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Last Updated: May 26, 2022

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Three Point Dolly

Introduction

The Three Point Dolly is a betting system based on craps. It is the flip side of the the Three Point Molly, making bets that win on a seven, as opposed to loss on a seven.

Using the Three Point Dolly will give the player a house advantage of 0.27%, which is as good as it gets in most casinos. It doesn't achieve this via the betting system, but because the player is making very good bets to begin with.

While I've seen players betting this way at the table, I am not aware of any term for this betting system. So, I created the name Three Point Dolly, the evil twin of the Three Point Molly.

Rules

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

Here is the short version of how to play the Three Point Dolly. Make a don't pass or don't come bet every roll, until you have three numbers covered. Back up all don't pass and don't come bets by laying full odds, preferably the maximum multiple allowed.

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

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 don't pass line bet. Every don't pass or don't 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 don't pass bet.
  2. If it is not a come out roll and the player has less than three numbers covered, then make a don't 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 by laying the odds, preferably the maximum allowed.
  5. Keep repeating the four steps above until a seven-out, which marks the end of the session.

Analysis

To analyze the Three Point Dolly, I ran through over 41 billion sessions playing it via computer simulation. I assumed the table allows 3-4-5x odds, meaning the player always lays 6x the don't pass or don't come bet. Here are some statistics about what to expect per session, defined as playing until the shooter sevens-out.

  • Average units bet: 30.313926
  • Averages units won: -0.083150
  • Ratio money won to money bet = -0.002743
  • Average dice rolls = 8.525547
  • Probability session win = 0.679841
  • Average units won, given a win = 7.393417
  • Probability session loss = 0.299207
  • Average units lost, given a loss = 17.076796
  • Probability session push = 0.020952

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
-349 1 0.000000
-346 1 0.000000
-343 1 0.000000
-342 1 0.000000
-341 1 0.000000
-337 1 0.000000
-336 1 0.000000
-333 1 0.000000
-331 1 0.000000
-328 2 0.000000
-325 2 0.000000
-323 1 0.000000
-322 2 0.000000
-320 1 0.000000
-319 3 0.000000
-317 2 0.000000
-316 4 0.000000
-315 1 0.000000
-314 3 0.000000
-313 6 0.000000
-312 1 0.000000
-311 6 0.000000
-310 7 0.000000
-309 6 0.000000
-308 2 0.000000
-307 4 0.000000
-306 6 0.000000
-305 4 0.000000
-304 1 0.000000
-303 6 0.000000
-302 3 0.000000
-301 4 0.000000
-300 4 0.000000
-299 5 0.000000
-298 5 0.000000
-297 2 0.000000
-296 8 0.000000
-295 6 0.000000
-294 11 0.000000
-293 9 0.000000
-292 7 0.000000
-291 12 0.000000
-290 12 0.000000
-289 10 0.000000
-288 11 0.000000
-287 6 0.000000
-286 15 0.000000
-285 19 0.000000
-284 18 0.000000
-283 20 0.000000
-282 19 0.000000
-281 23 0.000000
-280 18 0.000000
-279 29 0.000000
-278 24 0.000000
-277 25 0.000000
-276 30 0.000000
-275 30 0.000000
-274 29 0.000000
-273 33 0.000000
-272 42 0.000000
-271 41 0.000000
-270 38 0.000000
-269 36 0.000000
-268 40 0.000000
-267 45 0.000000
-266 36 0.000000
-265 34 0.000000
-264 51 0.000000
-263 72 0.000000
-262 48 0.000000
-261 65 0.000000
-260 76 0.000000
-259 74 0.000000
-258 71 0.000000
-257 94 0.000000
-256 118 0.000000
-255 73 0.000000
-254 101 0.000000
-253 118 0.000000
-252 109 0.000000
-251 129 0.000000
-250 132 0.000000
-249 141 0.000000
-248 159 0.000000
-247 146 0.000000
-246 163 0.000000
-245 143 0.000000
-244 186 0.000000
-243 186 0.000000
-242 229 0.000000
-241 194 0.000000
-240 269 0.000000
-239 266 0.000000
-238 287 0.000000
-237 279 0.000000
-236 356 0.000000
-235 328 0.000000
-234 378 0.000000
-233 357 0.000000
-232 370 0.000000
-231 400 0.000000
-230 441 0.000000
-229 482 0.000000
-228 532 0.000000
-227 604 0.000000
-226 584 0.000000
-225 591 0.000000
-224 619 0.000000
-223 717 0.000000
-222 747 0.000000
-221 842 0.000000
-220 802 0.000000
-219 885 0.000000
-218 916 0.000000
-217 951 0.000000
-216 1,129 0.000000
-215 1,213 0.000000
-214 1,259 0.000000
-213 1,320 0.000000
-212 1,351 0.000000
-211 1,432 0.000000
-210 1,569 0.000000
-209 1,695 0.000000
-208 1,889 0.000000
-207 1,975 0.000000
-206 1,962 0.000000
-205 2,129 0.000000
-204 2,169 0.000000
-203 2,372 0.000000
-202 2,703 0.000000
-201 2,822 0.000000
-200 3,021 0.000000
-199 3,169 0.000000
-198 3,350 0.000000
-197 3,431 0.000000
-196 3,717 0.000000
-195 4,043 0.000000
-194 4,535 0.000000
-193 4,790 0.000000
-192 4,974 0.000000
-191 5,129 0.000000
-190 5,446 0.000000
-189 5,729 0.000000
-188 6,372 0.000000
-187 6,958 0.000000
-186 7,289 0.000000
-185 7,526 0.000000
-184 7,974 0.000000
-183 8,266 0.000000
-182 8,913 0.000000
-181 9,956 0.000000
-180 11,109 0.000000
-179 11,685 0.000000
-178 11,577 0.000000
-177 12,107 0.000000
-176 12,669 0.000000
-175 13,866 0.000000
-174 15,458 0.000000
-173 16,954 0.000000
-172 17,733 0.000000
-171 18,425 0.000000
-170 18,539 0.000000
-169 19,472 0.000000
-168 21,452 0.000001
-167 23,866 0.000001
-166 26,470 0.000001
-165 27,854 0.000001
-164 28,335 0.000001
-163 28,487 0.000001
-162 30,177 0.000001
-161 33,426 0.000001
-160 37,550 0.000001
-159 41,555 0.000001
-158 43,705 0.000001
-157 43,810 0.000001
-156 44,389 0.000001
-155 46,779 0.000001
-154 51,776 0.000001
-153 58,871 0.000001
-152 64,193 0.000002
-151 67,643 0.000002
-150 67,928 0.000002
-149 67,985 0.000002
-148 71,347 0.000002
-147 79,793 0.000002
-146 90,808 0.000002
-145 100,786 0.000002
-144 104,743 0.000003
-143 105,155 0.000003
-142 105,227 0.000003
-141 110,273 0.000003
-140 124,010 0.000003
-139 142,640 0.000003
-138 157,332 0.000004
-137 164,308 0.000004
-136 162,050 0.000004
-135 159,953 0.000004
-134 170,158 0.000004
-133 192,443 0.000005
-132 223,194 0.000005
-131 246,656 0.000006
-130 254,875 0.000006
-129 250,895 0.000006
-128 247,073 0.000006
-127 260,710 0.000006
-126 297,807 0.000007
-125 348,598 0.000008
-124 385,362 0.000009
-123 396,886 0.000010
-122 386,098 0.000009
-121 378,076 0.000009
-120 399,790 0.000010
-119 461,508 0.000011
-118 542,355 0.000013
-117 606,451 0.000015
-116 619,362 0.000015
-115 596,253 0.000014
-114 579,807 0.000014
-113 614,138 0.000015
-112 716,824 0.000017
-111 849,465 0.000021
-110 949,523 0.000023
-109 964,534 0.000023
-108 919,200 0.000022
-107 885,786 0.000022
-106 942,423 0.000023
-105 1,113,293 0.000027
-104 1,333,139 0.000032
-103 1,485,696 0.000036
-102 1,504,049 0.000037
-101 1,412,457 0.000034
-100 1,349,589 0.000033
-99 1,441,825 0.000035
-98 1,725,585 0.000042
-97 2,090,861 0.000051
-96 2,335,996 0.000057
-95 2,336,960 0.000057
-94 2,173,303 0.000053
-93 2,060,412 0.000050
-92 2,208,374 0.000054
-91 2,678,764 0.000065
-90 3,282,556 0.000080
-89 3,670,435 0.000089
-88 3,646,581 0.000089
-87 3,333,674 0.000081
-86 3,125,240 0.000076
-85 3,378,054 0.000082
-84 4,159,761 0.000101
-83 5,169,380 0.000126
-82 5,774,776 0.000140
-81 5,679,152 0.000138
-80 5,110,291 0.000124
-79 4,742,732 0.000115
-78 5,155,616 0.000125
-77 6,469,426 0.000157
-76 8,141,988 0.000198
-75 9,093,149 0.000221
-74 8,840,044 0.000215
-73 7,809,482 0.000190
-72 7,164,587 0.000174
-71 7,863,075 0.000191
-70 10,063,019 0.000245
-69 12,849,179 0.000312
-68 14,334,094 0.000348
-67 13,776,483 0.000335
-66 11,922,391 0.000290
-65 10,791,886 0.000262
-64 11,959,468 0.000291
-63 15,664,666 0.000381
-62 20,299,422 0.000493
-61 22,621,260 0.000550
-60 21,448,092 0.000521
-59 18,147,199 0.000441
-58 16,189,989 0.000393
-57 18,163,881 0.000441
-56 24,374,015 0.000592
-55 32,152,120 0.000781
-54 35,739,302 0.000869
-53 33,401,907 0.000812
-52 27,542,783 0.000669
-51 24,187,100 0.000588
-50 27,552,095 0.000670
-49 37,968,841 0.000923
-48 50,990,211 0.001239
-47 56,508,926 0.001373
-46 52,002,969 0.001264
-45 41,642,600 0.001012
-44 35,945,342 0.000874
-43 41,677,542 0.001013
-42 59,153,276 0.001438
-41 80,971,038 0.001968
-40 89,444,790 0.002174
-39 80,984,922 0.001968
-38 62,779,226 0.001526
-37 53,125,188 0.001291
-36 62,893,192 0.001528
-35 92,113,076 0.002238
-34 128,847,712 0.003131
-33 141,704,041 0.003444
-32 126,120,841 0.003065
-31 94,141,256 0.002288
-30 77,840,920 0.001892
-29 94,505,017 0.002297
-28 143,361,839 0.003484
-27 205,391,652 0.004991
-26 224,815,834 0.005463
-25 197,062,105 0.004789
-24 141,479,917 0.003438
-23 114,400,372 0.002780
-22 141,937,586 0.003449
-21 222,893,289 0.005417
-20 327,625,530 0.007962
-19 356,565,298 0.008665
-18 306,893,201 0.007458
-17 208,617,391 0.005070
-16 162,538,120 0.003950
-15 210,664,910 0.005119
-14 345,995,246 0.008408
-13 525,862,376 0.012779
-12 575,094,059 0.013976
-11 506,186,057 0.012301
-10 355,267,152 0.008633
-9 287,758,280 0.006993
-8 328,454,031 0.007982
-7 536,504,683 0.013038
-6 838,154,135 0.020368
-5 903,714,844 0.021961
-4 757,019,526 0.018397
-3 451,972,081 0.010984
-2 324,182,693 0.007878
-1 470,993,547 0.011446
0 862,177,144 0.020952
1 1,475,802,637 0.035864
2 1,966,020,072 0.047777
3 3,134,801,174 0.076180
4 3,227,145,242 0.078424
5 2,925,595,450 0.071096
6 1,070,503,000 0.026015
7 1,328,049,870 0.032273
8 2,245,337,384 0.054565
9 2,437,755,805 0.059241
10 2,001,363,460 0.048636
11 900,248,512 0.021877
12 383,862,607 0.009328
13 534,359,330 0.012986
14 947,140,171 0.023017
15 1,444,149,683 0.035095
16 1,084,274,535 0.026349
17 632,653,447 0.015374
18 164,648,522 0.004001
19 45,249,571 0.001100
20 16,597,713 0.000403
21 6,458,485 0.000157
22 2,274,071 0.000055
23 762,051 0.000019
24 261,002 0.000006
25 91,611 0.000002
26 32,066 0.000001
27 11,170 0.000000
28 3,924 0.000000
29 1,397 0.000000
30 480 0.000000
31 177 0.000000
32 49 0.000000
33 23 0.000000
34 11 0.000000
35 3 0.000000
36 2 0.000000
Total 41,150,000,000 1.000000

The following graph shows the probability of the most common outcomes, between a loss of 50 and a win of 25 units.

three point dolly

Comparison to Three Point Molly

The following table compares various statistics between the Three Point Molly and Three Point Dolly.

Comparison of Three Point Molly to Dolly

Statistic Molly Dolly
Expected units bet 21.318409 30.313926
Expected win -0.086295 -0.083150
House Edge 0.004048 0.002743
Probability Win 0.304783 0.679841
Probability Loss 0.673288 0.299207
Average win given win 15.880052 7.393417
Average loss given loss 7.316730 17.076796
Average rolls 8.525470 8.525547
Standard deviation 13.966288 14.635488

Video

Please enjoy my video on the Three Point Dolly.

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 Dolly is not the method, but that it's played on very low house edge bets. The don't pass and come bets carry a 1.36% house edge, while all the odds bets carry a 0.00% house edge. Taking a blended average, the overall house edge is 0.27%. In most casinos, those are the best odds you are going to get.

External Links

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


Written by: 

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