Omega creates one more copy of you, then he asks each of you to say either “zero” or “one”; he will give each of you $10 unless you both pick the same number. You have no idea which copy you are, and cannot communicate with the other copy before you both make your choice.
The strategies “choose 0” and “choose 1” both lose, but the strategy “choose 0 with 50% probability and 1 with 50% probability” has a 50% probability of winning.
Omega creates one more copy of you, then he asks each of you to say either “zero” or “one”; he will give each of you $10 unless you both pick the same number. You have no idea which copy you are, and cannot communicate with the other copy before you both make your choice.
The strategies “choose 0” and “choose 1” both lose, but the strategy “choose 0 with 50% probability and 1 with 50% probability” has a 50% probability of winning.