My kids wanted me to play along with them in this racing game. There is no skill at all involved in playing the game. The player throws the dice until reaching the goal. If the player falls on certain squares, has to advance or go back a certain number.
The kids offered me to play with a special dice, though. I could choose to play with a dice that had the following values: 2, 4, 8, 16, 32 and 64. I immediately accepted, only to be told that I had to land on the exact goal square to win. If I overshoot, I had to go another round.
After playing (and losing) I have been wondering what may chances really where, and whether I should accept their offer again. To find out I programmed a simulation of the game between two players in python, one using an ordinary dice, and another using an exponential one.
My kids started by placing the game tokens on the first square. With this configuration the ordinary dice has a slight advantage. Results showed 52% wins for ordinary against 48% for exponential. But if one starts behind the first square, the odds are 42% against 58% for the exponential. The reason for the difference is that there are 52 squares in the board. If the player starts on square 1, using the exponential dice, the player has to land first on a square where an odd number of squares is added to be able to land on the goal. If one starts behind square one, there is no such constraint.
Next time they want to play, I will accept, but I will ask to start behind the first square, not on it.
Last updated: 2022-01-09