The Ace-Queen Betting Game
Several firms, Five Rings among them, run a simplified poker game in the technical rounds. You are given a card, the opponent knows your strategy, and you are asked how often you would bluff. It is the most direct test of everything in this section, so it is worth solving completely once.
The setup
You are dealt an Ace or a Queen, each with probability one half. Your opponent always holds a King, which beats a Queen and loses to an Ace. You both put 1 in, so the pot is 2.
You act first: bet 1, or check. If you check, the cards are shown. If you bet, the opponent calls or folds.
Two decisions are yours, one is theirs. Crucially, the opponent knows your strategy, so there is no hiding a pattern.
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