Game Guy's Magic Boxes
When the minigame starts, the two treasure chests are hidden by the curtains and may be switched after the curtains close. After the curtains reopen, the player must pick the chest containing Toad instead of Baby Bowser. If the player is successful, their coins are doubled. If the player picks the chest containing Baby Bowser, they lose all of their coins. If having chosen the correct chest, the player is then given the option to either 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 multiply the player's coins by eight, but the player may also opt to quit at any time after the first win and take their winnings.
Let B be the number of coins 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 does not 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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