Game Guy's Magic Boxes
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.
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
This is the only Game Guy game where the player cannot make a profit in the long run, and will instead break even. However, Game Guy still doesn't turn a profit in most situations. Due to the in game limit of 999 coins; if a player has 500 coins, they are risking 500 coins to win 499 coins, resulting in a negative expected value of 0.5 coins.
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