Say I have a hypothetical computer gambling game that is very basic and just involves the player trying to score points before dying - with a score of 5 points being the maximum (beating the game). The player makes a wager before playing the game and will receive a payout based on how many points they score in the game. The payout is based on the probability of how likely the player is to score the amount of points that they do, with higher point totals getting progressively less likely (higher payouts) until 5 when the player receives the maximum payout. My question is how would I calculate the payout odds for the player reaching each point total given the probabilities? Here are the probabilities that the player scores > or = to the listed number of points:
0: 100% (No Payout)
1: 90%
2: 75%
3: 55%
4: 30%
5: 10%
I’m thinking that some of the lower scores would provide a total payout that is less than the player wagered but still greater than \$0. A score of 0 would be a \$0 total payout since every player makes it this far. Then I would also like to factor in something like a 5% theoretical advantage for the house. An explanation with the math behind it shown would be great. Thank you!