Average Number of Points Hit Per Shooter in Craps

For those that have asked for this table. here you go.

Pass Line Decisions per shooter.
The expected number of Pass Line decisions per seven out is 495/196 or 2.5255
The average from the sample below is: 2.5221

1 decision per shooter should be obvious. Just a 7out.

decisions	relative	cumulative
per shooter	frequency	frequency
1	0.396221374	(or less)
2	0.238030534	0.634251908
3	0.145664122	0.779916031
4	0.087515267	0.867431298
5	0.051889313	0.919320611
6	0.032167939	0.95148855
7	0.019068702	0.970557252
8	0.011767176	0.982324427
9	0.006977099	0.989301527
10	0.004167939	0.993469466
11	0.002580153	0.996049618
12	0.001564885	0.997614504
13	0.000889313	0.998503817
14	0.000629771	0.999133588
15	0.000335878	0.999469466
16	0.000229008	0.999698473
17	0.000122137	0.999820611

Quote: JimmyMac

If this is the case, then why do casino's offer Fire Bets?

If you are just as likely to have 10 passes in a row as you are to have 1 pass, why would the house offer 999-1 odds against it happening?

You seriously, seriously need to read my blog on this subject:

http://wizardofvegas.com/member/goatcabin/blog/#post16

If you confuse the probability of a series of events at its beginning with the shifting probabilities as you go through the series, you fall into an abyss of illogic.
Cheers,
Alan Shank
Woodland, CA

Alan,

Your blog was excellent and now I fully understand what you have been trying to explain to me. Thanks again for all the help. I've realized the only way to guarantee a win at craps is simply not to play. But, if you are going to play and want to minimize your losses, stick to the bets with the lowest HA and try your best to quit a winner when you have the opportunity.

Quote: JimmyMac

Alan,

Your blog was excellent and now I fully understand what you have been trying to explain to me. Thanks again for all the help. I've realized the only way to guarantee a win at craps is simply not to play. But, if you are going to play and want to minimize your losses, stick to the bets with the lowest HA and try your best to quit a winner when you have the opportunity.

Well, not playing does not guarantee a win, just that you won't lose. There is NO way to guarantee a win, but you can give yourself a reasonable chance to win by minimizing your expected loss and accepting some variance, always keeping in mind that variance works both ways. If you are lucky, variance is your friend, giving you a better chance to overcome the expected loss that is always, always there; if you are not lucky, then the more variance, the more you lose. You have to decide what your tolerance is and adjust your strategy accordingly. The way to get variance without increasing your expected loss is to take or lay odds behind your line bet.
Cheers and good luck,
Alan Shank
Woodland, CA

Quote: Wizard

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.

201/495 = 0.460606 should be corrected to 201/495 = 0.406060606