The Seven (7) bet in Craps winning frequencies

Craps: The Seven 7 bet

Seven is the most common total from the roll of 2 dice.

$5 pass line wager made on the come out roll.
The bet will win with a natural 7 or 11 on the first roll
The Pass Line will lose with a natural 2, 3 or 12 rolled on the come out roll

8 bets that win on a come out roll 7
6 Lay bets, Pass Line bet and the any 7 bet
The World or Whirl bet (not shown) also wins with a roll of a seven. It is a push when the 7 rolls.

8 bets win on a 7 rolled on the come-out roll

13 bets that win on a 7 out. When a 7 rolls while a point is established on a number
6 Lay bets, 5 Don't Come bets, Don't Pass Line bet and the any 7 bet
The World or Whirl bet (not shown) also wins with a roll of a seven. It is a push when the 7 rolls.

13 wagers win while a 7 is rolled while a point is established. Called a 7-out.

screen shots from WinCraps software. get your free copy here

Win/Loss (Frequency) Table for the 7.
Probability 1/6
Table applies to any bet with a probability of 1/6
(horn, C&E, 4&10, pairs or doubles bet)

As seen in the highlighted cells below:
51.77% (that's slightly more than half) of all 7s that roll
never get past four (4) rolls
66.51% (that's almost 2 out of 3) of all 7s
never get past six (6) rolls
90.65% (that's slightly more than 9 out of 10) of all 7s
never get past thirteen (13) rolls
7	1 in	16.67%	No Past	1 in / out of	1/6	Yes Past	1 in
roll	Indv	Indv %	Win%	Win% Odds	roll	Loss%	Loss% Odds
1	6.00	16.6667%	16.6667%	6.00	1	83.33%	5 out of 6
2	7.20	13.8889%	30.5556%	3.27	2	69.44%	2 out of 3
3	8.64	11.5741%	42.1296%	2.37	3	57.87%	4 out of 7
4	10.37	9.6451%	51.7747%	1.07 out of 2.07	4	48.23%	2.07
5	12.44	8.0376%	59.8122%	1.49 out of 2.49	5	40.19%	2.49
6	14.93	6.6980%	66.5102%	1.99 out of 2.99	6	33.49%	2.99
7	17.92	5.5816%	72.0918%	2.58 out of 3.58	7	27.91%	3.58
8	21.50	4.6514%	76.7432%	3.3 out of 4.3	8	23.26%	4.30
9	25.80	3.8761%	80.6193%	4.16 out of 5.16	9	19.38%	5.16
10	30.96	3.2301%	83.8494%	5.19 out of 6.19	10	16.15%	6.19
11	37.15	2.6918%	86.5412%	6.43 out of 7.43	11	13.46%	7.43
12	44.58	2.2431%	88.7843%	7.92 out of 8.92	12	11.22%	8.92
13	53.50	1.8693%	90.6536%	9.7 out of 10.7	13	9.35%	10.70
14	64.20	1.5577%	92.2113%	11.84 out of 12.84	14	7.79%	12.84
15	77.04	1.2981%	93.5095%	14.41 out of 15.41	15	6.49%	15.41
16	92.44	1.0818%	94.5912%	17.49 out of 18.49	16	5.41%	18.49
17	110.93	0.9015%	95.4927%	21.19 out of 22.19	17	4.51%	22.19
18	133.12	0.7512%	96.2439%	25.62 out of 26.62	18	3.76%	26.62
19	159.74	0.6260%	96.8699%	30.95 out of 31.95	19	3.13%	31.95
20	191.69	0.5217%	97.3916%	37.34 out of 38.34	20	2.61%	38.34
21	230.03	0.4347%	97.8263%	45.01 out of 46.01	21	2.17%	46.01
22	276.03	0.3623%	98.1886%	54.21 out of 55.21	22	1.81%	55.21
23	331.24	0.3019%	98.4905%	65.25 out of 66.25	23	1.51%	66.25
24	397.48	0.2516%	98.7421%	78.5 out of 79.5	24	1.26%	79.50
25	476.98	0.2097%	98.9517%	94.4 out of 95.4	25	1.05%	95.40
7	1 in	16.67%	No Past	1 in / out of	1/6	Yes Past	1 in
roll	Indv	Indv %	Win%	Win% Odds	roll	Loss%	Loss% Odds
26	572.38	0.1747%	99.1265%	113.48 out of 114.48	26	0.87%	114.48
27	686.85	0.1456%	99.2720%	136.37 out of 137.37	27	0.73%	137.37
28	824.22	0.1213%	99.3934%	163.84 out of 164.84	28	0.61%	164.84
29	989.07	0.1011%	99.4945%	196.81 out of 197.81	29	0.51%	197.81
30	1186.88	0.0843%	99.5787%	236.38 out of 237.38	30	0.42%	237.38
31	1424.26	0.0702%	99.6489%	283.85 out of 284.85	31	0.35%	284.85
32	1709.11	0.0585%	99.7074%	340.82 out of 341.82	32	0.29%	341.82
33	2050.93	0.0488%	99.7562%	409.19 out of 410.19	33	0.24%	410.19
34	2461.12	0.0406%	99.7968%	491.22 out of 492.22	34	0.20%	492.22
35	2953.34	0.0339%	99.8307%	589.67 out of 590.67	35	0.17%	590.67
36	3544.01	0.0282%	99.8589%	707.8 out of 708.8	36	0.14%	708.80
37	4252.81	0.0235%	99.8824%	849.56 out of 850.56	37	0.12%	850.56
38	5103.37	0.0196%	99.9020%	1019.67 out of 1020.67	38	0.10%	1020.67
39	6124.05	0.0163%	99.9184%	1223.81 out of 1224.81	39	0.08%	1224.81
40	7348.86	0.0136%	99.9320%	1468.77 out of 1469.77	40	0.07%	1469.77
41	8818.63	0.0113%	99.9433%	1762.73 out of 1763.73	41	0.06%	1763.73
42	10582.36	0.0094%	99.9528%	2115.47 out of 2116.47	42	0.05%	2116.47
43	12698.83	0.0079%	99.9606%	2538.77 out of 2539.77	43	0.04%	2539.77
44	15238.59	0.0066%	99.9672%	3046.72 out of 3047.72	44	0.03%	3047.72
45	18286.31	0.0055%	99.9727%	3656.26 out of 3657.26	45	0.03%	3657.26
46	21943.57	0.0046%	99.9772%	4387.71 out of 4388.71	46	0.02%	4388.71
47	26332.29	0.0038%	99.9810%	5265.46 out of 5266.46	47	0.02%	5266.46
48	31598.74	0.0032%	99.9842%	6318.75 out of 6319.75	48	0.02%	6319.75
49	37918.49	0.0026%	99.9868%	7582.7 out of 7583.7	49	0.01%	7583.70
50	45502.19	0.0022%	99.9890%	9099.44 out of 9100.44	50	0.01%	9100.44
51	54602.63	0.0018%	99.9908%	10919.53 out of 10920.53	51	0.01%	10920.53
52	65523.15	0.0015%	99.9924%	13103.63 out of 13104.63	52	0.01%	13104.63
53	78627.79	0.0013%	99.9936%	15724.56 out of 15725.56	53	0.01%	15725.56
54	94353.34	0.0011%	99.9947%	18869.67 out of 18870.67	54	0.01%	18870.67
55	113224.01	0.0009%	99.9956%	22643.8 out of 22644.8	55	0.00%	22644.80
56	135868.81	0.0007%	99.9963%	27172.76 out of 27173.76	56	0.00%	27173.76

Individual (Relative) Frequency Chart for the Seven or 1/6 probability.
The Expected Curve slopes down and off to the right

Individual (Relative) Frequency Chart for the Seven.
Actual distribution from 323 rolls Nugget 2007.

Actual and expected distribution from 323 rolls Nugget 2007

Superimposed Frequency Chart for the Seven.
Actual and expected outcomes. In the short run the curve has disappeared.

Cumulative Frequency Chart for the Seven or 1/6 probability.
4 is slightly above 50% and the line curves up to the right.

Cumulative Frequency Chart for the Seven from 323 rolls Nugget 2007

Cumulative Frequency Chart for the Seven or 1/6 probability.
Actual distribution from 323 rolls Nugget 2007.

Actual and expected Cumulative Frequency Chart for the Seven from 323 rolls Nugget 2007

Superimposed Cumulative Frequency Chart for the Seven from 323 rolls Nugget 2007
Actual and expected outcomes. In the short run the curves are very similar.

It is true that the Seven's probability to appear in one roll is 1 in 6 (6/36 to be exact) as many of us know, but it does NOT ALWAYS roll 1 time in 6 rolls or roll 6 times in 36 rolls.

Binomial Distribution table
the Seven (1/6) for 6 rolls
7s	Exact	at most	at least	7s
#	6 rolls	or less	or more	#
0	33.49%	33.49%	100.00%	0
1	40.19%	73.68%	66.51%	1
2	20.09%	93.77%	26.32%	2
3	5.36%	99.13%	6.23%	3
4	0.804%	99.93%	0.870%	4
5	0.064%	99.998%	0.0664%	5
6	0.0021%	100.00%	0.0021%	6

It can be seen from the above table that almost 3 out of 4 times (73.68%) in a group of 6 consecutive dice rolls
exactly 1 or 0 (zero) 7s will appear. And slightly more than 1 in 4 (26.32%) groups of 6 rolls will contain 2 or more 7s.

Part of a Binomial Distribution table
the Seven (1/6) for 36 rolls
7s	Exact	at most	at least	7s
#	36 rolls	or less	or more	#
0	0.14%	0.14%	100.00%	0
1	1.02%	1.16%	99.86%	1
2	3.56%	4.71%	98.84%	2
3	8.06%	12.77%	95.29%	3
4	13.30%	26.07%	87.23%	4
5	17.02%	43.09%	73.93%	5
6	17.59%	60.67%	56.91%	6
7	15.07%	75.75%	39.33%	7
8	10.93%	86.68%	24.25%	8
9	6.80%	93.48%	13.32%	9
10	3.67%	97.15%	6.52%	10
11	1.74%	98.89%	2.85%	11
12	0.72%	99.61%	1.11%	12
13	0.27%	99.88%	0.39%	13
14	0.09%	99.97%	0.12%	14
15	0.03%	99.99%	0.034%	15
16	0.01%	99.998%	0.009%	16
17	0.00%	99.9996%	0.002%	17
18	0.00%	99.9999%	0.0004%	18
19	0.00%	99.99999%	0.0001%	19
20	0.00%	99.999998%	1.27137E-07	20
21	0.00%	99.9999997%	1.90266E-08	21
22	0.00%	99.99999997%	2.55265E-09	22
23	0.00%	99.999999997%	3.0621E-10	23
24	0.00%	99.9999999997%	3.27297E-11	24

Sevens to Rolls Ratio (SRR) for all you precision dice setters (you know who you are) is at least 7.2 or HIGHER 43.09% of the time.
That is slightly more than 2 out of 5 for groups of 36 consecutive dice rolls. Looks like the random rollers can do just fine without trying if the goal is to have a 6.55 SRR or better!

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Craps: The Seven 7 bet