Odds and Even game - TOP Game Theory chapter

[teajay]

I was just thinking about the game described by skylansky in TOP chapter on bluffing and game theory.

I believe it was along the lines of playing odd-even with 101:100 payouts. The idea behind it was that if you were to use a coin flip to determine whether to show an odd or even number of fingers you could end up with a +0.5 EV, assuming all the conditions explained are met.

This made me wonder what would happen to your EV in a few different situations. Assume you are the opponent who is doing the guessing.

1) your opponent is not using a coin (or any external randomness) to make his decision. You are using a coin to decide. (This is just the reverse of what skylansky explains)

2) Both you and your opponent are using a coin make your decision. Since you have a 50/50 chance at heads or tails, I don't think it would matter if you use heads to decide odd and your opponent uses tails, or vice versa. Would it?

Thanks for any help you can provide... And sorry if i'm unclear on any of it. Just ask I may be able to explain better.

cheers,
travis