# Sunday Times Teaser 3175 – Blindfold Roulette

**by John Owen**

**by John Owen**

#### Published Sunday July 30 2023 (link)

Our roulette wheel has fewer than 100 equal-sized sectors. Before each game a fixed number (fewer than half) of the sectors are randomly designated winning ones and the others as losing. A player can see which are the winning sectors, then is blindfolded. A ball is then placed at random in a winning sector and the player chooses to spin (S) the wheel or move (M) the ball clockwise by one sector. The game continues from there (the player has the same choices) and ends when the ball lands in a losing sector.

Alfâ€™s longest winning run was MMSM while Bertâ€™s was SSS and Charlieâ€™s was MMMS. Being expert logicians, they had always chosen the option that gave the better chance of the ball landing in a winning sector. Remarkably, the probabilities of achieving each run of success were the same.

How many sectors are there and how many are winning sectors?