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"Hollywood Squares" is a game show, based on the popular children's game of Tic-Tac-Toe, where the two contestants try and place their symbol (be it X or O) on the board, in an effort to make a line of three consecutive symbols. There are, however, several wrinkles that require special attention:
- Players don't automatically get the square of their choice, but rather, must listen to an open-ended question by the host and the ostensible answer provided by the celebrity in the square they chose, then either agree or disagree with the celebrity's assertion
- If the player guesses wrong, their opponent gets a marker in their square, unless that square would give them a three-symbol line, in which case the square remains empty, and
- In the case that all nine squares are filled and no one has three symbols in a row, the player who has the most symbols on the board wins (as opposed to regular Tic-Tac-Toe, in which case the game is a draw).
In this game, they tend to place the 'A-List celebrity' in the center square, with the notion that this is the optimal opening play, thus that celebrity will get maximum air time. In my experience watching the show, players do indeed select the center square in every case I have seen. However, there are two things that stick out in my mind as being wrong with that:
- Even in regular Tic-Tac-Toe, the optimal play is not in the center square, but in one of the corners, as it gives you the maximum chance to catch your opponent unaware with a fork on the 5th play, and
- Because the player that goes first has a decided edge in the alternate win condition (the race to five-of-nine squares to win a tie), it may be in his best interest to play in a way that maximizes the chance of a tie occurring, and losing the center square on a missed first question may make it impossible to hold a tie.
As a result, and as a public service should any Future Sight Gaming reader ever wind up as a contestant on that show, I will be providing an in-depth analysis of the optimal strategy for the contestant who goes first, as a function of their probability of accurately predicting the truth of the celebrity's assertion, as well as the probability of their opponent doing the same.
So, stay tuned for this first installment of what I hope will be a regular feature on Future Sight Gaming.. the front page will have an update when this information has been posted!
Charles.
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