An Analysis of the Game Tenzi
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In the game Tenzi, a player has ten six-sided dice and repeatedly rolls any subsets of the dice in order to have all ten show the same number with as few rolls as possible. A simple strategy is to choose a number at the start of the game and always re-roll any dice not showing that number. For this strategy we find that the expected number of rolls to win the game is 16.6, and we derive the expected number of rolls with playing the game with any number of dice instead of ten.