Another Craps Probability Question...

In the WizardofOdds site, someone asks the Wizard the following question:

Based on approximately 150 rolls per hour in dice, how many decisions with regard to the point will be made. I was told by someone that there is a decision every 3.6 rolls. Is this correct? - Jeff from Las Vegas, US

...and he gives the following answer:

The following are the possible outcomes of the pass/come bet and their associated probabilities:
Player wins on come out roll: 22.22%
Player loses on come out roll: 11.11%
Player wins on a point: 27.07%
Player loses on a point: 39.60%
So the player will win on a point about 1 in 3.7 rolls. Nov. 28, 2002

So assuming this is for Pass line play, is it correct to assume that betting on the Pass wins 49.29% of the time, and betting on the DP wins 50.71% of the time? Or are the percentages for the Don't side different, and independent of these?

TheArchitect

No. The following are the possible outcomes of the DON'T pass/come bet and their associated probabilities:
Player wins on come out roll: 8.333%
Player loses on come out roll: 22.22%
Player pushes on a come out roll: 2.78%
Player loses on a point: 27.07%
Player wins on a point: 39.60%

So the actual win % on don't pass is 47.93%. But the 12 is a push on the come out roll and happens 1/36 times. So add 1/2 of 1/36 to add 1.39% for a total of 49.32%. That gives your 1.364% HA as advertised.

Quote: boymimbo

No. The following are the possible outcomes of the DON'T pass/come bet and their associated probabilities:
Player wins on come out roll: 8.333%
Player loses on come out roll: 22.22%
Player pushes on a come out roll: 2.78%
Player loses on a point: 27.07%
Player wins on a point: 39.60%

So the actual win % on don't pass is 47.93%. But the 12 is a push on the come out roll and happens 1/36 times. So add 1/2 of 1/36 to add 1.39% for a total of 49.32%. That gives your 1.364% HA as advertised.

Thank you boyminbo, very clear and concise.