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James_Miller comments on A simple game that has no solution - Less Wrong Discussion
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"The reason player 1 would choose B is not because it directly has a higher payout but because including B in a mixed strategy gives player 2 an incentive to include Y in its own mixed strategy, "
No since Player 2 only observes Player 1's choice not what probabilities Player 1 used.
Player 2 observes "not A" as a choice. Doesn't player 2 still need to estimate the relative probabilities that B was chosen vs. that C was chosen?
Of course Player 2 doesn't have access to Player 1's source code, but that's not an excuse to set those probabilities in a completely arbitrary manner. Player 2 has to decide the probability of B in a rational way, given the available (albeit scarce) evidence, which is the payoff matrix and the fact that A was not chosen.
It seems reasonable to imagine a space of strategies which would lead player 1 to not choose A, and assign probabilities to which strategy player 1 is using. Player 1 is probably making a shot for 6 points, meaning they are trying to tempt player 2 into choosing Y. Player 2 has to decide the probability that (Player 1 is using a strategy which results in [probability of B > 0]), in order to make that choice.