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不公平轮盘：该不该玩

Fair roulette

专题
Probability / 概率
难度
L4

题目详情

I will spin a fair roulette wheel with only five sections. Four of the five sections pay 1;thefifthpays1; the fifth pays 5.

  1. If the cost is $1.50 per spin, and you may play as often as you want, should you play the game?

  2. If the cost is $1.50 per spin, and you may play exactly once, should you play the game?

解析

单次期望收益为

E[payoff]=4⋅1+55=95=1.8.\mathbb{E}[\text{payoff}]=\frac{4\cdot 1+5}{5}=\frac{9}{5}=1.8.

每次成本 1.5，因此单次期望净收益

1.8−1.5=0.3>0.1.8-1.5=0.3>0.

  1. 若可重复玩很多次且以期望收益为准（风险中性），应玩。

  2. 若只能玩一次，按期望收益仍应玩；但若极端风险厌恶（例如一次亏损会导致巨大效用损失），可能选择不玩。