I am working on a problem to use probabilities for a game with 2 dice. I have researched many methods (Bayesian, etc.) but I am not sure what the right path would be to answer these questions. Here is the use case:
Rules of the Game
The player rolls a pair of fair 6-sided dice. Then, takes the sum of both dice.
- If the sum is 7 or 11 -> Player Wins!
- If sum is 2, 3, or 12 -> Player Lost!
- If the sum is anything else -> Record Sum as “X” and continue to step 2.
The player rolls again.
- If the sum=X ->Player Wins!
- If the sum is 7->Player Lost!
- If the sum is anything else, repeat step 2.
Something strange occurs: One of the dice is not FAIR! It always comes up in the range of 2-5 with equal probability but never 1 or 6!
- Let's assume we are on our first roll and we do not win or lose. Instead, we get the sum X, which has roll probability of p. Given that you have already made it to this point, what is the chance of winning going forward?