Calling All Mathmeticians and Statisticians

[CT11]

I'm reluctant to respond in this thread but the other threads are so incoherent I can't even tell what the argument is about.

If the question is what I think it is Beavis68 seems to be on the right track though his argument is a little informal.

Can I assume the game is this:
I may choose heads or tails using whatever strategy I feel like. You will flip a coin where P(heads) =p and P(tails)=1-p. I win k dollars if I guess the same as the coin flip and I loose c dollars if I guess the opposite. One of these outcomes will happen almost surly.

Is that the game?

ok whats the question?

is this the question:
you have a choice between playing two games, A and B.
game A:
as above k=11, c=10, p=0.5. you play the game.
game B:
as above k=12, c=10, p is fixed and unknown and an element of [0,1]. you play the game.

which game has a higher expected value if you use the optimal strategy for each one?

edit: made it a bit more clear