Imploding / Exploding Die

Mon Jan 4 15:48:58 2016 by Ishpeming

I would like to figure out probabilities for the old world of darkness. I would like the program to count 8s, 9s, 10s on a variable number of d10s. 10s explode infinitely. However, 1s subtract from the total number of counted die.

Tue Jan 5 10:32:54 2016 by Torben

You can do it this way:

N := 4;  \ number of dice in pool
pool := N # accumulate x := d10 while x=10;
(count 7<pool) - (count 1=pool)

However, that is very slow when N is 4 or more. To speed it up, we note that 2-7 behave the same, as does 8 and 9, so instead of a d10 we use a die with one 1, six 2s, two 8s and one 10:

N := 4;  \ number of dice in pool
pool := N # accumulate x := choose {1,6#2,2#8,10} while x=10;
(count 7<pool) - (count 1=pool)

The reason this is faster is that there are fewer different pools possible.

Tue Jan 5 17:35:03 2016 by Ishpeming

Marvelous!

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