Background: The snake eyes paradox market.

Algorithm description:

We start with 3 people willing to play the gruesome snake eyes game. First 1 person will be chosen at random for the initial 1-person group. If that person survives (rolls non-snake-eyes) then we choose the remaining 2 people for the second group and roll for them. You only die by rolling snake eyes.

We repeat the above a [million] times. Each time, we record who was chosen and who died. We then count how many of the [million] times person 1 (WLOG) was chosen to play. (Again, that happens either when person 1 is chosen first, with probability 1/3, or when whoever was chosen first survives.) Call that count C. Finally, we count the number of times, D, that person 1 died.

Output D/C.

Is the probability of dying in the Snake Eyes Paradox 1/36?

93% chance. You’re offered a gamble where a pair of six-sided dice are rolled and unless they come up snake eyes you get a bajillion dollars. If they do come up snake eyes, you’re devoured by snakes. So far it sounds like you have a 1/36 chance of dying, right? Now the twist. First, I gather up an…