Hi Stunna! Thanks for the reply.

You're right, the post excludes dice sites.

For other casinos, however, there is no amount of randomization that the player can do to prevent the attack. Even entering their own seed won't help. The optimized shuffle will win more often than expected.

A quick example of roulette using a pretend seed space of 5000 (0 - 4999) and running the code:

0000000000000000001111111111111111111: 2561
0000000000000000011111111111101111111: 2562
0000000000000000100111111111111111111: 2590
0000000000000000101111110111111111111: 2599
0000000000000000101111111101111111111: 2605
0000000000000000101111111111101111111: 2611
0000000000000001101111110111101111111: 2613
0000000000000001101111111101101111111: 2619
0000000000000001101111111111100111111: 2623
0000000000000010101111110111101111111: 2624
0000000000000010101111111101101111111: 2630
0000000000000010101111111111100111111: 2634
0000000000000011101111110111100111111: 2636
0000000000000011101111111101100111111: 2642
...
0000010111000110111110101111000011100: 2743

I stopped after a few moments. According to this setup, the probability of a win (for the house) is (19/37) = .5135. However, the last permutation wins 2743/5000, or .5486. We now have an arrangement that will always result in an average higher win rate. There is nothing the player can do (with this implementation) to overcome the optimized shuffle.