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Last Updated: May 12, 2022

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Three Point Molly

Introduction

The Three Point Molly is a betting system based on craps. There is no easy way to implement it on other games. The concept is simple -- The player keeps making pass or come bets until he has at least three, backing them up with full odds.

Using the Three Point Molly will give the player a house advantage under 0.5%, which is very good. It doesn't achieve this via the betting system, but because the player is making very good bets to begin with. I used to play this system, not knowing there was a name for it at the time.

Rules

The following rules understand the player knows the rules of craps. If you don't, please at least review the rules of the pass, come, and odds bets in craps before going further.

Here is the short version of how to play the Three Point Molly. Make a pass or come bet every roll, until you have three numbers covered. Back up all pass and come bets with the odds, preferably the maximum multiple allowed.

Next, here is the longer version of how to play the Three Point Molly.

The player will have to decide how much money a betting unit is. For example $10. It will have to at least be the minimum pass line bet. Every pass or come bet will be for one unit.

  1. If it is a come out roll and the player has less than three numbers covered, then make a pass line bet.
  2. If it is not a come out roll and the player has less than three numbers covered, then make a come bet.
  3. If three numbers are already covered, then don't make any new bets.
  4. If a pass or come bet was made the previous roll and a point number (4, 5, 6, 8, 9, or 10) was rolled, then back it up with the odds, preferably the maximum allowed.
  5. On a come out roll, turn off the odds on any outstanding come bets.
  6. Keep repeating the four steps above until a seven-out, which marks the end of the session.

Analysis

To analyze the Three Point Molly, I ran through over 32 billion sessions playing it via computer simulation. I assumed the player always took full 3-4-5x odds. Here are some statistics about what to expect per session, defined as playing until the shooter sevens-out.

  • Average units bet: 21.318409
  • Averages units won: -0.086295
  • Ratio money won to money bet = -0.004048
  • Average dice rolls = 8.525470
  • Probability session win = 0.304783
  • Average units won, given a win = 15.880052
  • Probability session loss = 0.673288
  • Average units lost, given a loss = 7.316730
  • Probability session push = 0.021929
  • Net points won (not counting come bets on a come out roll) = -0.688804
  • Probability losing three points (not counting come bets on a come out roll) = 0.114039

The spoiler box below shows the raw results of the count of each net win in the simulation.

 

Simulation Results — Net Units Won

Net Win Count Probability
-28 2 0.000000
-27 7 0.000000
-26 63 0.000000
-25 412 0.000000
-24 2,867 0.000000
-23 20,077 0.000001
-22 134,791 0.000004
-21 869,965 0.000027
-20 5,283,822 0.000163
-19 29,276,571 0.000905
-18 140,054,558 0.004330
-17 505,734,437 0.015637
-16 847,665,043 0.026209
-15 1,070,934,993 0.033112
-14 670,280,254 0.020724
-13 352,443,711 0.010897
-12 278,945,010 0.008625
-11 739,681,501 0.022870
-10 1,595,074,146 0.049318
-9 1,923,363,355 0.059469
-8 1,717,525,038 0.053104
-7 1,009,831,502 0.031223
-6 860,061,437 0.026592
-5 2,273,628,075 0.070298
-4 2,532,516,176 0.078303
-3 2,453,703,762 0.075866
-2 1,590,852,863 0.049188
-1 1,177,924,337 0.036420
0 709,247,041 0.021929
1 418,005,746 0.012924
2 348,914,435 0.010788
3 474,520,818 0.014672
4 659,962,642 0.020405
5 746,209,688 0.023072
6 670,131,253 0.020720
7 453,417,199 0.014019
8 281,844,697 0.008714
9 217,130,866 0.006713
10 261,596,855 0.008088
11 365,365,278 0.011297
12 431,269,636 0.013334
13 402,459,901 0.012444
14 290,068,463 0.008969
15 190,356,909 0.005886
16 148,875,109 0.004603
17 168,971,362 0.005224
18 222,536,389 0.006881
19 258,730,303 0.008000
20 243,848,069 0.007540
21 183,847,545 0.005684
22 126,712,604 0.003918
23 100,938,946 0.003121
24 109,853,273 0.003397
25 137,408,404 0.004249
26 156,412,528 0.004836
27 148,145,000 0.004581
28 115,654,061 0.003576
29 83,203,562 0.002573
30 67,504,800 0.002087
31 71,149,502 0.002200
32 85,219,705 0.002635
33 94,997,541 0.002937
34 90,199,021 0.002789
35 72,437,048 0.002240
36 54,084,552 0.001672
37 44,653,965 0.001381
38 45,923,694 0.001420
39 53,009,464 0.001639
40 57,913,108 0.001791
41 55,062,481 0.001702
42 45,282,109 0.001400
43 34,900,804 0.001079
44 29,257,203 0.000905
45 29,511,169 0.000912
46 33,021,850 0.001021
47 35,422,854 0.001095
48 33,711,968 0.001042
49 28,262,050 0.000874
50 22,384,612 0.000692
51 19,029,160 0.000588
52 18,910,013 0.000585
53 20,611,313 0.000637
54 21,741,065 0.000672
55 20,686,720 0.000640
56 17,631,119 0.000545
57 14,301,005 0.000442
58 12,314,655 0.000381
59 12,080,858 0.000374
60 12,871,214 0.000398
61 13,380,196 0.000414
62 12,720,728 0.000393
63 10,996,692 0.000340
64 9,105,439 0.000282
65 7,922,403 0.000245
66 7,700,089 0.000238
67 8,043,796 0.000249
68 8,255,742 0.000255
69 7,848,058 0.000243
70 6,865,255 0.000212
71 5,783,499 0.000179
72 5,078,376 0.000157
73 4,898,927 0.000151
74 5,034,619 0.000156
75 5,103,691 0.000158
76 4,847,033 0.000150
77 4,283,029 0.000132
78 3,660,754 0.000113
79 3,238,821 0.000100
80 3,108,409 0.000096
81 3,150,362 0.000097
82 3,165,959 0.000098
83 2,999,627 0.000093
84 2,674,553 0.000083
85 2,311,446 0.000071
86 2,062,521 0.000064
87 1,970,926 0.000061
88 1,973,623 0.000061
89 1,965,000 0.000061
90 1,861,453 0.000058
91 1,670,294 0.000052
92 1,461,087 0.000045
93 1,310,897 0.000041
94 1,247,190 0.000039
95 1,234,522 0.000038
96 1,220,060 0.000038
97 1,154,054 0.000036
98 1,044,137 0.000032
99 920,394 0.000028
100 832,175 0.000026
101 787,011 0.000024
102 773,880 0.000024
103 757,517 0.000023
104 718,633 0.000022
105 653,186 0.000020
106 580,952 0.000018
107 525,360 0.000016
108 497,143 0.000015
109 484,725 0.000015
110 472,951 0.000015
111 445,616 0.000014
112 407,531 0.000013
113 365,717 0.000011
114 332,604 0.000010
115 313,971 0.000010
116 304,434 0.000009
117 295,887 0.000009
118 278,744 0.000009
119 255,852 0.000008
120 230,156 0.000007
121 210,020 0.000006
122 198,054 0.000006
123 189,933 0.000006
124 183,510 0.000006
125 173,189 0.000005
126 159,974 0.000005
127 144,554 0.000004
128 132,215 0.000004
129 124,269 0.000004
130 119,071 0.000004
131 114,510 0.000004
132 108,716 0.000003
133 100,078 0.000003
134 91,216 0.000003
135 83,570 0.000003
136 78,006 0.000002
137 74,593 0.000002
138 72,325 0.000002
139 67,766 0.000002
140 62,234 0.000002
141 57,088 0.000002
142 52,607 0.000002
143 48,854 0.000002
144 46,992 0.000001
145 44,948 0.000001
146 42,257 0.000001
147 39,063 0.000001
148 35,878 0.000001
149 32,842 0.000001
150 30,842 0.000001
151 29,896 0.000001
152 27,741 0.000001
153 26,310 0.000001
154 24,503 0.000001
155 22,429 0.000001
156 20,836 0.000001
157 19,530 0.000001
158 18,360 0.000001
159 17,527 0.000001
160 16,597 0.000001
161 15,348 0.000000
162 13,773 0.000000
163 13,047 0.000000
164 12,509 0.000000
165 11,737 0.000000
166 10,958 0.000000
167 10,199 0.000000
168 9,501 0.000000
169 8,880 0.000000
170 8,396 0.000000
171 7,634 0.000000
172 7,399 0.000000
173 6,839 0.000000
174 6,566 0.000000
175 6,050 0.000000
176 5,745 0.000000
177 5,277 0.000000
178 4,783 0.000000
179 4,447 0.000000
180 4,378 0.000000
181 4,001 0.000000
182 3,696 0.000000
183 3,570 0.000000
184 3,243 0.000000
185 3,031 0.000000
186 2,820 0.000000
187 2,688 0.000000
188 2,599 0.000000
189 2,405 0.000000
190 2,228 0.000000
191 2,161 0.000000
192 1,867 0.000000
193 1,756 0.000000
194 1,704 0.000000
195 1,568 0.000000
196 1,439 0.000000
197 1,383 0.000000
198 1,288 0.000000
199 1,210 0.000000
200 1,117 0.000000
201 1,007 0.000000
202 942 0.000000
203 917 0.000000
204 883 0.000000
205 821 0.000000
206 719 0.000000
207 688 0.000000
208 653 0.000000
209 612 0.000000
210 559 0.000000
211 525 0.000000
212 511 0.000000
213 506 0.000000
214 435 0.000000
215 395 0.000000
216 386 0.000000
217 340 0.000000
218 336 0.000000
219 301 0.000000
220 286 0.000000
221 277 0.000000
222 251 0.000000
223 243 0.000000
224 228 0.000000
225 227 0.000000
226 179 0.000000
227 180 0.000000
228 156 0.000000
229 153 0.000000
230 142 0.000000
231 136 0.000000
232 136 0.000000
233 130 0.000000
234 127 0.000000
235 117 0.000000
236 113 0.000000
237 111 0.000000
238 77 0.000000
239 99 0.000000
240 90 0.000000
241 69 0.000000
242 74 0.000000
243 68 0.000000
244 67 0.000000
245 55 0.000000
246 56 0.000000
247 49 0.000000
248 50 0.000000
249 48 0.000000
250 38 0.000000
251 37 0.000000
252 38 0.000000
253 30 0.000000
254 23 0.000000
255 42 0.000000
256 30 0.000000
257 16 0.000000
258 24 0.000000
259 22 0.000000
260 15 0.000000
261 21 0.000000
262 20 0.000000
263 16 0.000000
264 19 0.000000
265 16 0.000000
266 10 0.000000
267 21 0.000000
268 8 0.000000
269 16 0.000000
270 9 0.000000
271 13 0.000000
272 8 0.000000
273 13 0.000000
274 7 0.000000
275 4 0.000000
276 13 0.000000
277 9 0.000000
278 5 0.000000
279 13 0.000000
280 4 0.000000
281 4 0.000000
282 3 0.000000
283 12 0.000000
284 6 0.000000
285 2 0.000000
286 7 0.000000
287 2 0.000000
288 3 0.000000
290 4 0.000000
291 1 0.000000
292 5 0.000000
294 1 0.000000
295 2 0.000000
296 5 0.000000
297 1 0.000000
298 1 0.000000
299 4 0.000000
300 2 0.000000
302 4 0.000000
303 1 0.000000
305 1 0.000000
307 1 0.000000
309 1 0.000000
310 1 0.000000
311 1 0.000000
312 1 0.000000
313 1 0.000000
316 1 0.000000
317 1 0.000000
318 1 0.000000
322 1 0.000000
345 1 0.000000
Total 32,342,500,000 1.000000

The following chart shows the probability of a net win of -25 to +100 units.

three point molly

I ran a separate simulation of 7.6 billion sessions that looked at the net points won, not counting wins on a come out roll (because the odds were turned off). The spoiler button below shows the results.

 

Simulation Results — Net Points Won

Net
Points
Won
Count Probability
-3 866,696,937 0.114039
-2 1,799,063,609 0.236719
-1 2,707,830,104 0.356293
0 859,942,908 0.113150
1 509,181,625 0.066998
2 318,786,035 0.041946
3 200,282,777 0.026353
4 125,828,052 0.016556
5 79,035,018 0.010399
6 49,629,205 0.006530
7 31,167,223 0.004101
8 19,559,543 0.002574
9 12,280,517 0.001616
10 7,710,235 0.001015
11 4,842,391 0.000637
12 3,039,626 0.000400
13 1,907,701 0.000251
14 1,197,193 0.000158
15 751,657 0.000099
16 471,330 0.000062
17 296,874 0.000039
18 186,123 0.000024
19 116,693 0.000015
20 73,449 0.000010
21 45,690 0.000006
22 28,787 0.000004
23 18,141 0.000002
24 11,410 0.000002
25 7,248 0.000001
26 4,395 0.000001
27 2,775 0.000000
28 1,759 0.000000
29 1,081 0.000000
30 714 0.000000
31 426 0.000000
32 276 0.000000
33 182 0.000000
34 98 0.000000
35 69 0.000000
36 40 0.000000
37 31 0.000000
38 20 0.000000
39 17 0.000000
40 8 0.000000
41 2 0.000000
42 4 0.000000
43 1 0.000000
45 1 0.000000
Total 7,600,000,000 1.000000

Improving on the Three Point Molly

The player can lower the overall house edge from 0.405% to 0.374% by keeping the odds on a come bet working on a come out roll.

Conclusion

What is important in gambling is the game played, bet made, and sometimes your skill in making decisions. What is not important is the reason for making a bet. For that reason, betting systems are not mathematical voodoo that put the odds in the player's favor. No, not only don't betting systems lower the house edge, they don't even dent it.

The great thing about the Three Point Molly is not the method, but that it's played on very low house edge bets. The pass and come bets carry a 1.41% house edge, while all the odds bets carry a 0.00% house edge. Taking a blended average, the overall house edge is 0.40%. It is hard to beat that in the casino.

External Links

Discussion about the Three Point Molly in my forum at Wizard of Vegas.


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