5 格轮盘：该不该玩

Fair roulette

I will spin a fair roulette wheel with only five sections. Four of the five sections pay $\mathbb{S}1$ ; the fifth pays $\mathbb{S}5$ .

If the cost is $\mathbb{S}1.50$ per spin, and you may play as often as you want, should you play the game?
If the cost is $\mathbb{S}1.50$ per spin, and you may play exactly once, should you play the game?

解析

每次期望支付为

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

成本 1.5，单次期望净收益 $1.8-1.5=0.3>0$ 。