I place one dollar on the table. I repeatedly flip a coin. Each time the coin comes up heads, I double the money on the table. The first time the coin comes up tails, you take the money and the game is over.

What's a fair admission price for the game?

Would you play the game with me for $100?

here's the non mathmatician's simple, but infinitely logical answer; I am guaranteed only a dollar.  If you flip 2 heads consecutively I win $2, 3 consecutive heads wins me $4, etc. The odds are against 3 consecutive heads, I'll pay $3 to "buy in" and no more, even though theoretically I could win a ton depending on how many heads you flip consecutively. $3 is a "fair admission price", and no way I'll pay you $100 to play, you'd have to flip 7 consecutive heads for me to come out ahead.