Craps Odds question about points.

Hello there! I recently had a very nice roll at a craps table and made 9 points before sevening-out. 5 of those points were different. Most of the people at the table (myself included) made a good amount of money. I was trying to explain how rare this event was to some non-craps players, but I really wanted to do the math on this. So what are the odds of rolling 9 points before a seven out? What are the odds of 5 of those being different? Better yet, what are the odds of X points being made? and Y of those being different? For anyone who can help I really appreciate it! I tried searching the site, I found one table but I didn't really understand it.

Thanks!

Craps Side Bets

"Sharp Shooter" & "Firebet" - look at the "probability". I don't think it's THAT simple, because 5 different would include 5 & 6 for the firebet... and 9 would include 9 or more. Do you understand what I'm saying?

Regardless, it's a good starting point.

Your second question, x points being y different is one that would probably require someone here to crunch numbers.

Edit: I think there are better charts somewhere, but I couldn't find them.

Well, the "how many are different" problems require a little thinking, but the "what are the odds of making N points before a seven-out" is easier.

First, determine the probability of making a point instead of sevening out.
Actually, there are two ways of doing this; one that includes the possibility of one or more 2/3/11/12s on come-outs, and one that does not.
For the first one, 24 of the 36 possible rolls are points.
There is a 3/24, or 1/8, chance of your point being 4; there is a 1/3 chance of making the 4, so the probability of having 4 as a point and then making it is 1/8 x 1/3 = 1/24.
For a 5, there is a 1/6 chance of establishing it and a 2/5 chance of making it; 1/6 x 2/5 = 1/15.
Similarly, for a 6, 5/24 x 5/11 = 25/264.
8, 9, and 10 are 25/264, 1/15, and 1/24 respectively.
The probability of making any point is the sum of these, which is 67/165, or 0.406061.
Since each comeout/point is independent, the probability of making N in a row is (67/165)^N.
For 9 points in a row, this is about 1 in 3332.

For 9 in a row where you did not have any 2s/3s/11s/12s as come-out rolls, multiply the fraction by 2/3 (since the denominators for establishing the points are now 36 instead of 24); the probability is now (134/495)^N, and for N = 9, this is about 1 in 128,000.

Quote: ThatDonGuy

Well, the "how many are different" problems require a little thinking, but the "what are the odds of making N points before a seven-out" is easier.

First, determine the probability of making a point instead of sevening out.
Actually, there are two ways of doing this; one that includes the possibility of one or more 2/3/11/12s on come-outs, and one that does not.
For the first one, 24 of the 36 possible rolls are points.
There is a 3/24, or 1/8, chance of your point being 4; there is a 1/3 chance of making the 4, so the probability of having 4 as a point and then making it is 1/8 x 1/3 = 1/24.
For a 5, there is a 1/6 chance of establishing it and a 2/5 chance of making it; 1/6 x 2/5 = 1/15.
Similarly, for a 6, 5/24 x 5/11 = 25/264.
8, 9, and 10 are 25/264, 1/15, and 1/24 respectively.
The probability of making any point is the sum of these, which is 67/165, or 0.406061.
Since each comeout/point is independent, the probability of making N in a row is (67/165)^N.
For 9 points in a row, this is about 1 in 3332.

For 9 in a row where you did not have any 2s/3s/11s/12s as come-out rolls, multiply the fraction by 2/3 (since the denominators for establishing the points are now 36 instead of 24); the probability is now (134/495)^N, and for N = 9, this is about 1 in 128,000.

Thank you! This is tremendously helpful!!

Quote: ThatDonGuy

Well, the "how many are different" problems require a little thinking

and a little bit more math. Not at all impossible, just some more time.

When the Sharp Shooter bet came out a few years ago,
I remember starting the math and nothing more?
I have sim data, but not showing how large my sims were.
Care not to do this again.

So, take this info for what it is.
3 points hit
1#: 0.03855
2#: 0.4414
3#: 0.52005

4 points hit
1#: 0.0068
2#: 0.2019
3#: 0.5506
4#: 0.2407

5 points hit
1#: 0.0014
2#: 0.0772
3#: 0.4168
4#: 0.4228
5#: 0.0818

(6 to 8 missing)

9 points hit
1#: 0.000
2#: 0.000
3#: 0.063
4#: 0.350
5#: 0.473
6#: 0.113

(10 points missing)

Nice hand.
Lightning can and does strike twice.
Let us know when you are going to do this again.