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Last Updated: June 17, 2021

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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

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  1. The Anti-Martingale is generally played on even money bets.
  2. 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.
  3. 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.
  4. Your first bet should be one unit.
  5. If the result of your last bet is a loss, then quit a loser.
  6. If the result of your last bet is a win and the winning goal has not been achieved, then double the previous bet.
  7. 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.

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