Question

100-side dice with number 1,2,...,100 on each side. You get paid $50 if you roll a 50, $75 if you roll a 75 etc. If you are unsatisfied with the result, you can pay $1 to roll again, you can roll as many times as you want. Question: what's the maximal amount you are willing to pay to enter this game (roll for the first time). Note that each subsequent play you only need to pay $1 to play again. What's your strategy

Answer 1

Since there is a 100-side it says with number 1,2, ..., 100 on each side, and I get paid $ 50 if you roll a 50, $ 75 if I roll a 75 etc, and if I are unsatisfied with the result, I can pay $ 1 to roll again, and I can roll as many times as I want, to determine what's the maximal amount I are willing to pay to enter this game for the first time knowing that each subsequent play you only need to pay $ 1 to play again the following logical reasoning must be performed:

Since there is a maximum possible win of $ 100 in the game, and a minimum possible win of $ 1, and that each shot is worth $ 1 after the first shot, with possibilities of repeating indefinitely (with which no more money would be lost, since that 99% of the time more money would be obtained than was paid), the maximum amount that would be willing to pay for the first shot is $ 100, while said sum is the maximum presumed profit for a single shot, the which will finally be overcome.