Suppose that on the first roll, you do not win or lose, but rather, you get the sum X, which has roll probability p. Given that you have already made it to this point, what’s your chance of winning going forward?
Game of Craps played in a casino.
Stage 1- Roll 1- The player rolls a pair of standard 6-sided dice and takes their sum
- sum equals 7 or 1- then the player wins and the game is over
- sum equals 2, 3, or 12- then the player loses (this is called “crapping out”) and
the game is over
- sum equals anything else, then we record the sum (lets call it “X”) and move to stage 2
Stage 2 - Roll 2: The player then rerolls the dice and takes their sum
- Sum equals X- the player wins and the game is over
- Sum equals 7- the player loses and the game is over
- sum equals anything else- repeat step 2.
Now suppose that you notice something odd - one of the two dice isn’t balanced that well, and always comes up in the range 2-5 (with equal probability) but never 1 or 6.
Question
Suppose that on the first roll, you do not win or lose, but rather, you get the sum X, which
has roll probability p. Given that you have already made it to this point, what’s your
chance of winning going forward?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
