Trying to help my college kid with a probability problem, but sad to say I can't figure it out! Is there a simple explanation?
- What is the probability you win in a game of r/p/s.
I think this one is just 1/9, since the events are independent but didn't know for sure.
- Say you and your friends are playing rock-paper-scissors. Suppose your friend knows which choice they’ll make this round (so one of P(r), P(p), P(s) = 1, and the other two are 0), and tells you this, but doesn’t tell you which choice they made. How do you choose a strategy (i.e your P(r), P(p), P(s)) to maximize your winning in the worse-case situation in this scenario?
No idea how to approach this question. I remember making some type of tables, but can't for the life of me figure this out. Wouldn't any choice simply lead to an expected value of 0? Since you don't know which choice your opponent will be taking?
Please help me out!
In the second question, unless you make all your probabilities $=\frac13$, you must make at least one of them $>\frac13$. It may happen that this is the one choice losing against your opponent’s fixed choice. As we are asked about the worst case, we lose with more than $\frac13$ unless we make $P(r)=P(p)=P(s)=\frac13$.