[HesseJam]

In decision theory one of the most basic concepts is the Expected Value (EV) concept. If your are facing a decision to choose between alternatives, you should choose the alternative with the highest EV. But there are situations where this concept is impractical:

A casino with unlimited ressources proposes the following game to the public which will auction off the game to the highest bidder (the game will only be held once):

a) You need to pick heads or tails on a coin flip.
c) In stage 1, if you guessed correctly the casino will pay you $1, which is your profit. You also get a freeroll for stage 2. If you missed, the game is over.
c) In stage 2, the pay out will be doubled. If you guessed correctly the casino will pay you $2, which is your profit for now a total profit of $3. You also get a freeroll for stage 3. If you missed, the game is over and you total profit remains the 1$ from the previous stage.
d) If you make it to stage 3, the casino will again double the pay out to $4.
e) You stay in the game until your first miss. The pay outs will always be doubled in each subsequent stake.

The auctions starts. How high would you go with your bid? Try to apply the EV concept. Obviously, according to that concept you can increase your bid as long as it stays below the EV. Would you take your decision according to that concept in this case?