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Toby and Leia are sitting in a pub arguing over who should buy the next
round. To settle the argument they decide to play the following game. They
place 17 pennies on the table and take turns to remove them. Each player
can remove either 1 , 2 or 3 coins when it is their turn. The person who
picks up the last coin buys the next round.
(u) Find an optimal strategy for each player.
(b) If both players use optimal strategies and Toby goes first, who wins?
(.) Who wins if we start with 100 coins on the table?

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关键词：Strategies following Strategy argument Strateg 请教 博弈

谁先选谁输，因为如果前者选x，后者的最有策略为4—x，以至于4轮后只剩下一个硬币。

what's the optimal strategy for the first player?

is there a equilibrium?

100 呢？

the first win with 100 coins. take away 3 first, leave 97 on the table. then play the x and 4-x strategy