Game Guy's Magic Boxes

Game Guy's Magic Boxes is a Game Guy minigame found in Mario Party 3.

Description
"Toad is hiding in one of these treasure chests. If you guess right, you'll get more coins.  But if you guess wrong, your coins will be mine.

"Let's begin."

Gameplay
When the minigame starts, the two boxes are hidden by the curtains and may be switched; when that's done, the player must pick the box containing Toad instead of Baby Bowser. If successful, the player's coins are doubled. If the player picks the box containing Baby Bowser, they lose all of their coins. The player is then given the option either to take the coins or risk them all for a second doubling--and, if lucky enough to guess right the second time, a third. Three correct guesses multiplies the player's coins by eight, but of course players may also opt to quit at any time after the first win and take their winnings.

There is a secret to winning. Each time Game Guy jumps, Toad switches boxes. Just keep track on the number of jumps.

Expected Value
Let B be the amount bet. At each point, the player has a 1/2 chance of doubling their coins and a 1/2 chance of losing them. Thus, at each point, the EV is:

EV = 1/2 * 2B = B

Interestingly, this is the only Game Guy game where the player can not make a profit in the long run, and will instead break even. However, Game Guy still doesn't turn a profit.