986,765,779,424,367,511,808,208,573
132	296,036,768,064,025,483,713,379,265
133	81,744,586,715,239,518,045,882,767
134	20,656,148,597,387,653,356,833,638
135	4,748,130,952,351,528,093,642,654
136	986,078,275,883,113,881,622,466
137	183,432,166,109,935,423,128,490
138	30,220,979,971,588,417,880,682
139	4,345,806,089,356,535,434,310
140	535,689,570,857,930,519,370
141	55,398,212,735,054,346,786
142	4,686,864,142,420,932,462
143	314,881,561,031,662,453
144	16,202,572,843,654,989
145	610,155,677,518,435
146	15,826,581,891,736
147	259,100,396,820
148	2,333,509,420
149	9,140,635
150	9,999
151	1
TOTAL	1,971,117,274,719,741,650,707,244,872,321,990,656

So, how many outcomes are we talking about here?

>>> sum(totalDamage.values())
1971117274719741650707244872321990656

1,971,117,274,719,741,650,707,244,872,321,990,656. ..Nearly 2 undecillion! That's a lot alright...how many of those are 133 damage or more?

>>> sum(x[1] for x in totalDamage.items() if x[0]>=133)
108353539599390806738008113

108,353,539,599,390,806,738,008,113...over 100 septillion. That's comparatively tiny...What are the odds of that?

>>> 108353539599390806738008113/1971117274719741650707244872321990656
5.497062046437434e-11

...yeah. While that's an approximation, that comes to...

0.00000000549706204643743%. Not very likely to happen by chance, to understate it mildly.

---

Alright. Hypothetically...what if we added another die to Haley's sneak attack and assumed it was always a 6? We can have that effect easily by dropping our target number by 6 and keeping the current results, so....

>>> sum(x[1] for x in totalDamage.items() if x[0]>=127)
96387769083675487808454824873

96,387,769,083,675,487,808,454,824,873. That's 96 octillion. That's around a thousand times more likely, but still...pretty unlikely. Oh well, odds!

>>> 96387769083675487808454824873/1971117274719741650707244872321990656
4.890006815925255e-08

Which comes to...0.00000489000681592525%. Yeah...comparatively more likely, but I think we're weighing iotas here.

So long story short, we're talking some exceptional rolling here. 0.00000000549706204643743% chance of killing all four giants with level 16. Even bumping it up to level 17 Haley and assuming her extra sneak attack die is always a 6 still only gets us to 0.00000489000681592525% chance.

And could you do a set where V had maximised the fireball (for 90damage).

Spoiler: ZOMG MOAR MATH AND PYTHON

Show

For that, we'll just use the numbers for Haley's damage from last time, and take Vaarsuvius' 90 damage off the target number of 133. So with the 8d6 Haley....

>>> sum(x[1] for x in haleyDamage.items() if x[0]>=43)
32563206319062802795425841
>>> sum(x[1] for x in haleyDamage.items())
32598675906340458022469369856

So 32,563,206,319,062,802,795,425,841 (about 32.5 septillion) out of 32,598,675,906,340,458,022,469,369,856 (about 32 octillion). That comes out to....

>>> 32563206319062802795425841/32598675906340458022469369856
0.0009989119316569923

That's the number there; to get the percentage you'd multiply by 100, which would get us around 0.1%. One tenth of a percent is a great deal better than the others, but still not in betting range.

---

OK, since we're dealing only with Haley's damage now, it's easy enough to run alternate numbers with 9d6 sneak attack. So let me do that....

>>> altSneakAttackRoll=GenerateProductAggregate(itemCount=9)
>>> altArrowDamage={}
>>> altArrowDamage=collections.defaultdict(lambda: 0)
>>> for x in altSneakAttackRoll.keys():
	for y in [1,2,3,4,5,6,7,8]:
		altArrowDamage[x+y+5]+=altSneakAttackRoll[x]

>>> altHaleyDamage=collections.defaultdict(lambda: 0)
>>> for x in itertools.product(altArrowDamage.items(),repeat=4):
	lowestDamage=functools.reduce(lambda x,y: min(x,y), (z[0] for z in x))
	numberOfTries=functools.reduce(operator.mul, (z[1] for z in x))
	altHaleyDamage[lowestDamage]+=numberOfTries

Spoiler: altHaleyDamage

Show

altHaleyDamage
Result	Number of Outcomes
15	2,096,108,236,871,633,984,864,255
16	20,961,078,078,824,195,856,615,120
17	115,285,790,012,114,488,087,965,985
18	461,140,800,614,626,907,378,109,440
19	1,498,681,530,467,137,732,908,361,455
20	4,196,096,160,219,545,871,609,816,496
21	10,470,013,482,557,524,140,060,347,504
22	23,778,725,812,968,606,871,443,723,600
23	49,858,689,758,712,803,017,020,328,896
24	97,499,952,645,779,358,158,640,310,000
25	179,142,843,879,587,131,885,894,091,264
26	310,917,040,645,232,523,584,401,598,736
27	511,614,057,098,493,828,070,823,206,864
28	800,025,907,110,397,056,083,373,719,600
29	1,190,217,573,295,291,697,595,283,169,760
30	1,684,789,837,319,703,659,771,005,669,840
31	2,267,171,289,712,419,038,716,751,633,936
32	2,895,381,290,239,208,000,546,347,225,584
33	3,500,862,396,495,601,138,907,420,224,416
34	3,995,953,270,369,880,365,961,882,101,264
35	4,291,345,828,510,346,338,960,866,465,920
36	4,320,413,057,355,691,948,156,001,185,200
37	4,062,320,999,216,842,104,767,429,869,360
38	3,553,556,866,532,558,366,695,574,703,440
39	2,880,740,996,586,797,022,761,601,384,816
40	2,155,812,376,935,085,552,810,119,801,904
41	1,483,551,115,713,651,579,097,188,188,160
42	935,185,065,492,539,119,357,895,594,960
43	537,899,846,846,690,089,843,842,104,976
44	281,181,909,247,155,864,038,444,692,144
45	133,037,081,483,662,450,664,547,746,000
46	56,727,114,137,374,747,019,740,811,856
47	21,699,933,644,394,744,663,682,885,504
48	7,410,360,356,052,521,263,879,789,040
49	2,246,982,660,040,208,331,912,975,456
50	601,390,581,952,893,223,633,776,144
51	141,129,322,773,425,370,580,623,856
52	28,820,702,039,014,096,696,372,784
53	5,077,637,342,053,823,581,101,600
54	764,061,827,501,870,178,992,080
55	97,046,873,621,846,529,400,880
56	10,259,505,574,442,508,818,160
57	887,566,532,603,564,408,320
58	61,537,532,204,048,161,040
59	3,330,771,835,629,188,160
60	136,069,278,067,239,600
61	4,012,627,897,643,920
62	80,320,480,320,080
63	997,315,418,385
64	6,671,610,880
65	18,960,095
66	14,640
67	1
TOTAL	42,247,883,974,617,233,597,120,303,333,376

So how's it look this way?

>>> sum(x[1] for x in altHaleyDamage.items() if x[0]>=43)
1040980518940259710373453055601
>>> sum(x[1] for x in altHaleyDamage.items())
42247883974617233597120303333376

So that's 1,040,980,518,940,259,710,373,453,055,601 (about 1 novillion) out of 42,247,883,974,617,233,597,120,303,333,376 (about 42 novillion)....Quite an improvement so far. That gives us:

>>> 1040980518940259710373453055601/42247883974617233597120303333376
0.02463982621154912

Again, you'd multiply by 100 to get the percentage, which is around 2.5%.

OK, so if for some reason this is the first time we've seen a maximized spell without it being called maximized, and Haley is level 17/18 for 9d6 sneak attack, the odds of this scene being pulled off by rolling comes to 2.5%, so half as likely as a natural 20. An improvement over the earlier approaches, to be sure; but it's still a lot of guesswork and assumption to end up at "still pretty darn unlikely".


I remain standing by "exceptional rolling happened here!"

[Douglas]

You all realize it's extremely unlikely Rich actually checked the numbers before drawing this, right?

I'd guess his thought process went something like "Fireball's a pretty big blast of an element they take extra damage from, and Haley's throwing high level sneak damage on every single shot. Frost giants are tough, but not that tough. Seems about right."

[Quild]

You all realize it's extremely unlikely Rich actually checked the numbers before drawing this, right?

I'd guess his thought process went something like "Fireball's a pretty big blast of an element they take extra damage from, and Haley's throwing high level sneak damage on every single shot. Frost giants are tough, but not that tough. Seems about right."

Of course we know this! We're aware that we're crazy to overthink things like that. It would be terrible if we were not!

But I don't see where this discussion is going either. Even if the chances for V and Haley to kill those Giants with one fireball and 4 arrows are in the vicinity of 0,001%, it's still possible, so...

[Ephemera]

Jasidoif, that is some nice work (well, I'll assume it is, I'm far, far too lazy to actually read your code so I'll happily take it on faith that you're right).

Presumably, if we still care, the greatest chances of this happening would involve the giants (not the Giants) all having below average HP. I'm confident that my intuition is good enough to posit that while it's not that likely they all rolled significantly below average, it's not going to be so unlikely as to shift the odds slightly in Haley's favor given just how low they are as is.

It won't help for the purposes of the thread (since we can't rule out what we saw anyway) but is it plausible that there's another factor? Maybe V cast an off-panel flame arrow? Or is there something useful Haley could be carrying since we know she stocks at least cold iron and silver arrows as special ammunition? Presumably we'd see a visual effect if she were using flaming burst arrows, but they could be giantbane, I guess. Admittedly, this seems like a bit of a stretch.

[Tobtor]

OK, so if for some reason this is the first time we've seen a maximized spell without it being called maximized, and Haley is level 17/18 for 9d6 sneak attack, the odds of this scene being pulled off by rolling comes to 2.5%, so half as likely as a natural 20. An improvement over the earlier approaches, to be sure; but it's still a lot of guesswork and assumption to end up at "still pretty darn unlikely".


I remain standing by "exceptional rolling happened here!"

Exceptional yes, both with and without maximised, but we also do assumption on the basis of the giants (average), which could tip it more or less likely. This is sort of my point: to model it we need multiple scenarios, calculate averages etc, and this should then be done for every combat (etc), to get LIKELY stats for them. But we don't want "likely" stats, we wants "what stats do they actually have as a minimum and maximum".

Whenever we see a wizard we could assume he has at least 14 int (how many wizards dont? I bet it is less than 2.5% of wizards I have seen withint less than 14), but we dont do that, since we want confirmation.

[Jasdoif]

You all realize it's extremely unlikely Rich actually checked the numbers before drawing this, right?

Yes, but this is way more fun!

Exceptional yes, both with and without maximised, but we also do assumption on the basis of the giants (average), which could tip it more or less likely.

The DMG specifically says monsters usually have average HP; so unless we have evidence that these giants don't, we're probably OK here.

This is sort of my point: to model it we need multiple scenarios, calculate averages etc, and this should then be done for every combat (etc), to get LIKELY stats for them. But we don't want "likely" stats, we wants "what stats do they actually have as a minimum and maximum".

I figure if the "change it to appeal to the average" proposals don't even shift the odds enough to appeal to the average, they fail on their own merits...and wouldn't be valid even if that was the kind of thing this thread did. And it certainly doesn't move me to consider altering the thread's approach; this isn't the first scenario where our determination-by-upper-and-lower-bounds approach has been questioned.


I've been testing scenarios, and so far I've only seen one idea mentioned that would actually accomplish on probabilities: If Vaarsuvius were using an empowered maximized fireball, and Haley was doing the as-her-currently-listed-level-entails 8d6 sneak attack, there's a 99.67% chance of all the giants being killed. Of course, then the questions become why Vaarsuvius didn't say it was empowered or maximized unlike the overwhelming majority of metamagic-ed spells, and why Vaarsuvius would prepare it instead of an 8th level spell.

Even my intentionally absurd "standard fireball plus 21d6 sneak attack to succeed on all average everywhere!" ends up only pulling it off 28.69% of the time when Haley has to roll individually for all four giants.

[zimmerwald1915]

I've been testing scenarios, and so far I've only seen one idea mentioned that would actually accomplish on probabilities: If Vaarsuvius were using an empowered maximized fireball, and Haley was doing the as-her-currently-listed-level-entails 8d6 sneak attack, there's a 99.67% chance of all the giants being killed.

Has anyone mentioned the possibility of a delayed blast fireball? It can explode immediately like a regular fireball, and would do 16d6*1.5 damage even unmodified (in order to modify the spell with metamagic, V would need 9th-level spell slots or a rod).

Of course, then the questions become why Vaarsuvius didn't say it was empowered or maximized unlike the overwhelming majority of metamagic-ed spells

comic way too wordy for chief grukgruk sometimes.

It'd be an odd cut to make, to be sure.