WongBo
Joined: Feb 3, 2012
• Posts: 2126
February 25th, 2012 at 10:21:58 AM permalink
From the wizard's page on craps probabilities: http://wizardofodds.com/ask-the-wizard/craps/probability/

On average, during the course of 100 points being established in craps:
(1) How many of those would be 4/10, 5/9 or 6/8,
(2) During the 100 how many times would each point (4/10, 5/9, 6/8) vs. a 7 be made?
— Jon from Danville, New Hampshire

Of those 100 points established,
on average 45.45 would be on a 6 or 8, 40 would be on a 5 or 9, and 33.33 would be on a 4 or 10.
You could expected on average 18.94 points made on a 6 or 8, 13.33 on a 5 or 9, and 8.33 on a 4 or 10.

Of the 100 established points wouldn't the points established be
41.66 on 6 or 8, 33.33 on a 5 or 9, and 25 on a 4 or a 10?
41.66 + 33.33 + 25 = 100

I think the 45.45, 40, and 33.33 are the pass percentages....
In a bet, there is a fool and a thief. - Proverb.
boymimbo
Joined: Nov 12, 2009
• Posts: 5988
February 25th, 2012 at 4:15:36 PM permalink
On average,
4/10 passes 3/9ths of the time or 33.33% of the time
5/9 passes 4/10th of the time. or 40% of the time
6/8 passes 5/11ths of the time or 45.45% of the time

On average,
4 or 10 come up 1/8 of the time (3/24) or 12.5 times in 100 rolls
5 or 9 come up 1/6 of the time (4/24) or 16.667 times in 100 rolls
6 or 8 come up 5/24 of the time or 20.833 times in 100 rollss

Total odds of making pass:

(1/3 x 6/24 + 4/10 x 8/24 + 5/11 x 10/24) = .406161 or 201/495ths!

Therefore, in 100 come out rolls where the point is made, you will, on average, experience.

12.5 fours of which 4.167 will pass
12.5 tens of which 4.167 will pass
16.667 fives in which 6.667 will pass
16.667 nines in which 6.667 will pass
20.833 sixes in which 9.467 will pass
20.833 eights in which 9.467 will pass

Of course (to make jjj and bob happy), all is this is averages, subject to variances, progressive betting, martingale, and dice bias, among other things.
----- You want the truth! You can't handle the truth!