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The Twiddle shuffling algorithm was theoretically parity-unbalanced:

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it performed a fixed number of shuffling moves, and on each one it
had a 2/3 chance of flipping the permutation parity and a 1/3 chance
of keeping it the same. Markov analysis shows that over a run of
1500-odd shuffle moves this will end up being an undetectably small
actual bias in the parity of the generated grid, but it offends my
sense of pedantry nonetheless so here's a small change to make the
number of shuffling moves itself have randomly chosen parity. The
parity of generated grids should now be _exactly_ 50:50.

[originally from svn r5742]
This commit is contained in:
Simon Tatham
2005-05-04 12:52:51 +00:00
parent 1c77e0df94
commit 38c1f9b702
1 changed files with 1 additions and 1 deletions
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twiddle.c
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@ -317,7 +317,7 @@ static char *new_game_seed(game_params *params, random_state *rs,
* and simply shuffle the grid by making a long sequence of * and simply shuffle the grid by making a long sequence of
* randomly chosen moves. * randomly chosen moves.
*/ */
total_moves = w*h*n*n*2; total_moves = w*h*n*n*2 + random_upto(rs, 1);
for (i = 0; i < total_moves; i++) { for (i = 0; i < total_moves; i++) {
int x, y; int x, y;