Random Lightning Strikes (The weather outside is frightful...)

[PrinceOfMadness]

Greetings Playground!

The short version: I'm looking for a random method, ideally that is both relatively simple and nonbiased towards a particular outcome, to determine the landing point of a given 5' radius lightning strike, primarily within a cylinder of 60' (but could also fall within a 30' or 120' radius).

More context: I'm playing in a freshly started and heavily homebrewed 5e game, and one of the other players in this group has a character themed around storms and lightning, with an ability set that includes the power to influence weather patterns to a moderate degree. (For those familiar, he is using the 5e Spheres of Power system, Weather sphere: http://spheres5e.wikidot.com/weather#toc21). A Storm of Severity 2 or higher generates a bolt of lightning at intervals of 1 minute or 1 round, affects all targets within a 5 foot radius of the strike point, and the landing point of that bolt must be within the bounds of the spell's effect. That area will most commonly be a 60 foot radius cylinder, but could be resized, up to a current maximum of 120 feet.

The issue, as we discovered last session, is that the player has no control whatsoever over where the bolts land, and thus collateral damage is a very real possibility; he could pick up that control via a talent, but at the level we're starting, that could be a long ways off. We experimented with a couple of different ideas for generating random bolts: first, by measuring from the center and using a 'spinner' (or d360) to determine direction and a d12 to determine distance (using 5ft intervals), but quickly realized that would skew more lightning strikes towards the center of the storm's effect. We also considered a 'Battleship' method with labeled rows and columns, but realized that we had potential to roll 'illegal' landing zones by rolling results at the effect's corners.

Ultimately, what we'd really like to have is a method to determine where the lightning bolts are landing, that doesn't slow down play significantly, but also is relatively random. I've done some searching and haven't had much luck, but I'm no mathematician, so any assistance would be greatly appreciated!

[Amnestic]

Does it matter if the lightning hits an object?

If it's only creatures that matter, could be as simple as d20. If it rolls a number equal to or lower than the number of creatures in the area (I doubt there'll ever be more than 20!) then it hits a creature. If it does, the number rolled determines the creature hit, in order from top left to bottom right, row by row.

[Unoriginal]

Greetings Playground!

The short version: I'm looking for a random method, ideally that is both relatively simple and nonbiased towards a particular outcome, to determine the landing point of a given 5' radius lightning strike, primarily within a cylinder of 60' (but could also fall within a 30' or 120' radius).

More context: I'm playing in a freshly started and heavily homebrewed 5e game, and one of the other players in this group has a character themed around storms and lightning, with an ability set that includes the power to influence weather patterns to a moderate degree. (For those familiar, he is using the 5e Spheres of Power system, Weather sphere: http://spheres5e.wikidot.com/weather#toc21). A Storm of Severity 2 or higher generates a bolt of lightning at intervals of 1 minute or 1 round, affects all targets within a 5 foot radius of the strike point, and the landing point of that bolt must be within the bounds of the spell's effect. That area will most commonly be a 60 foot radius cylinder, but could be resized, up to a current maximum of 120 feet.

The issue, as we discovered last session, is that the player has no control whatsoever over where the bolts land, and thus collateral damage is a very real possibility; he could pick up that control via a talent, but at the level we're starting, that could be a long ways off. We experimented with a couple of different ideas for generating random bolts: first, by measuring from the center and using a 'spinner' (or d360) to determine direction and a d12 to determine distance (using 5ft intervals), but quickly realized that would skew more lightning strikes towards the center of the storm's effect. We also considered a 'Battleship' method with labeled rows and columns, but realized that we had potential to roll 'illegal' landing zones by rolling results at the effect's corners.

Ultimately, what we'd really like to have is a method to determine where the lightning bolts are landing, that doesn't slow down play significantly, but also is relatively random. I've done some searching and haven't had much luck, but I'm no mathematician, so any assistance would be greatly appreciated!

My idea:

- Start at the center of the circle on the ground.

- Roll 4d6.

- First die: if number uneven, then left, if number even, then right

- Second die: take number*10, move the lightning's end point of this number of feet in the direction indicated by the first die

- Third die: if number uneven, then up, if number even, then down

- Fourth die: take number*10, move the lightning's end point of this number of feet in the direction indicated by the third die

[PrinceOfMadness]

Does it matter if the lightning hits an object?

If it's only creatures that matter, could be as simple as d20. If it rolls a number equal to or lower than the number of creatures in the area (I doubt there'll ever be more than 20!) then it hits a creature. If it does, the number rolled determines the creature hit, in order from top left to bottom right, row by row.

Next session we're expecting to have a combat with at least 26 creatures involved (5 PCs, 2 familiars, 5 non-combatant hostages, and 14 enemies). Our GM likes big epic combats. I think in general objects probably don't matter, but could foresee edge cases where there's an especially fragile object we'd want to not have hit; and while I'd hope the player in question isn't foolish enough to fire off indiscriminate magic in that scenario, I can't dismiss the possibility out of hand.

If I've done my math correctly, there are 501 squares that are touched by a 60' radius cylinder that originates from a single square. So a d501 is technically a possibility, but seems like a pain in play. Here's a quick grid I put together to demonstrate the area.

My idea:

- Start at the center of the circle on the ground.

- Roll 4d6.

- First die: if number uneven, then left, if number even, then right

- Second die: take number*10, move the lightning's end point of this number of feet in the direction indicated by the first die

- Third die: if number uneven, then up, if number even, then down

- Fourth die: take number*10, move the lightning's end point of this number of feet in the direction indicated by the third die

This method is somewhat complicated, but I think more importantly it means there will always be spaces that are safer than others; since you can't ever have lightning strike, for example, 3 squares or 30 feet to the right. While I theoretically like the idea of being able to plan around our party's lightning to a certain extent, I can't be sure the GM will approve a method with predictable outcomes.

EDIT: Grammar. Thinking about this some more, this method also doesn't solve the 'Battleship' problem described in my original post; it's possible for lightning to fall out of bounds of the spell's area (by rolling high on distance for both distance dice).

[TrueAlphaGamer]

Greetings Playground!

The short version: I'm looking for a random method, ideally that is both relatively simple and nonbiased towards a particular outcome, to determine the landing point of a given 5' radius lightning strike, primarily within a cylinder of 60' (but could also fall within a 30' or 120' radius).

More context: I'm playing in a freshly started and heavily homebrewed 5e game, and one of the other players in this group has a character themed around storms and lightning, with an ability set that includes the power to influence weather patterns to a moderate degree. (For those familiar, he is using the 5e Spheres of Power system, Weather sphere: http://spheres5e.wikidot.com/weather#toc21). A Storm of Severity 2 or higher generates a bolt of lightning at intervals of 1 minute or 1 round, affects all targets within a 5 foot radius of the strike point, and the landing point of that bolt must be within the bounds of the spell's effect. That area will most commonly be a 60 foot radius cylinder, but could be resized, up to a current maximum of 120 feet.

The issue, as we discovered last session, is that the player has no control whatsoever over where the bolts land, and thus collateral damage is a very real possibility; he could pick up that control via a talent, but at the level we're starting, that could be a long ways off. We experimented with a couple of different ideas for generating random bolts: first, by measuring from the center and using a 'spinner' (or d360) to determine direction and a d12 to determine distance (using 5ft intervals), but quickly realized that would skew more lightning strikes towards the center of the storm's effect. We also considered a 'Battleship' method with labeled rows and columns, but realized that we had potential to roll 'illegal' landing zones by rolling results at the effect's corners.

Ultimately, what we'd really like to have is a method to determine where the lightning bolts are landing, that doesn't slow down play significantly, but also is relatively random. I've done some searching and haven't had much luck, but I'm no mathematician, so any assistance would be greatly appreciated!

This question may have been better asked on the math stack exchange, but some quick googling has brought me this: https://mathworld.wolfram.com/DiskPointPicking.html I think that it may be relevant to your problem and provide an overall solution. Hope your DM has a calculator handy. That, or a quick little MATLAB script.

[notthegiant]

We also considered a 'Battleship' method with labeled rows and columns, but realized that we had potential to roll 'illegal' landing zones by rolling results at the effect's corners.

Why couldn't you just reroll if the lightning struck outside of the radius?

[PrinceOfMadness]

This question may have been better asked on the math stack exchange, but some quick googling has brought me this: https://mathworld.wolfram.com/DiskPointPicking.html I think that it may be relevant to your problem and provide an overall solution. Hope your DM has a calculator handy. That, or a quick little MATLAB script.

This seems like it achieves the desired goal as long as I can figure out how to actually run the calculation described, which may require more research. Thank you!

Why couldn't you just reroll if the lightning struck outside of the radius?

That's a workable solution, but even trimming the 'template' to just barely bound the circle, there's still a non-negligible number of squares (around 112, I think?) that would require a re-roll. If both my rough countings are correct (501 valid target squares, and 112 illegal squares), roughly 1 in 6 rolls would need to be re-rolled which does slow down play to a certain extent if lightning is striking every round. I'm hoping to hit on a solution that slows down gameplay as little as possible while still being sufficiently unbiased.

[Zhorn]

My idea:
- Start at the center of the circle on the ground.
- Roll 4d6.
- First die: if number uneven, then left, if number even, then right
- Second die: take number*10, move the lightning's end point of this number of feet in the direction indicated by the first die
- Third die: if number uneven, then up, if number even, then down
- Fourth die: take number*10, move the lightning's end point of this number of feet in the direction indicated by the third die

This method is somewhat complicated, but I think more importantly it means there will always be spaces that are safer than others; since you can't ever have lightning strike

variant of this for the location of the strike since you're already working with a circle and the distance on your grid is ~12 spaces in radius
- Two d12's of different colour
- One for clock direction (12 o'clock as north on the map)
- Other for distance from centre (in equivalent space distances; none of that taxi-cab nonsense)
- Finally the lightning strike is a aoe template (5ft or 10ft radius) just to up the danger a bit.

[Unoriginal]

Next session we're expecting to have a combat with at least 26 creatures involved (5 PCs, 2 familiars, 5 non-combatant hostages, and 14 enemies). Our GM likes big epic combats. I think in general objects probably don't matter, but could foresee edge cases where there's an especially fragile object we'd want to not have hit; and while I'd hope the player in question isn't foolish enough to fire off indiscriminate magic in that scenario, I can't dismiss the possibility out of hand.

If I've done my math correctly, there are 501 squares that are touched by a 60' radius cylinder that originates from a single square. So a d501 is technically a possibility, but seems like a pain in play. Here's a quick grid I put together to demonstrate the area.




This method is somewhat complicated, but I think more importantly it means there will always be spaces that are safer than others; since you can't ever have lightning strike, for example, 3 squares or 30 feet to the right. While I theoretically like the idea of being able to plan around our party's lightning to a certain extent, I can't be sure the GM will approve a method with predictable outcomes.

EDIT: Grammar. Thinking about this some more, this method also doesn't solve the 'Battleship' problem described in my original post; it's possible for lightning to fall out of bounds of the spell's area (by rolling high on distance for both distance dice).

Fair, but you can go that way, then:


-Roll 2d6 + 2d4

- the d6s is the number of square from the center (1 being the center) in a given direction

- for the d4s, you have 1= up, 2= down, 3= right, 4= left

[JackPhoenix]

If you're playing in person, get a sheet of paper of sufficient size with a grid, and flip a coin (or some other token) on it. The lightning strikes at whatever coordinates the coin lands at.

Alternatively, if that's too much and you're worried rerolls may be too slow, instead of using grid coordinates, simply number the squares 1 to Whatever, and then roll 1dWhatever to determine the square the lightning hits.

[Yspoch]

I think i would first do a probability -roll to see if anything interesting was hit and then a second roll to see what target was actually hit.

In your example there were 26 creatures. Let's add 14 objects that have an effect if hit by lightning. Divide by 500 possible locations and you get a probability-roll of 8% (40/500=0.08).

Rolling 8 or lower on a d100 leads to a roll on a list of 40 entries ((d4-1)*10 + d10) and you see what gets hit.

Cons using this method: you don't get "wow, that was close!" moments.

[GeoffWatson]

Mundane lightning usually hits the tallest thing nearby.

Divide the area into a number of zones - roll a random zone - tallest structure or creature in the zone is hit.

[PrinceOfMadness]

variant of this for the location of the strike since you're already working with a circle and the distance on your grid is ~12 spaces in radius
- Two d12's of different colour -snip-

This is a variant of the first method I tried (discussed in the OP). The issue with this method is that there's always an approximately 1/12 chance of striking the center of the circle (frequently the caster...)

-snip- -Roll 2d6 + 2d4 -snip-

This creates lightning bolts hitting on a bell curve of distance (average 7) which is not desirable and which I think will be a problem that needs solving for almost dice-based method that measures from the center point (as described in the OP). However, I thank you for the suggestion!

If you're playing in person, get a sheet of paper of sufficient size with a grid, and flip a coin (or some other token) on it. The lightning strikes at whatever coordinates the coin lands at.

Alternatively, if that's too much and you're worried rerolls may be too slow, instead of using grid coordinates, simply number the squares 1 to Whatever, and then roll 1dWhatever to determine the square the lightning hits.

These are both good suggestions; some up-front work would be required to number approximately 500 squares, but I'd prefer front-end load before session than loading up effort during game. Thank you!

-snip- Cons using this method: you don't get "wow, that was close!" moments.

Yeah; this method works, but I think removing the tense moments from play would remove the excitement from the ability and make it mostly annoying. Thank you for the suggestion!

Mundane lightning usually hits the tallest thing nearby.

Divide the area into a number of zones - roll a random zone - tallest structure or creature in the zone is hit.

This would be realistic lightning behavior, but more or less removes the random element if there are any especially large creatures in play, which is not desired.

[PrinceOfMadness]

After examining the responses here, conferring with my group, and doing some more research I'm going to bring a few different options to our next session and see which one feels the best in play:

A Google Sheet set to auto-calculate randomized distance and direction as per Mathworld article linked by TrueAlphaGamer (thank you!)

A printed grid with labeled squares that we can roll a d501 against (thanks JackPhoenix!)

Battleship it and see if I'm worrying too much about the out-of-bounds re-rolls (thanks notthegiant!)

Thank you all for your suggestions and help!

[Unoriginal]

This is a variant of the first method I tried (discussed in the OP). The issue with this method is that there's always an approximately 1/12 chance of striking the center of the circle (frequently the caster...)

This creates lightning bolts hitting on a bell curve of distance (average 7) which is not desirable and which I think will be a problem that needs solving for almost dice-based method that measures from the center point (as described in the OP). However, I thank you for the suggestion!

These are both good suggestions; some up-front work would be required to number approximately 500 squares, but I'd prefer front-end load before session than loading up effort during game. Thank you!

Yeah; this method works, but I think removing the tense moments from play would remove the excitement from the ability and make it mostly annoying. Thank you for the suggestion!

This would be realistic lightning behavior, but more or less removes the random element if there are any especially large creatures in play, which is not desired.

Any dice-generated number will have an "average", you know?

But yeah, numbering each square of the circle them using an online dice roller than let you simulate a d500+ would be your best bet, I think.

[Zhorn]

This is a variant of the first method I tried (discussed in the OP). The issue with this method is that there's always an approximately 1/12 chance of striking the center of the circle (frequently the caster...)

only if you do go with an AoE for the strike, measuring 1 (minimum roll on a d12) space away from the centre clears the caster.
If going with a AoE for the strike, 1d10+2, even with a 10ft strike radius that will always be outside of reach of the centre

[PrinceOfMadness]

Any dice-generated number will have an "average", you know? -snip-

Yes. The issue is that rolling multiple dice (instead of a single many-sided die) creates a bell curve of outcomes and makes the result less random, skewing towards certain results. For example, 2d6 is much more likely to roll 7 than it is to roll 3 or 10. A d12, however, is just as likely to roll any of those 3 numbers as it is to roll any other number.

only if you do go with an AoE for the strike, measuring 1 (minimum roll on a d12) space away from the centre clears the caster.
If going with a AoE for the strike, 1d10+2, even with a 10ft strike radius that will always be outside of reach of the centre

The ability creates a 5ft radius AoE (described in the OP) and should be able to hit the center space since it strikes a random point; in other words, the caster isn't any safer from the ability than anyone else in the effect. I realize this may seem counterintuitive, but the magic is intended to be indiscriminate, wild, destructive to fit with the character's themes.

The problem with rolling a random direction (by any method measuring from the center) and a random distance via dice is that this creates a scenario where the minimum 'distance' result - in any direction - also hits the center point, skewing results toward the center. The Mathworld article linked earlier in this discussion solves this by using math more complicated than what we can generally expect from die rolls to unskew the results. I created a Google Sheet that runs this calculation for our table, determining a random direction via a d360 and a random distance using the linked calculation which appears to generate suitably random results...but may end up being painful to execute at table, since we'll need to break out a compass every time. That's why we're bringing multiple methods to next session, so we can test and see what feels best in play