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Three Point Molly

Introduction

The Three Point Molly is a unique betting strategy derived from craps. It may be challenging to apply it to other games. The fundamental idea is straightforward: the player places pass or come bets continuously until at least three numbers are secured, enhancing these bets with full odds.

Utilizing the Three Point Molly strategy can give players an impressive house edge of less than 0.5%. This achievement is not necessarily due to the betting technique itself, but rather because the player is making judicious initial bets. I previously utilized this method without knowing it had a specific name.

Rules

The rules that follow assume the player is already familiar with the game mechanics of craps. craps If you’re not acquainted with them, it’s advisable to review the rules regarding pass, come, and odds bets in craps before proceeding any further.

Here’s a brief overview of how to approach the Three Point Molly. Place a pass or come bet for every roll until you have a total of three numbers covered. Additionally, support every pass and come bet with odds, ideally at the maximum multiple permissible.

Now, let’s discuss a more detailed explanation of playing the Three Point Molly.

The player must determine the value of a betting unit, for instance, $10, which should be at least the minimum required for a pass line bet. Each pass or come bet will represent one unit.

  1. During a come out roll, if the player has fewer than three numbers covered, they should place a pass line bet.
  2. If it's not a come out roll and there are still fewer than three numbers covered, the player should opt for a come bet.
  3. Once three numbers are covered, the player should refrain from making any additional bets.
  4. If a pass or come bet was placed on the previous roll resulting in a point number (4, 5, 6, 8, 9, or 10), it's crucial to back that bet with the odds, ideally at the maximum allowed.
  5. For any come bets still outstanding during a coming out roll, ensure to turn off the odds.
  6. Continue this cycle of four steps until a seven occurs, signaling the conclusion of the session.

Analysis

In order to evaluate the effectiveness of the Three Point Molly, I conducted over 32 billion simulated sessions, assuming the player consistently utilized the maximum 3-4-5x odds. Below are some statistics representing what can be anticipated per session, which is defined as playing until the shooter rolls a seven.

  • Average units bet: 21.318409
  • Average 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 (excluding come bets during a come out roll) = -0.688804
  • Probability of losing three points (excluding come bets during a come out roll) = 0.114039

The spoiler box below contains the raw data displaying the count of net wins from 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 chart below illustrates the likelihood of experiencing a net win ranging from -25 to +100 units.

three point molly

I also performed a separate simulation involving 7.6 billion sessions that focused on net points won, not considering wins on a come out roll (as the odds were turned off). The spoiler button below reveals the findings.

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

Video

Feel free to watch my video discussing the Three Point Molly.

Improving on the Three Point Molly

A player can reduce the overall house edge from 0.405% to 0.374% by activating the odds on a come bet during a come out roll.

Conclusion

In gambling, what truly matters are the games you choose, the bets you place, and sometimes your skill in decision-making, while the motivations behind your bets are often irrelevant. Therefore, betting systems are not some kind of mathematical magic that shifts the odds in the player's favor. In reality, not only do they fail to reduce the house edge, but they don’t even affect it significantly.

The most appealing aspect of the Three Point Molly is not the strategy itself, but rather that it involves bets that carry a very low house edge. Pass and come bets have a house edge of 1.41%, while all odds bets hold a house edge of 0.00%. When averaged together, the overall house edge stands at 0.40%, which is quite difficult to surpass in a casino setting.

Internal Links

Three Point Dolly — An alternative strategy to the Three Point Molly involves placing don't pass, don't come bets, and laying odds. This approach has even better odds than the Three Point Molly, but anticipate some disapproving looks at the tables.

External Links

Let's discuss the Three Point Molly in more depth. in my forum at Wizard of Vegas.