Game Guy's Roulette

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

Gameplay
The player attempts to pick which space on the roulette wheel the Red Shell will spin into, from wide to narrow and from less to more. After that, Game Guy spins the shell around the roulette. If the shell spins into another spot instead of the spot the player picked, the player loses all the coins.

Spaces on the roulette

 * Koopa Troopa (green) – Six slots on the roulette wheel, coins ×2
 * Bob-omb (dark blue) – Five slots on the roulette wheel, coins ×4
 * Goomba (brown) – Four slots on the roulette wheel, coins ×8
 * Boo (light blue) – Three slots on the roulette wheel, coins ×16
 * Toad (pink) – Two slots on the roulette wheel, coins ×32
 * Game Guy (red) – Just one slot on the roulette wheel, coins ×64

Expected value
Let B be the number of coins bet and observe that there are 21 spaces on the roulette wheel. Then, for each space, the EV is:


 * Koopa Troopa (green) – 2B * 6/21 = 12B/21 ~ 0.5714B
 * Bob-omb (dark blue) – 4B * 5/21 = 20B/21 ~ 0.9524B
 * Goomba (brown) – 8B * 4/21 = 32B/21 ~ 1.5238B
 * Boo (light blue) – 16B * 3/21 = 48B/21 ~ 2.2857B
 * Toad (pink) – 32B * 2/21 = 64B/21 ~ 3.0476B
 * Game Guy (red) – 64B * 1/21 = 64B/21 ~ 3.0476B

By betting Toad or Game Guy constantly, the player can actually, in the long run, triple their coins. On the other hand, the most likely option to hit is the most profitable for Game Guy, with an EV of only around half the number bet.

In-game text

 * Game Guy – "Place your bet, then make your guess. If the shell stops in the area you chose, your coins will increase according to the odds. If the shell lands in another area, your coins will be mine."