[archargelod]

> After 5000 runs, they were all 8.4-9.7%

This sample size is really small. I ran 100 million simulations in Nim[0] (takes around a minute). And distribution converges toward 9.09% on all positions equally:

    Average turns: 65.99609065001634
    Final position distribution:
     4: 9.095%
    11: 9.093%
     7: 9.091%
     3: 9.091%
    10: 9.090%
     9: 9.090%
     1: 9.090%
     8: 9.090%
     2: 9.090%
     6: 9.090%
     5: 9.089%
     0: 0.000%

[0] - https://play.nim-lang.org/#pasty=hwdfbsfh (reduced amount of runs to not abuse playground server resources)

[JKCalhoun]

Damn good. Does it matter that you're (presumably) using a psuedo random number? I mean you seem to nail the probabilities regardless.

Perhaps our pseudorandom algorithms are better at flipping a coin (this case) versus having to choose a random value over a range greater than 2 (or "1" if you like).

[archargelod]

It should not be a problem, pseudorandom numbers are used in simulations, like monte-carlo, all the time.

Nim uses xoroshiro[0] algorithm for std/random module and it produces good quality statistically random bits until 5TB of output. And lower 4 bits have a little bias, but it should not matter as we only use upper 64 out of available 128 bits.

Also, I just now realise that xoroshiro-128+ is really cheap, so perhaps my batching optimisation was unnecessary here.

[0] - https://en.wikipedia.org/wiki/Xorshift#xoroshiro