# Talk:Dice game probabilities

## Test runs

Test runs with 10000 samples show
0.5751 player 1 wins (agrees with shown probabilities)
0.3535 player 2 wins
0.0714 draws
and for the second part:
0.6405 player 1 wins (differs considerably)
0.3147 player 2 wins
0.0448 draws

Can somebody show the pseudo code ?

--Walterpachl (talk) 15:14, 16 January 2015 (UTC)

Second part is ten 5-sided dice vs seven 6-sided dice, no? Never mind, everyone else (i.e. Bearophile and I) used the wrong numbers. Your result is correct. --Ledrug (talk) 05:38, 18 January 2015 (UTC)
:-) Still: Is your solution built analytically? Pseudocode? My attempt to translate it to REXX got stuck in the recursion. :-( --Walterpachl (talk) 07:34, 18 January 2015 (UTC)
Oh well. REXX and ooRexx show now the algorithm. What have we learned? Testing is always a good idea! --Walterpachl (talk) 07:40, 19 January 2015 (UTC)

Change of D's results: I don't have D, so I can't test. How did the corrected (or the previous, incorrect) results come about? Just being curious: --Walterpachl (talk) 06:40, 21 January 2015 (UTC)

## Results compared

```Numeric Digits 130
Say 3781171969/5882450000
/*
0.642788628717626159168373721835
C              0.6427886287176260
D              0.6427886287176262
ooRexx         0.642788628717626159168373721835
REXX version 1 0.642788628717626159168373721835
REXX optimized 0.6427886287176261591683737218335897457691948082856632865557718297648088806534692177579069945345901792620421763040909824987887699852952426284966
PL/I           0.642703175544738770
Python         0.642788628718
Python ver. 2  0.6427886287176262
Python ver. 3  0.6427886287176262
Racket         0.6427886287176261591683737218335897457691948082856632865557718297648088806534692177579069945345901793
0.6427886287176261591683737218335897457691948082856632865557718297648088806534692177579069945345901792620421763040909824987887699853
ooRexx     (*) 0.64278862871762615916837372183358974576919480828566328655577182976480888065346921775790699453459017926204217630409098249878876998529524262849
Racket          (3781171969/5882450000)
*/
```

--Walterpachl (talk) 08:20, 22 January 2015 (UTC)

Updated to reflect the optimized REXX example.     -- Gerard Schildberger (talk) 14:07, 1 July 2020 (UTC)

## Rational Arithmetic

Inspired by Racket I boosted ooRexx and PL/I by using Rational Arithmetic. Actually I should have used the implementation that can be found here on RC! but I rolled my own before looking. --Walterpachl (talk) 18:57, 22 January 2015 (UTC)

## Possible extension?

Nice task. While implementing it, I found myself briefly misunderstanding the "draw" scenario and an interesting alternative occurred to me. What if a "draw" resulted in the game being re-run? This changes the probabilities fairly significantly (not just W/(W+L), but (W + D*k)/(W+L+D) for some k, which can be determined by running lots of trials or by calculus. That probably puts it more in the realm of a Project Euler task than RosettaCode, but might make a fun extension. --Aspectcl (talk) 04:50, 20 June 2015 (UTC)