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View Full Version : What are the statistical odds of this eipic failure?

Pika...
2011-06-19, 12:37 PM
So a friend was playing yesterday, and he rolled his furry-of-blows and rolled this:

http://i47.photobucket.com/albums/f173/celestialkin/0618202714.jpg

http://i47.photobucket.com/albums/f173/celestialkin/0618202721.jpg

http://i47.photobucket.com/albums/f173/celestialkin/0618202728.jpg

http://i47.photobucket.com/albums/f173/celestialkin/0618202740.jpg

Yup, and we use the crit failure/success rules. The Paizo decks are quite useful to us. :smallbiggrin:

Yuki Akuma
2011-06-19, 12:38 PM
One in one hundred and sixty thousand, just like any other combination.

DonDuckie
2011-06-19, 12:40 PM
I think I'm seeing 3 ones with 3d20...
so odds:
1/(20*20*20) = 1/8000

EDIT:
if 4 ones with 4d20 then: 1/160000 like said above.

Pika...
2011-06-19, 12:41 PM
I think I'm seeing 3 ones with 3d20...
so odds:
1/(20*20*20) = 1/8000

Nope. Four...

Yuki Akuma
2011-06-19, 12:45 PM
Remember, a roll of 1, 12, 18, 20 would also have a chance of one in one hundred and sixty thousand.

There's nothing special about four 1s.

Jack_Simth
2011-06-19, 12:50 PM
Remember, a roll of 1, 12, 18, 20 would also have a chance of one in one hundred and sixty thousand.

There's nothing special about four 1s.
Yes, but at the same time, it is a remarkably Epic Fail of a roll.

However, a slight correction on the 1, 12, 18, 20: That only has the exact same probability if the rolls are ordered. If the rolls are not ordered, a 1, 12, 18, 20 is much more likely than 1, 1, 1, 1 (as there's 24 ways in that 160,000 to roll 1, 12, 18, 20 if order is not important, but there's only one way to roll 1, 1, 1, 1 in that 160,000, regardless of whether or not order is important).

ffone
2011-06-19, 12:51 PM
The movie 'Rosencrantz and Gildenstern are Dead' (sp?) had a scene where one guy flips a coin and gets 50 heads in a row. The two then debate over whether this is amazing (and proves the coin is a trick coin, despite the presence of its tails side, something supernatural is afoot etc.) or completely obvious (b/c if you flip a coin 50 times, you are guaranteed to get a sequence which had the same 1/2^50 prob).

This is why in science, it's encouraged to state a hypothesis ahead of time, so you can measure how well the outcome comports to that hypothesis (the p-value) rather than finding *some* pattern, which humans are good at.

That said, with d20s, a string of all 1s or all 20s are probably the most 'conspicuous' things.

DonDuckie
2011-06-19, 12:52 PM
Remember, a roll of 1, 12, 18, 20 would also have a chance of one in one hundred and sixty thousand.

There's nothing special about four 1s.

rolls like this aren't usually considered as ordered, and with special rules for rolling a 1 I would claim that it is special. And special rolls leads to great explanations of how this fail inpacts the character.

But you are correct; the role has the same probability, but a roll of four 1s gives you much funner(more fun? nah, I like 'funner'), roleplaying/storytelling.

Yuki Akuma
2011-06-19, 12:52 PM
Yes, but at the same time, it is a remarkably Epic Fail of a roll.

However, a slight correction on the 1, 12, 18, 20: That only has the exact same probability if the rolls are ordered.

Yep. That's why I didn't say 18, 20, 12, 1.

I just like pointing out tha any result would have the same chance of appearing. :smallwink: Assuming perfectly fair dice, of course - which yours aren't. At all. No dice are perfectly fair.

Destro_Yersul
2011-06-19, 12:56 PM
Yep. That's why I didn't say 18, 20, 12, 1.

I just like pointing out tha any result would have the same chance of appearing. :smallwink: Assuming perfectly fair dice, of course - which yours aren't. At all. No dice are perfectly fair.

Not quite correct. Perfectly fair dice just have to be machined exactingly, and balanced equally on all sides. This is, of course, ludicrously expensive. The only dice anyone bothers doing it for are the ones used on Casino craps tables.

Jack_Simth
2011-06-19, 01:00 PM
Not quite correct. Perfectly fair dice just have to be machined exactingly, and balanced equally on all sides. This is, of course, ludicrously expensive. The only dice anyone bothers doing it for are the ones used on Casino craps tables.
Even casino dice aren't perfect - but they are about as close as is humanly possible.

Yuki Akuma
2011-06-19, 01:02 PM
Not quite correct. Perfectly fair dice just have to be machined exactingly, and balanced equally on all sides. This is, of course, ludicrously expensive. The only dice anyone bothers doing it for are the ones used on Casino craps tables.

Nope. You can't get a perfectly fair die without directly manipulating the subatomic particles that make it up.

You can get very close, though.

Cicciograna
2011-06-19, 01:05 PM
Nope. You can't get a perfectly fair die without directly manipulating the subatomic particles that make it up.

And even then, quantum vacuum polarization processes guarantee that the infinitesimal system isn't stable nor predictable.

Destro_Yersul
2011-06-19, 01:20 PM
Nope. You can't get a perfectly fair die without directly manipulating the subatomic particles that make it up.

You can get very close, though.

close enough so as to make no difference, even.

ffone
2011-06-20, 02:24 AM
You can actually get "fair dice" out of "unfair dice" although it's more cumbersome (requires extra rolls and thinking and isn't worth it for any sane application):

For example, if you want to 'flip a coin', just roll the die twice - if the first number is higher, "heads", if the second is higher, "tails," if equal, reroll twice, and repeat as needed. (Now you only need the assumption that each roll of the die has the *same* distribution, i.e. it isn't changing over time as the die loses and gains molecules to/from the environment.)

Yuki Akuma
2011-06-20, 09:15 AM
close enough so as to make no difference, even.

It does make a difference. A small one, but it's a difference.

You'll likely turn the die into a perfect sphere before you notice, though, if it's machined well. Casino dice get retired very quickly.

Edit: "but" has a "b", Yuki.

Destro_Yersul
2011-06-20, 09:18 AM
It does make a difference. A small one, ut it's a difference.

You'll likely turn the die into a perfect sphere before you notice, though, if it's machined well. Casino dice get retired very quickly.

I challenge you to discern it. An indiscernible difference is as good as none at all.

That they do. Couldn't tell you the exact rate, though.

Anxe
2011-06-20, 09:52 AM
So did the monk spontaneously combust or something?

Grommen
2011-06-20, 10:01 AM
I would retire from gaming, as it would be ordained by the gods that I no longer have any luck what so ever.

And yes he needed to explode, and a 100 foot radius of smoke and fire that did absolutely nothing to anyone.

Zaranthan
2011-06-20, 12:12 PM
Yup, and we use the crit failure/success rules. The Paizo decks are quite useful to us. :smallbiggrin:

Since the Statisticians have done their thing, I'll just mention that I hate you and all that you stand for because you use critical failure rules. Failing is bad enough without your sword turning into a bucket of spoiled bacon.

Not to say that turning the fighter's sword into a bucket of bacon is a bad thing, just that it shouldn't be the dice who decide when it happens.

subject42
2011-06-20, 12:18 PM
I'll just mention that I hate you and all that you stand for because you use critical failure rules.

A critical failure deck actually got me out of a bad situation once. I crit missed on a touch attack that would have opened me up to a huge counterattack, but the crit fail card launched me about 60 squares away, which was enough of a lead to escape.

Vent Reynolt
2011-06-20, 12:20 PM
With one of my DMs, three 1s in a row would fumble your character to death (three 20s ascends you character to godhood), so I have no idea what he would do if someone got four 1s.

I hope the DM is good at ad-libbing because rolls like that call for a spectacular fumble; possibly so astounding that it solves the entire encounter.

Yuki Akuma
2011-06-20, 12:37 PM
Critical fumbles are horrible and you should never use them. Because it means that characters get more likely to fumble the better they get at fighting.

Which is just retarded.

Vent Reynolt
2011-06-20, 12:56 PM
Critical fumbles are horrible and you should never use them. Because it means that characters get more likely to fumble the better they get at fighting.

Which is just retarded.

It worked for the campaign that I mentioned because the entire campaign was built on shenanigans with special emphasis given to the awesome and hilarious. Also, the extreme critical fumble and success never actually came up in play.

I do agree, though, that critical fumbles should not be used for any serious campaign.

Zaranthan
2011-06-20, 12:58 PM
A critical failure deck actually got me out of a bad situation once. I crit missed on a touch attack that would have opened me up to a huge counterattack, but the crit fail card launched me about 60 squares away, which was enough of a lead to escape.

That's... well... um...

Are you all having fun? Yes? Okay, I'll stop now.

Originally Posted by Yuki Akuma
Critical fumbles are horrible and you should never use them. Because it means that characters get more likely to fumble the better they get at fighting.

Which is just retarded.

Yeah. This.

Flame of Anor
2011-06-20, 01:06 PM
I challenge you to discern it. An indiscernible difference is as good as none at all.

Pff, empiricism. See how far that gets you with a Neo-Platonist. :smalltongue:

TroubleBrewing
2011-06-20, 01:35 PM
Pff, empiricism. See how far that gets you with a Neo-Platonist. :smalltongue:

This discussion is rapidly turning into Dungeons and Discourse, and I fully support this transition.

Fully.

I am behind it 100%.

Asheram
2011-06-20, 01:45 PM
The movie 'Rosencrantz and Gildenstern are Dead' (sp?) had a scene where one guy flips a coin and gets 50 heads in a row. The two then debate over whether this is amazing (and proves the coin is a trick coin, despite the presence of its tails side, something supernatural is afoot etc.) or completely obvious (b/c if you flip a coin 50 times, you are guaranteed to get a sequence which had the same 1/2^50 prob).

Actually, as long as you can pick which side is up when you flip it, it shouldn't be That difficult getting the timing right for 50 heads in a row.
I can do it about nine times out of ten as I'm prone to missing the timing a bit.

But that's more cheating than statistics. :)

Malimar
2011-06-20, 02:15 PM
Critical fumbles are horrible and you should never use them. Because it means that characters get more likely to fumble the better they get at fighting.

Only if you don't have to roll to confirm critical fumbles. Which is as bad as not rolling to confirming critical hits.

Arbane
2011-06-20, 02:23 PM
Only if you don't have to roll to confirm critical fumbles. Which is as bad as not rolling to confirming critical hits.

I'd argue its worse - critical hits make characters look like Conan. Critical failures make them look more like Inspector Clouseau, and I didn't plan on spending part of my my weekend starring in Happy Fun Miserable Failure Hour.

----

Which isn't to say they can't occasionally be awesome... (http://funnydndstories.com/apps/blog/show/3432504-sameo)

----

On the topic of my dice hating me, I had a fine example last night - my new character (a Barbarian) hit second level. The DM does make us roll for HP, but we can reroll ones. Naturally, I roll a 2. He says I can use a hero point (we're playing Pathfinder) to reroll. I get ANOTHER 2.

:smallfurious:

After the game, it occurred to me to ask him if I can spend 2 hero points to get a reroll AND +8 on the roll. Maybe at level 3...:smallamused:

Malimar
2011-06-20, 02:33 PM
I'd argue its worse - critical hits make characters look like Conan. Critical failures make them look more like Inspector Clouseau, and I didn't plan on spending part of my my weekend starring in Happy Fun Miserable Failure Hour.

Yeah, I waffled for awhile on whether to say "as bad as", "worse than", or "almost worse than".

I guess you're right and it's probably worse, to the extent that the human brain punishes a big failure more than it rewards an equally big success. The anger a person feels about a critical fumble is greater than the happiness they feel about a critical hit, so mishandling fumbles is worse than mishandling hits because the former involves greater deviation from the baseline than the latter.

That said, not rolling to confirm critical hits is still almost as bad as not rolling to confirm critical fumbles.

Also: that story was awesome.

Yuki Akuma
2011-06-20, 02:38 PM
Only if you don't have to roll to confirm critical fumbles. Which is as bad as not rolling to confirming critical hits.

Because when you get two attacks per round, you're totally not more likely to roll a 1!

Arbane
2011-06-20, 02:47 PM
Because when you get two attacks per round, you're totally not more likely to roll a 1!

Could be worse, you could be playing RuneQuest. Some wiseguy once went over their fumble tables, and figured out that in a squad of 40(?) soldiers, at least one will die in an average battle from autodecapitation.

And for the record the most dark and brutal game world I had ever seen was a D&D campaign that Psycho Dave had run many years ago. For this game he had created a hybrid damage system that combined the standard D&D hit point system with the Arduin Grimoire critical hit chart and the infamous Rolemaster critical damage tables. And he used this table for any kind of injury whatsoever for players and NPCs alike. In doing so he created a desolate, blood soaked ruin of a world where carpenters died from complications of bruising their thumbs, people picking at hangnails had their flesh suddenly fall away from their bones in wet red strips and mothers in childbirth frequently detonated.

:smalleek:

http://albruno3.blogspot.com/2010/06/rpgnet-rant22-last-straw-trilogy-part.html

Malimar
2011-06-20, 02:47 PM
Because when you get two attacks per round, you're totally not more likely to roll a 1!

You're more likely to roll a 1, but you're less likely to miss your target's AC when you confirm. Unless your targets' AC increases faster than your tohit increases, in which case you may be facing foes who are so dodgetastic that they're actively getting in exactly the right place to make you hit yourself when you miss them, which is a trope as old as fight scenes.

Alternately, if you want to get even deeper into the murky waters of houseruling: you only hurt yourself on a fumble if that would be the last attack you make that turn. If it's not your last attack, you simply lose the rest of your attacks that turn. Now the number of attacks you make goes up but your likelihood of hitting yourself remains the same goes down, because your likelihood of not missing your enemy's AC to confirm goes down.

Zaranthan
2011-06-20, 02:58 PM
Only if you don't have to roll to confirm critical fumbles. Which is as bad as not rolling to confirming critical hits.

Um, what? "Confirming" or not, more attacks per round means more chances to roll a 1. That means, no matter how vast your Table of Hilarity may be, a level 20 fighter is much more likely to stab himself each round than a level 1 commoner is.

Asheram
2011-06-20, 04:06 PM
Um, what? "Confirming" or not, more attacks per round means more chances to roll a 1. That means, no matter how vast your Table of Hilarity may be, a level 20 fighter is much more likely to stab himself each round than a level 1 commoner is.

"the more you hurry..."

ericgrau
2011-06-20, 04:45 PM
Well there are thousands of people in gaming forums who make hundreds of rolls each, though not all make attack rolls and not all take pics, so I'd say about 50:50 :smalltongue:

But ya 1/160,000 per roll.

Could be worse, you could be playing RuneQuest. Some wiseguy once went over their fumble tables, and figured out that in a squad of 40(?) soldiers, at least one will die in an average battle from autodecapitation.

It could be worse. There was some system lauded for its in depth combat system with pages and pages of tables. Then someone ran through the numbers and proved that the optimal tactic regardless of the situation is a called shot to the crotch.

Jack_Simth
2011-06-20, 04:56 PM
That's... well... um...

Are you all having fun? Yes? Okay, I'll stop now.
Always nice to run into someone who actually understands that sort of thing. Bravo.