Imagine you play a dice rolling game with a friend. If you roll a '6' in 8 rolls, you win the entire stake, otherwise you lose. Suppose you have rolled 3 times and haven't won yet. Your friend now suggests to skip the 4th roll, but he will compensate you fairly for it. You will still get to roll your 5th, 6th, 7th, and 8th roll. For the compensation of skipping the 4th roll, he will take out a fair amount from the stake and give it to you, keeping the rest of the stake at play. What would be considered a fair compensation? Discussion I talked to a genius and she gave me the following argument "I think of it as two options, to skip or not to skip. I will only skip if the option gives me an expectation that is higher than, or at least the same as, if I don't skip." Expectation if I don't skip: E1= 1/6 * S + 5/6 * (1 - (5/6)^4) * S where S is the stake Expectation if I skip: E2 = c + (1 - (5/6)^4) * (S - c) where c is the compensation We want E1 <= E2. We