7craps's Blog

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3. Question: In a hour of normal craps play, assuming 30 pass line bets at $5 each and taking no odds, how often does one expect to win or come out ahead?

3. Answer:
The answer is 54.14% chance of being even or showing a profit.
39.74% chance of showing a $10 profit or more.

Below is a binomial distribution table of exactly 30 pass line bets at $5 each.
The value of this type of table is that you do not need to run computer simulations, you can find the same answers right in the table. Of course computer sims can help to validate a table and there is nothing wrong with that.
The main difference is a table contains Theoretical data where a simulation is Empirical Data (gathered or observed data)

(How to create your own distribution table coming soon)
3 Columns of exactly an outcome happening, or less and or more.
Example: 54.14%(slightly more than half) or more outcomes will be to break even or be ahead.
Example: 14.40% (slightly less than 1 in 7) will be EXACTLY 15 wins AND 15 losses.

Includes Net/Net% based off $5 bets.
Expected loss is $-2.12 ($150 * 1.41414%) and we can see from the table that can not happen in just 30 trials.

Most common outcome is 15 wins/15 losses and a $0 net win (break even)
2nd most common outcome is 14 wins/16 losses for a $10 net loss
3rd most common outcome is 16 wins/14 losses for a $10 net win

pass line	wins	losses	(or less)	(or more)	exact	(exact) 1 in	NET $	NET %
$5 bets	0	30	0.00000000142	100.00%	0.00000014%	704,602,733.3	-150	-100.00%
Handle	1	29	0.00000004	99.99999986%	0.0000041%	24,160,558.2	-140	-93.33%
$150	2	28	0.00000063	99.9999957%	0.000058%	1,714,047.5	-130	-86.67%
	3	27	0.0000059	99.9999%	0.00053%	188,916.5	-120	-80.00%
	4	26	0.0000407	99.9994%	0.00347%	28,790.6	-110	-73.33%
	5	25	0.000216231	99.9959%	0.01756%	5,695.5	-100	-66.67%
	6	24	0.000927402	99.98%	0.07%	1,406.1	-90	-60.00%
	7	23	0.003297703	99.91%	0.24%	421.9	-80	-53.33%
	8	22	0.00992227	99.67%	0.66%	151.0	-70	-46.67%
	9	21	0.025664047	99.01%	1.57%	63.5	-60	-40.00%
	10	20	0.057799849	97.43%	3.21%	31.1	-50	-33.33%
	11	19	0.114599095	94.22%	5.68%	17.6	-40	-26.67%
	12	18	0.202023165	88.54%	8.74%	11.4	-30	-20.00%
	13	17	0.319696018	79.80%	11.77%	8.5	-20	-13.33%
	14	16	0.458599545	68.03%	13.89%	7.2	-10	-6.67%
	15	15	0.602631251	54.14%	14.40%	6.9	0	0.00%
	16	14	0.733895205	39.74%	13.13%	7.6	10	6.67%
	17	13	0.838980199	26.61%	10.51%	9.5	20	13.33%
	18	12	0.91275833	16.10%	7.38%	13.6	30	20.00%
	19	11	0.958055535	8.72%	4.53%	22.1	40	26.67%
	20	10	0.9822742	4.19%	2.42%	41.3	50	33.33%
	21	9	0.993485269	1.77%	1.12%	89.2	60	40.00%
	22	8	0.997943709	0.65%	0.45%	224.3	70	46.67%
	23	7	0.999451222	0.21%	0.15%	663.3	80	53.33%
	24	6	0.999878652	0.05%	0.04%	2,339.6	90	60.00%
	25	5	0.999978374	0.0121%	0.009972%	10,027.9	100	66.67%
	26	4	0.999997016	0.0022%	0.001864%	53,640.9	110	73.33%
	27	3	0.999999701	0.00030%	0.000268%	372,463.3	120	80.00%
	28	2	0.999999981	0.000030%	0.000028%	3,576,054.5	130	86.67%
	29	1	0.99999999939	0.0000019%	0.0000019%	53,340,370.5	140	93.33%
	30	0	0.999999999999998	0.00000006%	0.00000006%	1,646,118,811.0	150	100.00%

Theoretical SD is 2.7383
63.70% / 13 to 17 wins (almost 1 SD)
95.66% / 10 to 20 wins (2 SD)
99.85% / 7 to 23 wins (3 SD)

10,000 simulations, empirical data snap shots

rolls needed to see 30 pass line bets resolved.


table for pass line only session loss and win/even probabilities.
Excel formula for even or win session probability = 1 - BINOMDIST(N/2-1,N,244/495,TRUE) where N = number of pass line trials
Example: N=30, 1-BINOMDIST(30/2-1,30,244/495,TRUE) = 0.541400455

pass line trials	loss	even or win
2	0.257120702	0.742879298
4	0.323180338	0.676819662
6	0.35709953	0.64290047
8	0.37885466	0.62114534
10	0.394472039	0.605527961
12	0.406476548	0.593523452
14	0.416137586	0.583862414
16	0.424173105	0.575826895
18	0.431024246	0.568975754
20	0.436979308	0.563020692
22	0.442235918	0.557764082
24	0.446934813	0.553065187
26	0.451179389	0.548820611
28	0.455047605	0.544952395
30	0.458599545	0.541400455
32	0.461882399	0.538117601
34	0.464933833	0.535066167
36	0.46778435	0.53221565
38	0.470458962	0.529541038
40	0.472978412	0.527021588
42	0.475360071	0.524639929
44	0.477618624	0.522381376
46	0.479766583	0.520233417
48	0.481814689	0.518185311
50	0.483772228	0.516227772
52	0.485647274	0.514352726
54	0.487446889	0.512553111
56	0.489177285	0.510822715
58	0.490843949	0.509156051
60	0.492451754	0.507548246
62	0.494005041	0.505994959
64	0.495507697	0.504492303
66	0.496963214	0.503036786
68	0.498374738	0.501625262
70	0.499745114	0.500254886
72	0.501076925	0.498923075
74	0.502372518	0.497627482
76	0.503634035	0.496365965
78	0.504863435	0.495136565
80	0.506062515	0.493937485
82	0.507232924	0.492767076
84	0.508376182	0.491623818
86	0.509493691	0.490506309
88	0.510586749	0.489413251
90	0.511656557	0.488343443
92	0.51270423	0.48729577
94	0.513730805	0.486269195
96	0.514737247	0.485262753
98	0.515724457	0.484275543
100	0.516693276	0.483306724
102	0.517644492	0.482355508
104	0.518578842	0.481421158
106	0.519497016	0.480502984
108	0.520399666	0.479600334
110	0.521287402	0.478712598
112	0.522160799	0.477839201
114	0.523020401	0.476979599
116	0.523866718	0.476133282
118	0.524700234	0.475299766
120	0.525521406	0.474478594
122	0.526330668	0.473669332
124	0.52712843	0.47287157
126	0.52791508	0.47208492
128	0.528690989	0.471309011
130	0.529456506	0.470543494
132	0.530211966	0.469788034
134	0.530957686	0.469042314
136	0.531693969	0.468306031
138	0.532421103	0.467578897
140	0.533139364	0.466860636
142	0.533849013	0.466150987
144	0.534550301	0.465449699
146	0.535243469	0.464756531
148	0.535928746	0.464071254
150	0.53660635	0.46339365
152	0.537276494	0.462723506
154	0.537939377	0.462060623
156	0.538595194	0.461404806
158	0.539244129	0.460755871
160	0.539886361	0.460113639
162	0.54052206	0.45947794
164	0.541151392	0.458848608
166	0.541774514	0.458225486
168	0.542391577	0.457608423
170	0.54300273	0.45699727
172	0.543608111	0.456391889
174	0.544207858	0.455792142
176	0.544802101	0.455197899
178	0.545390965	0.454609035
180	0.545974574	0.454025426
182	0.546553045	0.453446955
184	0.54712649	0.45287351
186	0.54769502	0.45230498
188	0.548258741	0.451741259
190	0.548817755	0.451182245
192	0.549372161	0.450627839
194	0.549922055	0.450077945
196	0.550467529	0.449532471
198	0.551008674	0.448991326
200	0.551545577	0.448454423

1 blog

My Blog will start out with tables I make from questions about craps by friends and players alike.
This way they can be found in one place.
Note: Please do not ask me questions that can be better served to be answered in a regular thread.
keep any questions aimed to the questions and answers in my Blog.

1. Question: How do you figure the house edge if you do not know the bets probabilities?
1. Answer:
Easy way to figure the house edge when BOTH
1)the house payoff AND
2)true odds payoffs are known.
It is the only way this formula can work.
Other wise you have to figure the expected value first, and I know for some, that is too hard to do.

(John Scarne, real name:Orlando Carmelo Scarnecchia... first came up with this years ago)Scarne WAS the expert before his passing in the 80s and before computers were readily available. Now we have many experts and the most popular by far in my book is the Wizard of Odds.

HE= difference / down OR exactly
HE= (true payoff - house payoff) / ( total bet + true payoff )
Example:
Place bet on the 6 (or 8):
A $6 place bet on the 6 pays $7. The true odds payoff (6 to 5) for a $6 bet should pay $7.20
Difference: $.20
Total of true odds payoff and wager: $13.20

Answer:(.20)/13.20 = 0.0151515 = 1.515%
(difference)/(bet and true payoff)

see the below table for more examples.

2. Question: Because of rounding down of $3 payoffs for $3 place bets, what is the house edge on $3 place bets?
2. Answer:
$3 place bet house edge vs. proper unit place bets TABLE

place	bet	house pays	true payoff	diff	down	HA	Increase
4,10	5	9	10	1	15.00	6.666667%	.
5,9	5	7	7.5	0.5	12.50	4.000000%	.
6,8	6	7	7.2	0.2	13.20	1.515152%	.
.	.	.	.	.	.	.	.
4,10 exact	3	5.40	6	.6	9.00	6.6667%	0.00%
4,10	3	5	6	1	9.00	11.1111%	66.67%
5,9	3	4	4.5	0.5	7.50	6.6667%	66.67%
5,9 exact	3	4.20	4.5	0.3	7.50	4.0000%	0.00%
6,8 exact	3	3.5	3.6	0.1	6.60	1.5152%	0.00%
6,8	3	3	3.6	0.6	6.60	9.0909%	500.00%

As a player you are INCREASING the house edge when making these $3 place bets. The 6&8 turning into a BIG 6 and Big 8.
This increases your losses when you do lose and lowers your wins when you do win.(compared to correct unit bets)