Each of these puzzles involves a symmetric game. You will be asked about your best strategy, but what does "best strategy" mean? Here, we want a strategy that is a "Nash equilibrium" for all players; that is, one with the property that if it is followed by all other players, you can do no better than follow it yourself. Often, such a strategy requires that players do some randomization; for example, in the familiar game "Rock, Paper, Scissors," the Nash equilibrium strategy requires each player to choose rock, paper, or scissors with equal probability. As in "Rock, Paper, Scissors," plays in the games here are done simultaneously, with no collaboration allowed, so every man/woman for him/herself. For solutions and sources, see next month's column.
Corrections to "Solutions and Sources" (Dec. 2013) to "Coin Flipping" (Nov. 2013). Three careful readers pointed out there are 12, not 10 (as we said in the solution to Problem 1) head-tail sequences of length 5 that take on average only 32 flips to occur. In addition, Joseph Skudlarek found a sequence (HTTHH or its complement THHTT) that gets the first player a better than 1/3 chance to win in Problem 2, 9/26, to be exact.
Readers are encouraged to submit prospective puzzles for future columns to email@example.com.
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