[HesseJam]

Yes, EV is infinite

1/2 * 1 + 1/2*1/2*4 + 1/2*1/2*1/2*8 ....
= 0.5 + 0.5 + 0.5 + 0.5 .......

I have an answer, maybe not THE answer since this depends on each individual.

One thing seems clear: nobody will pay an infinite amount of money nor can anybody. Nobody will probably sell his home, cash out his bank account and put his whole fortune into the game even if this would be clearly +EV .

Why? Because your own risk-utility-function is not properly reflected. Even If you put in only $1000 you will fail about to 99,8% to get your money back (you need to guess right 9 times in a row). But the 0.2 % who get there suddenly face a fantastic game. 0.1 % of them will go and win a Million bucks and can now play for two Million and so on and on.
Now, the problem here is that the EV concepts treats each dollar with the same value. While at large each dollar has of course the same value (one dollar [img]/images/graemlins/crazy.gif[/img] ) not each dollar has the same value to you. Let's say you win one Million, which might be a life changing event for some people. Will it be the same life changing event if they win a second Million? Probably not. Now, this someone who had won the Million is proposed an even odds bet that he could triple his Million if he makes good. Otherwise he loses one Million which is all his money. Most people would not do this because the value of the second and third Million combined is much lower to them than the first Million.

So, in the coin flip proposition you would bid as much as you personally think you could afford to loose for that small chance to win big. It's like the lottery, the difference is that it is infinite + in EV whereas the lotteries are negative. The result (how much to bid for the game)will be different for each person.