My initial guess (probably wrong) is that your strategy is to always say, "the sum is not 7" and you'll be right with a probability of 9/11. Actually, how about this. If it is 7, then there is an even number and an odd number. If he says an even number, then you say "it is 7." You'll be right in every case where there are not 2 even numbers. A pair of evens occurs 9 times out of 36, so this would have you be right 3/4 times, which is worse than the previous one. Oh, wait a minute. That first strategy is wrong, and it highlights the fact that something is wrong with saying "It would seem that this improves our a priori odds of rolling a 7 from 1/6 to 2/11." Right?
