Pluto Craps Edge

As any other popular casino game has its variations, so it does craps – Pluto craps. Here is how it is played (nothing too weird from its parent). Pluto craps it is played with 1 or 2 dice and uses also a shaking cup, which is used to prevent dice setting. In a two players game one of the players calls the point and the other is the shooter. If the point is hit the winner is the roller. If the point is not hit, the shot goes to the next person and the cup goes back and forth until a player wins. After a win is established the players switch roles for the next coup.

So, the game play is simple but now let’s discuss about more important things of the Pluto craps game. The Pluto craps edge. For this I have created a scenario in which the two players are Frank and Ed. The same as in all casino games in Pluto craps the laws of probability also bring us the answer. So, consider P the probability of winning on any roll and Q the probability for loses and Q=1-P having P = 1/6 if you roll one die and Q = 5/6.

Frank is the first roller and Ed calls and Ed's overall chance of getting a first roll and hitting is Q x P. Widen this interpretation. The craps odds Ed won't win on his starting toss is Q. If he doesn't, there have been 2 no-win rolls in a row (the chance of which is Q x Q), and Frank keeps the cup for a new throw. Frank then has a chance of winning equal to P. In the same way, Ed will get a second try after 3 straight no-wins Q x Q x Q, then has probability P of winning. Continue and combine terms for an infinite series since neither may ever make the point.

This offers Frank's last chance as P + Q x Q x P + Q x Q x Q x Q x P + ... each term being multiplied by Q twice more than the last. Analogously, Ed's last possibility is Q x P + Q x Q x Q x P + Q x Q x Q x Q x Q x P + ... The math mavens have a shortcut to do the arithmetic for these two series if you remember how to do fractions and long division. Frank's odd is 1/(1+Q) and Ed's is Q/(1+Q).

In a Pluto craps game played with only one dice we have P = 1/6 and Q = 5/6.
Frank's odds are (1)/(1+5/6) = 6/11 = 54.5%
Ed's odds are (5/6)/¬(1+5/6) = 5/11 = 45.5 %

In conclusion, the Pluto craps edge is of 54.5-to-45.5. Divided out, that's 1.2-to-1.

In a Pluto craps game played with two dice we have the odds for hitting a 2 or 12 = 1/36 and for hitting a 7 = 6/36 = 1/6. Frank still has an edge but it is 50.7-to-49.3 (1.03-to-1) on a point of 2 or 12, and 54.5-to-45.5 (1.2-to-1) on a point of 7.