Game Guy's Lucky 7

Game Guy's Lucky 7 is a Game Guy minigame found in Mario Party 3, and it's Game Guy's personal favorite of the four.

Description
"Hit the Dice Block, then climb up that many steps. You can hit the die once or twice.  If you climb higher than me or stop on the same step as me, I'll double your coins!  But if you stop below me, or if you fall off the stairway, I'll get to keep all of your coins."

"However! If you land exactly on the seventh step, your coins will increase tenfold!"

"Well, shall we start?"

Gameplay
Game Guy rolls a die numbered one through six and climbs the number of steps he rolled, and then the player does the same. Game Guy will then decide if he wants to roll a second die to climb additional steps, and then give the player that option. If the player finishes the game on the second through sixth step and Game Guy is on the same step, a lower step, or falls off the staircase, the player's coins are doubled; if the player ends up on the seventh step, their coins are multiplied by ten regardless of where Game Guy lands. But if the player steps past the seventh or ends up lower than Game Guy, the player loses all the coins. Game Guy will only roll the dice a second time if he gets a four on his first roll.

Analysis
This game's analysis of the expected value needs further expansion, but the chance of rolling a sum of 7 on 2 d6 dice is 1 in 6. Since the initial bet is multiplied tenfold when landing right on the 7, it is usually best to go for broke to maximize the expected value of the bet, which is greater than unity. The fact that the first 2 rolls may sum to less than 7 gives the player an even greater chance to win 10x his bet (since he may roll again), and the ability of the player to beat Game Guy by being higher on the staircase increases it still. Overall, this game provides a greater-than-unity expected value of coins for his bet.