I’m not sure where you got that 95% number from for your strategy #3; it sounds like the “both numbers are the same” situation only happens once ever several thousand of runs.
Anyway, if you’re using strategy 1, then if the two numbers are the same, that means that the number is prime, and your payout for this scenario is only 1 million dollars (you lost the lottery). If you’re using strategy 3, then that means the number is not prime, and the payout is $2.001 million dollars (the number is not prime, because you’re going to double box.)
There is no difference between strategy 1 and strategy 3 except in the one scenario where both numbers are the same, and the one scenario where both numbers are the same, strategy 3 is better. Therefore, strategy 3 is always better.
I’m not sure where you got that 95% number from for your strategy #3; it sounds like the “both numbers are the same” situation only happens once ever several thousand of runs.
Anyway, if you’re using strategy 1, then if the two numbers are the same, that means that the number is prime, and your payout for this scenario is only 1 million dollars (you lost the lottery). If you’re using strategy 3, then that means the number is not prime, and the payout is $2.001 million dollars (the number is not prime, because you’re going to double box.)
There is no difference between strategy 1 and strategy 3 except in the one scenario where both numbers are the same, and the one scenario where both numbers are the same, strategy 3 is better. Therefore, strategy 3 is always better.