We have $1 on the table and a quarter. Every time we flip the coin and it lands on heads, the money on the table doubles but once it lands on tails, the money on the table goes to 0 and the game ends. You can decide to leave the table with your money at any point. How much would you pay to play this game?
Is this a correct approach?
E[game] = (1/2) * (2E[game]) + (1/2)*(0) = E[game]
The first case is where we get a heads, and so the EV is twice as much (this seems logical, but I don't know if this is the right way to mathematically express this).
Yes, this is the correct approach.