coin game

[Kangxi]

Here is a coin game as follows. We each have three fair coins, and we flip all of them at once. After we flip them, we look at the outcomes. If we have the same number of heads out of our own coins I pay you $1 and if we have a different number you pay me $2. Do you want to play this game?

 

[diegosanaz]

The probability of winning is 0.3125 (if I did things right), so no, I would not play this game, even if the payments were the other way around. Is this the correct answer????

 

[Kangxi]

I got the same answer as yours, but I am not sure if it is correct either​

 

[pplstuff]

Ran 100k iterations in Excel. Won 31,273/100,000. So you're both probably correct.

 

[Kangxi]

thanks