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Anti-Martingale Betting System
Introduction
The Anti-Martingale, also known as the Reverse Martingale, is the opposite of the Martingale. Where the Martingale is good for achieving small winning goals, the Anti-Martingale is appropriate for achieving big winning goals. The flip side of that coin is the Anti-Martingale usually results in a session loss.
Rules
The following are the rules of the Anti-Martingale
.- The Anti-Martingale is generally played on even money bets.
- Start by deciding what your winning goal is and your bankroll size. The greater the ratio of bankroll to winning goal, the greater your chances of a session success are.
- The winning goal should be some power of 2. For example, 32, 64, 128, 256, etc. The player should quit when his bankroll equals the winning goal.
- Your first bet should be one unit.
- If the result of your last bet is a loss, then quit a loser.
- If the result of your last bet is a win and the winning goal has not been achieved, then double the previous bet.
- If the result of your last bet is a win and the winning goal has been reached, then quit a winner.
In other words, keep parlaying your wins until you have achieved your winning goal.
Simulation Results
The following tables show my results of simulations of billions of sessions played of the Anti-Martingale under various games, bets, and winning goals. The winning goals include the original unit bet. Negative integers appear in parenthesis. In these simulations, a session ended in either a loss of one unit or achieving the winning goal.
Baccarat — Player Bet
| Outcome | 32 Unit Goal | 64 Unit Goal | 128 Unit Goal | 256 Unit Goal | 512 Unit Goal | 1024 Unit Goal |
|---|---|---|---|---|---|---|
| Sessions | 26,080,000,000 | 25,780,000,000 | 25,620,000,000 | 25,260,000,000 | 25,200,000,000 | 25,500,000,000 |
| Winning bets | 24,637,620,081 | 24,724,388,250 | 24,753,135,083 | 24,493,825,422 | 24,479,195,241 | 24,791,954,396 |
| Losing bets | 25,319,101,570 | 25,409,064,740 | 25,438,204,846 | 25,171,605,593 | 25,156,504,282 | 25,478,292,141 |
| Tie bets | 5,253,724,716 | 5,272,135,071 | 5,278,270,266 | 5,222,915,016 | 5,219,911,289 | 5,286,540,930 |
| Ratio winning bets | 0.493179 | 0.493171 | 0.493175 | 0.493177 | 0.493177 | 0.493174 |
| Successful sessions | 760,898,430 | 370,935,260 | 181,795,154 | 88,394,407 | 43,495,718 | 21,707,859 |
| Losing sessions | 25,319,101,570 | 25,409,064,740 | 25,438,204,846 | 25,171,605,593 | 25,156,504,282 | 25,478,292,141 |
| Profit | (1,731,250,240) | (2,040,143,360) | (2,350,220,288) | (2,631,031,808) | (2,930,192,384) | (3,271,152,384) |
| Total bet | 140,234,320,547 | 165,215,636,857 | 190,268,185,405 | 212,951,190,693 | 237,400,868,341 | 265,126,805,450 |
| Avg bets per session | 2.116965 | 2.149169 | 2.165090 | 2.172935 | 2.176810 | 2.178698 |
| Expected value | -0.012345 | -0.012348 | -0.012352 | -0.012355 | -0.012343 | -0.012338 |
| Prob. session win | 0.029176 | 0.014388 | 0.007096 | 0.003499 | 0.001726 | 0.000851 |
Craps — Pass Bet
| Outcome | 32 Unit Goal | 64 Unit Goal | 128 Unit Goal | 256 Unit Goal | 512 Unit Goal | 1024 Unit Goal |
|---|---|---|---|---|---|---|
| Sessions | 28,620,000,000 | 28,490,000,000 | 28,300,000,000 | 27,940,000,000 | 28,010,000,000 | 28,160,000,000 |
| Winning bets | 27,012,039,067 | 27,298,086,262 | 27,316,055,023 | 27,066,136,420 | 27,182,344,036 | 27,351,209,098 |
| Losing bets | 27,787,113,101 | 28,081,303,381 | 28,099,875,612 | 27,842,600,329 | 27,961,883,927 | 28,136,149,487 |
| Tie bets | - | - | - | - | - | - |
| Ratio winning bets | 0.492928 | 0.492929 | 0.492928 | 0.492930 | 0.492932 | 0.492927 |
| Successful sessions | 832,886,899 | 408,696,619 | 200,124,388 | 97,399,671 | 48,116,073 | 23,850,513 |
| Losing sessions | 27,787,113,101 | 28,081,303,381 | 28,099,875,612 | 27,842,600,329 | 27,961,883,927 | 28,136,149,487 |
| Profit | (1,967,619,232) | (2,333,416,384) | (2,684,078,336) | (3,005,684,224) | (3,374,570,624) | (3,737,074,688) |
| Total bet | 139,108,132,264 | 165,008,959,076 | 189,891,082,068 | 212,767,483,778 | 238,293,739,094 | 264,330,866,420 |
| Average bets per session | 1.914715 | 1.943819 | 1.958160 | 1.965238 | 1.968734 | 1.970432 |
| Expected value | -0.014145 | -0.014141 | -0.014135 | -0.014127 | -0.014161 | -0.014138 |
| Probability session win | 0.029102 | 0.014345 | 0.007072 | 0.003486 | 0.001718 | 0.000847 |
Craps — Don't Pass Bet
| Outcome | 32 Unit Goal | 64 Unit Goal | 128 Unit Goal | 256 Unit Goal | 512 Unit Goal | 1024 Unit Goal |
|---|---|---|---|---|---|---|
| Sessions | 28,050,000,000 | 27,760,000,000 | 27,580,000,000 | 27,500,000,000 | 27,450,000,000 | 27,470,000,000 |
| Winning bets | 26,479,158,574 | 26,604,392,137 | 26,627,442,382 | 26,646,132,393 | 26,645,017,843 | 26,687,355,494 |
| Losing bets | 27,233,254,595 | 27,361,504,626 | 27,384,809,402 | 27,404,042,492 | 27,402,784,823 | 27,446,702,612 |
| Tie bets | 1,534,631,204 | 1,541,890,762 | 1,543,226,920 | 1,544,198,573 | 1,544,222,530 | 1,546,650,529 |
| Ratio winning bets | 0.492980 | 0.492985 | 0.492989 | 0.492989 | 0.492990 | 0.492986 |
| Successful sessions | 816,745,405 | 398,495,374 | 195,190,598 | 95,957,508 | 47,215,177 | 23,297,388 |
| Losing sessions | 27,233,254,595 | 27,361,504,626 | 27,384,809,402 | 27,404,042,492 | 27,402,784,823 | 27,446,702,612 |
| Profit | (1,914,147,040) | (2,256,296,064) | (2,595,603,456) | (2,934,877,952) | (3,275,829,376) | (3,613,474,688) |
| Total bet | 140,262,089,639 | 165,421,735,333 | 190,413,484,208 | 215,487,644,829 | 240,315,663,658 | 265,378,053,410 |
| Average bets per session | 1.969592 | 1.999560 | 2.014339 | 2.021614 | 2.025210 | 2.026964 |
| Expected value | -0.013647 | -0.013640 | -0.013631 | -0.013620 | -0.013631 | -0.013616 |
| Probability session win | 0.029117 | 0.014355 | 0.007077 | 0.003489 | 0.001720 | 0.000848 |
Double-Zero Roulette — Even Money Bets
| Outcome | 32 Unit Goal | 64 Unit Goal | 128 Unit Goal | 256 Unit Goal | 512 Unit Goal | 1024 Unit Goal |
|---|---|---|---|---|---|---|
| Sessions | 29,630,000,000 | 29,330,000,000 | 29,150,000,000 | 29,060,000,000 | 29,050,000,000 | 29,030,000,000 |
| Winning bets | 26,031,234,419 | 26,098,742,110 | 26,094,345,718 | 26,087,857,638 | 26,113,642,214 | 26,111,843,613 |
| Losing bets | 28,923,394,123 | 28,998,681,174 | 28,994,015,919 | 28,986,348,386 | 29,015,122,986 | 29,013,490,988 |
| Tie bets | - | - | - | - | - | - |
| Ratio winning bets | 0.473686 | 0.473684 | 0.473682 | 0.473686 | 0.473685 | 0.473681 |
| Successful sessions | 706,605,877 | 331,318,826 | 155,984,081 | 73,651,614 | 34,877,014 | 16,509,012 |
| Losing sessions | 28,923,394,123 | 28,998,681,174 | 28,994,015,919 | 28,986,348,386 | 29,015,122,986 | 29,013,490,988 |
| Profit | (7,018,611,936) | (8,125,595,136) | (9,184,037,632) | (10,205,186,816) | (11,192,968,832) | (12,124,771,712) |
| Total bet | 133,355,775,320 | 154,385,580,360 | 174,511,000,220 | 193,876,930,568 | 212,659,682,032 | 230,357,905,478 |
| Average bets per session | 1.854696 | 1.878535 | 1.889824 | 1.895189 | 1.897720 | 1.898909 |
| Expected value | -0.052631 | -0.052632 | -0.052627 | -0.052637 | -0.052633 | -0.052634 |
| Probability session win | 0.023848 | 0.011296 | 0.005351 | 0.002534 | 0.001201 | 0.000569 |
Single-Zero Roulette — Even Money Bets
| Outcome | 32 Unit Goal | 64 Unit Goal | 128 Unit Goal | 256 Unit Goal | 512 Unit Goal | 1024 Unit Goal |
|---|---|---|---|---|---|---|
| Sessions | 29,110,000,000 | 28,760,000,000 | 28,550,000,000 | 28,460,000,000 | 28,440,000,000 | 28,420,000,000 |
| Winning bets | 26,826,559,091 | 26,884,949,580 | 26,872,978,327 | 26,877,871,440 | 26,902,195,834 | 26,904,280,960 |
| Losing bets | 28,316,757,005 | 28,378,759,958 | 28,365,887,456 | 28,370,714,983 | 28,396,594,174 | 28,398,897,653 |
| Tie bets | - | - | - | - | - | - |
| Ratio winning bets | 0.486488 | 0.486485 | 0.486487 | 0.486490 | 0.486488 | 0.486487 |
| Successful sessions | 793,242,995 | 381,240,042 | 184,112,544 | 89,285,017 | 43,405,826 | 21,102,347 |
| Losing sessions | 28,316,757,005 | 28,378,759,958 | 28,365,887,456 | 28,370,714,983 | 28,396,594,174 | 28,398,897,653 |
| Profit | (3,726,224,160) | (4,360,637,312) | (4,983,594,368) | (5,603,035,648) | (6,216,217,088) | (6,811,196,672) |
| Total bet | 137,892,583,846 | 161,312,842,970 | 184,357,424,478 | 207,273,337,668 | 229,959,880,902 | 252,012,594,200 |
| Average bets per session | 1.894308 | 1.921548 | 1.934811 | 1.941271 | 1.944402 | 1.945925 |
| Expected value | -0.027023 | -0.027032 | -0.027032 | -0.027032 | -0.027032 | -0.027027 |
| Probability session win | 0.027250 | 0.013256 | 0.006449 | 0.003137 | 0.001526 | 0.000743 |
Video
In this video I explain and analyze the Anti-Martingale.