IPT2019-Problem 2- Yut (DTU, Denmark)

IPT 2019 Problem 2 Yut Technical University of Denmark: When making a choice or playing a game, we employ methods such as tossing a coin, rolling dice, or, throwing a Yut stick. Yut sticks are roughly half-cylindrical in shape and as such it is much easier to bias the outcome of up vs. down than it is for a coin or dice. If the floor is soft, then the stick is likely to have its flat side up, as the round side has a larger surface. If the floor is hard and the stick is ‘rolled’, the stick is likely to have its round side up. How does the probability of the outcomes depend on the relevant parameters?