Average Number of Points Hit Per Shooter in Craps

Does anyone know the average number of points hit by a shooter before they 7 out?

We all know the shooter can't keep hitting points forever. Sooner or later he eventually 7's out.

But, what do you guys think the average number of points a shooter is able to hit before rolling the seven and passing the dice?

8.53

Quote: Wizard

8.53

I believe that's rolls per shooter. Since rolls per passline decision is 3.376, that makes the average decisions per shooter about 2.5. Of those decisions, 27.1% are point winners, so the average number of points made by the shooter is about 0.68.

In other words, if you make even one point, you're having a better-than-average roll. Not very intuitive, is it?

Yes, you really do only have a bit better than 1 in 4 chance of establishing and making a point. A big chunk of winning passline bets happens from natural 7/11 rolls: 22.2% to be precise. When you add them in you get 49.3%, the overall chance of winning a line bet.

I was gonna say the same thing.

The Wiz linked to a page where he shows the math to come up with the 8.53 number.

Scroll down about 1/3 the page - just below the average rolls per hour charts.

It's 8.53 THROWS per shooter.

Quote: JimmyMac

Does anyone know the average number of points hit by a shooter before they 7 out?

A better question would be the math for:
The probability of a shooter making 0 points,
1 point,2 points, 3 points etc.

You're right, I answered the wrong question.

Let x be the answer. The probability of eventually making the next point is (6/24)*(1/3)+(8/24)*(2/3)+(10/24)*(5/11) = 201/495 = 0.460606.

The expected number of points made is 0.460606/(1-0.460606) = 201/294 = 0.683673469.

Quote: guido111

A better question would be the math for:
The probability of a shooter making 0 points,
1 point,2 points, 3 points etc.

I had run a sim of 8,522,945 million dice rolls. Here are those results:

1,000,000/shooters
682796/total points wins

count	points wins	%	or more	or less
594110	0	0.5941100000
241267	1	0.2412670000	0.4058900000	0.8353770000
97983	2	0.0979830000	0.1646230000	0.9333600000
39547	3	0.0395470000	0.0666400000	0.9729070000
16136	4	0.0161360000	0.0270930000	0.9890430000
6535	5	0.0065350000	0.0109570000	0.9955780000
2596	6	0.0025960000	0.0044220000	0.9981740000
1067	7	0.0010670000	0.0018260000	0.9992410000
425	8	0.0004250000	0.0007590000	0.9996660000
188	9	0.0001880000	0.0003340000	0.9998540000
91	10	0.0000910000	0.0001460000	0.9999450000
55	11+	0.0000550000	0.0000550000	1.0000000000

The math would be a challenge

Quote: guido111

A better question would be the math for:
The probability of a shooter making 0 points,
1 point,2 points, 3 points etc.

from the WoO site:

59.39% chance of not hitting a point
40.61% chance of hitting a point (or more)

edit:http://wizardofodds.com/askthewizard/craps-probability.html

Quote: MathExtremist

so the average number of points made by the shooter is about 0.68.

In other words, if you make even one point, you're having a better-than-average roll. Not very intuitive, is it?

Just goes to show that an "average" can be a useless number.
Knowing the standard deviation would give a better understanding to the "average", and that still may show a number that is still useless.

Quote: Wizard

Can you give me the URL where I say that?

you do not exactly say that.
http://wizardofodds.com/askthewizard/craps-probability.html

" So the probability of making a point, given that a point was established is, (5/12)*(5/11)+(4/12)*(4/10)+(3/12)*(3/9) = 40.61%"

So,
59.39% chance of not hitting a point
40.61% chance of hitting a point (or more)