Random game mating probabilities

sje · Post by **sje** » Sat Mar 12, 2016 6:01 am

Random game mating probabilities

Some data from 24,478,109 games, each made from randomly generated moves:

There were 3,747,489 checkmates (15.31%)
Of the checkmates, 1,872,426 were White getting checkmated (49.96%).
Of the checkmates, 1,875,063 were Black getting checkmated (50.04%).

There were 1,499,382 stalemates (6.13%)
Of the stalemates, 754,025 were White getting stalemated (50.29%).
Of the stalemates, 745,357 were Black getting stalemated (49.71%).

sje · Post by **sje** » Sat Mar 12, 2016 6:31 am

Random game repetition draw probabilities

Some more data from 24,478,109 games, each made from randomly generated moves:

There were 629,639 repetition draws (2.57%)
Of the repetition draws, 315,765 were White making the drawing move causing the repeated position (50.15%).
Of the repetition draws, 313,874 were Black making the drawing move causing the repeated position (49.85%).

sje · Post by **sje** » Sat Mar 12, 2016 7:24 am

Random game fifty move draw probabilities

Some more data from 24,478,109 games, each made from randomly generated moves:

There were 5,484,539 fifty move draws (22.41%)
Of the fifty move draws, 2,744,587 were White making the drawing move (50.04%).
Of the fifty move draws, 2,739,952 were Black making the drawing move (49.96%).

sje · Post by **sje** » Sat Mar 12, 2016 7:29 am

Random game insufficient material draw probabilities

Even more data from 24,478,109 games, each made from randomly generated moves:

There were 13,117,060 insufficient material draws (53.59%)
Of the insufficient material draws, 6,568,020 were White making the drawing move (50.07%).
Of the insufficient material draws, 6,549,040 were Black making the drawing move (49.93%).

sje · Post by **sje** » Sat Mar 12, 2016 7:42 am

Some comments

1) Randomness was provided by /dev/urandom

2) The double anomaly comes from the stalemate numbers. Of the five ways a random game can end, only stalemating has a majority of the games ending with a Black move. Also, only stalemating has a White/Black spread greater than a half percentage point (0.58%). Why?

3) Insufficient material = KvK, KNvK, or KBvK.

4) Fifty move trumps repetition.

sje · Post by **sje** » Sat Mar 12, 2016 7:59 am

Full trump hierarchy

checkmate > stalemate > fifty move > insufficient > repetition

Most pairs are mutually exclusive. The four which aren't:

checkmate, fifty move
stalemate, fifty move
stalemate, insufficient
fifty move, repetition

Uri Blass · Post by **Uri Blass** » Sat Mar 12, 2016 8:23 am

sje wrote:Full trump hierarchy

checkmate > stalemate > fifty move > insufficient > repetition

Most pairs are mutually exclusive. The four which aren't:

checkmate, fifty move
stalemate, fifty move
stalemate, insufficient
fifty move, repetition

Checkmate has preference to fifty move rule so I think that you can consider the pair checkmate, fifty move to be impossible(because it means that the fifty move rule has no relevance).