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JimmyMac
JimmyMac
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October 20th, 2010 at 9:45:10 AM permalink
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?
Wizard
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Wizard
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October 20th, 2010 at 9:51:35 AM permalink
8.53
It's not whether you win or lose; it's whether or not you had a good bet.
MathExtremist
MathExtremist
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October 20th, 2010 at 10:20:44 AM permalink
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.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
DJTeddyBear
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October 20th, 2010 at 10:26:50 AM permalink
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.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
guido111
guido111
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October 20th, 2010 at 10:26:51 AM permalink
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.
Wizard
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Wizard
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October 20th, 2010 at 10:36:58 AM permalink
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.
It's not whether you win or lose; it's whether or not you had a good bet.
7winner
7winner
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October 20th, 2010 at 10:58:18 AM permalink
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






countpoints wins%or moreor less
59411000.5941100000  
24126710.24126700000.40589000000.8353770000
9798320.09798300000.16462300000.9333600000
3954730.03954700000.06664000000.9729070000
1613640.01613600000.02709300000.9890430000
653550.00653500000.01095700000.9955780000
259660.00259600000.00442200000.9981740000
106770.00106700000.00182600000.9992410000
42580.00042500000.00075900000.9996660000
18890.00018800000.00033400000.9998540000
91100.00009100000.00014600000.9999450000
5511+0.00005500000.00005500001.0000000000





The math would be a challenge
7 winner chicken dinner!
guido111
guido111
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October 20th, 2010 at 11:08:29 AM permalink
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
guido111
guido111
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October 20th, 2010 at 11:39:49 AM permalink
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.
guido111
guido111
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October 20th, 2010 at 12:09:28 PM permalink
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)

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