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Exploding Dice probabilities

5 replies [Last post]
Thu, 03/31/2005 - 18:53
Jpwoo
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There was another thread on the forum about the probability of getting a 4 on d4 when rolling 5 dice. The discussion was very good.

1-(1-1/s)^n
where s is number of sides and n is number of rolls was the equation that came up and it is very useful.

Now my question is how does this change when dealing with exploding dice?

Exploding dice are dice that reroll and add when rolling their top number.

So for example I am rolling three exploding six sided dice. I roll a 3, 5, and a 6, I reroll the six and get a 4. I add the 'bonus die' to the six, giving me a 3, a 5, and a 10.

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Thu, 03/31/2005 - 20:55
#1
Zomulgustar
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Exploding Dice probabilities

Well, as the previous discussino likely indicated, what that formula really does is calculate the probability that NONE of the dice will show a certain number, then inverts it. The same principle will work in a broader context. Compute the probability of the desired event in a single trial (p), and the probability of at least one such event in n trials is 1-(1-p)^n. In the original context, p is 1/s, since each side of a die has an equal chance of being rolled (in theory, anyway). In the case of the exploding die, each number from
1 to 5 has probability 1/6, each from 7 to 11 has probability 1/36, each from 13 to 17 has probability 1/216, and so on.

BTW, I really wouldn't recommend that particular type of exploding die, as it leads to ugly discontinuities in the distribution. (there's no way to roll a 6, 12, etc.) Using 1-5 and 5+next is a lot cleaner, IMHO, if you must use this method at all.

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Mon, 04/04/2005 - 00:00
#2
Anonymous
Exploding Dice probabilities

It might be a little tedious, but instead of exploding from the highest number, why not explode from the 1 instead? It might not completely give the desired effect (nor does it live up to the name) but your results will be more balanced.

LA

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Mon, 04/04/2005 - 05:07
#3
sedjtroll
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Exploding Dice probabilities

Lardarse wrote:
why not explode from the 1 instead? It might not completely give the desired effect (nor does it live up to the name)

... IMploding dice?

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Mon, 04/04/2005 - 06:24
#4
Zzzzz
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Exploding Dice probabilities

sedjtroll wrote:
Lardarse wrote:
why not explode from the 1 instead? It might not completely give the desired effect (nor does it live up to the name)

... IMploding dice?

Hmmmm, imploding. Roll a die, say 1d6 get a 6 and roll again. Get a 4 on the re-roll and subtract it? For a result of 2, not sure why but that seems interesting to me. Imploding rolls...

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Mon, 04/04/2005 - 10:31
#5
Hedge-o-Matic
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Exploding Dice probabilities

Traditionally, the low result is a subtraction, allowing negative results.

I also like dividing the results of two dice, since this gives a bell curve, but one skewed toward the low end, with a diminishing probability f higher numbers. It's a great thing for when you want a small chance of large results, but a strong tendency toward a reasonable mean value.

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