Inside odds probability

I wanted to figure on the probabilities of number of hits before the seven on inside numbers at craps: the 5, 6, 8, and 9. In 36 rolls we have 6 7's and 18 inside numbers. So I assume a failure rate of 6/18+6 = .25 or 25%, that is a 7 before an inside number. How does one calculate the failure rate for 2 numbers to hit before the 7?

Quote: DeMango

How does one calculate the failure rate for 2 numbers to hit before the 7?

I don't know, but I think the calculation reaches a different result if you are a newbie at the Borgata in Atlantic City than if you are at a table on which I've been playing.

I think what you mean to say is that this six 7's and eighteen Insiders out of 36 rolls is a theoretical achievement based on some assumption that what is possible to occur will in fact occur in some mathematically precise fashion.

Quote: DeMango

I wanted to figure on the probabilities of number of hits before the seven on inside numbers at craps: the 5, 6, 8, and 9. In 36 rolls we have 6 7's and 18 inside numbers. So I assume a failure rate of 6/18+6 = .25 or 25%, that is a 7 before an inside number. How does one calculate the failure rate for 2 numbers to hit before the 7?

The chance that 2 numbers will hit before a 7 is 3/4 x 3/4, or 9/16. The chance that you won't, is 1 - 9/16, or 7/16. So you will not hit 2 of those 4 numbers (5,6,8,9) 43.75% of the time.

Thanks SOOPOO. Of course carrying that out one step farther, I thought the chances were even for 3 hits before the seven. But if we go 3/4 x 3/4 x 3/4 we certainly don't end up with .50 I'm missing something here, I always assumed that 18 chances for the inside numbers would equal 3(6 chances) for the 7.

Here are 2 handy place bet tables.
First is cumulative, meaning the chances of winning 1 or more
Second is exact, meaning the chances of winning exactly 1 place bet before losing them all. Or the chances of winning 0, none, before losing them all.
The most single common outcome of making any type of place bet is to lose them all.

Wins(or more)	4 bets	4 bets	6 bets	5 bets	5 bets	5 bets	2 bets
B4~7	inside	outside	across	across PT 4,10	across PT 5,9	across PT 6,8	6 & 8
0	25.00%	30.00%	20.00%	22.22%	23.08%	24.00%	37.50%
1+	75.00%	70.00%	80.00%	77.78%	76.92%	76.00%	62.50%
2+	56.25%	49.00%	64.00%	60.49%	59.17%	57.76%	39.06%
3+	42.19%	34.30%	51.20%	47.05%	45.52%	43.90%	24.41%
4+	31.64%	24.01%	40.96%	36.60%	35.01%	33.36%	15.26%
5+	23.73%	16.81%	32.77%	28.46%	26.93%	25.36%	9.54%
6+	17.80%	11.76%	26.21%	22.14%	20.72%	19.27%	5.96%
7+	13.35%	8.24%	20.97%	17.22%	15.94%	14.65%	3.73%
8+	10.01%	5.76%	16.78%	13.39%	12.26%	11.13%	2.33%
9+	7.51%	4.04%	13.42%	10.42%	9.43%	8.46%	1.46%
10+	5.63%	2.82%	10.74%	8.10%	7.25%	6.43%	0.91%
11+	4.22%	1.98%	8.59%	6.30%	5.58%	4.89%	0.57%
12+	3.17%	1.38%	6.87%	4.90%	4.29%	3.71%	0.36%
13+	2.38%	0.97%	5.50%	3.81%	3.30%	2.82%	0.22%
14+	1.78%	0.68%	4.40%	2.96%	2.54%	2.14%	0.14%
15+	1.34%	0.47%	3.52%	2.31%	1.95%	1.63%	0.09%
16+	1.00%	0.33%	2.81%	1.79%	1.50%	1.24%	0.05%
17+	0.75%	0.23%	2.25%	1.39%	1.16%	0.94%	0.03%
18+	0.56%	0.16%	1.80%	1.08%	0.89%	0.72%	0.02%
19+	0.42%	0.11%	1.44%	0.84%	0.68%	0.54%	0.01%
20+	0.32%	0.08%	1.15%	0.66%	0.53%	0.41%	0.01%
Exact Wins	4 bets	4 bets	6 bets	5 bets	5 bets	5 bets	2 bets
B4~7	inside	outside	across	across PT 4,10	across PT 5,9	across PT 6,8	6 & 8
0	25.00%	30.00%	20.00%	22.22%	23.08%	24.00%	37.50%
1	18.75%	21.00%	16.00%	17.29%	17.75%	18.24%	23.44%
2	14.06%	14.70%	12.80%	13.44%	13.65%	13.86%	14.65%
3	10.55%	10.29%	10.24%	10.45%	10.51%	10.54%	9.15%
4	7.91%	7.20%	8.19%	8.14%	8.08%	8.00%	5.72%
5	5.93%	5.05%	6.56%	6.32%	6.21%	6.09%	3.58%
6	4.45%	3.52%	5.24%	4.92%	4.78%	4.62%	2.23%
7	3.34%	2.48%	4.19%	3.83%	3.68%	3.52%	1.40%
8	2.50%	1.72%	3.36%	2.97%	2.83%	2.67%	0.87%
9	1.88%	1.22%	2.68%	2.32%	2.18%	2.03%	0.55%
10	1.41%	0.84%	2.15%	1.80%	1.67%	1.54%	0.34%
11	1.05%	0.60%	1.72%	1.40%	1.29%	1.18%	0.21%
12	0.79%	0.41%	1.37%	1.09%	0.99%	0.89%	0.14%
13	0.60%	0.29%	1.10%	0.85%	0.76%	0.68%	0.08%
14	0.44%	0.21%	0.88%	0.65%	0.59%	0.51%	0.05%
15	0.34%	0.14%	0.71%	0.52%	0.45%	0.39%	0.04%
16	0.25%	0.10%	0.56%	0.40%	0.34%	0.30%	0.02%
17	0.19%	0.07%	0.45%	0.31%	0.27%	0.22%	0.01%
18	0.14%	0.05%	0.36%	0.24%	0.21%	0.18%	0.01%
19	0.10%	0.03%	0.29%	0.18%	0.15%	0.13%	0.00%
20	0.32%	0.08%	1.15%	0.66%	0.53%	0.41%	0.01%

Quote: SOOPOO

...So you will not hit 2 of those 4 numbers (5,6,8,9) 43.75% of the time.

That's phrased incorrectly, and the wrong number stated. It's actually: ...So you will not hit 2 of those 4 numbers (5,6,8,9), or any one of them twice, 42.1875% of the time.

Quote: DeMango

...But if we go 3/4 x 3/4 x 3/4 we certainly don't end up with .50 I'm missing something here, I always assumed that 18 chances for the inside numbers would equal 3(6 chances) for the 7.

Nope. That kind of thinking is the same as saying a seven shows up every sixth roll. It's merely 1/6 chance EVERY roll.

There are 18 out of 36 total combinations for an inside number on any single roll. Similarly, there are 6 ways out of 36 for a 7.

So, on any single roll, you've got 18 ways to win out of the 24 combinations that resolve that bet. That's 75%.

But in three rolls, you do NOT get 18 combinations of rolling a 7.

In three rolls that either win or lose, you've got 18/24 x 18/24 x 18/24 = .75 x .75 x .75 = .421875 chance of winning all three, and therefore a 1 - .421875 = .578125 chance of getting a seven.