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# 2-1-2 Manhattan Betting System

## Introduction

The 2-1-2 is a mildly progressive betting system, meant to win more in a strong winning session, but at the expense of losing more in a choppy session. It is also called the Manhattan, I assume because 2-1-2 is the original area code for New York City and is today confined to Manhattan. Other resources on the 2-1-2 online contradict each other and sometimes are internally inconsistent. This page endeavors to present what I think is the simplest and most logical version of the 2-1-2. Let's call it the Wizard variant of the 2-1-2.

## Rules

Like most betting system, the 2-1-2 is designed for even money games and blackjack.

1. The player should decide on how much a betting "unit" is. For example, \$10.
2. After any losing hand, the player will end the session or start over.
3. After any push, the player will repeat the previous bet.
4. The player starts with a 2-unit wager.
5. If the player wins the first bet, the second bet shall be one unit.
6. If the player wins any bet, other than the first one, he shall increase his next bet by one unit.

Another way to explain it is the player starts with a two-unit bet and always increases his bet by one unit after a win, except he decreases his bet by one unit after the first win.

Here is my flowchart of how to use the 2-1-2. Start with the "Bet 2 units" square.

Other variants:

• In what I will call the Blackjack University Variant, the player increases his bet from one units to three units after a second win. In the video I linked to, start watching at 5:42 for an example of this. Guys, if the player were supposed to do that, they would call it the 2-1-3 (Los Angeles) system.
• On many sites, Betway Insider, to name just one, has the player stay at one-unit bet after losing a one-unit bet. In other words, the player must lose a two-unit bet or more to quit.

## Analysis

As mentioned in the rules, the player must lose to end a session of this system. So, in theory, the player could play endlessly. However, to not have to analyze an infinite number of possibilities, I will have the player walk away a winner if he wins 21 hands in a row (or a 20-unit bet). The probability of getting this far in craps, on the player bet, is 1 in 2.8 million.

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on the Player bet in baccarat. The lower right cell shows an expected loss of 0.053506 units per session. The average number of bets per session is 4.332144. The ratio of expected money lost to money bet per session is 0.012351, the same as the house edge on the Player bet.

### Baccarat Player Bet

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2 0.506825 -1.013650
Loss on bet 2 1 1 0.249953 0.249953
Loss on bet 3 2 1 0.123271 0.123271
Loss on bet 4 3 2 0.060794 0.121588
Loss on bet 5 4 4 0.029982 0.119929
Loss on bet 6 5 7 0.014786 0.103505
Loss on bet 7 6 11 0.007292 0.080215
Loss on bet 8 7 16 0.003596 0.057542
Loss on bet 9 8 22 0.001774 0.039020
Loss on bet 10 9 29 0.000875 0.025367
Loss on bet 11 10 37 0.000431 0.015961
Loss on bet 12 11 46 0.000213 0.009787
Loss on bet 13 12 56 0.000105 0.005876
Loss on bet 14 13 67 0.000052 0.003467
Loss on bet 15 14 79 0.000026 0.002016
Loss on bet 16 15 92 0.000013 0.001158
Loss on bet 17 16 106 0.000006 0.000658
Loss on bet 18 17 121 0.000003 0.000370
Loss on bet 19 18 137 0.000002 0.000207
Loss on bet 20 19 154 0.000001 0.000115
Loss on bet 21 20 172 0.000000 0.000063
Win 21 bets 20 212 0.000000 0.000076
Total     1.000000 -0.053506

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on the Banker bet in baccarat. The lower right cell shows an expected loss of 0.047746 units per session. The average number of bets per session is 4.513230. The ratio of expected money lost to money bet per session is 0.010579, the same as the house edge on the Player bet.

### Baccarat Banker Bet

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2.00 0.493175 -0.986350
Loss on bet 2 1 0.90 0.249953 0.224958
Loss on bet 3 2 0.85 0.126683 0.107680
Loss on bet 4 3 1.75 0.064206 0.112360
Loss on bet 5 4 3.60 0.032541 0.117148
Loss on bet 6 5 6.40 0.016493 0.105553
Loss on bet 7 6 10.15 0.008359 0.084843
Loss on bet 8 7 14.85 0.004236 0.062912
Loss on bet 9 8 20.50 0.002147 0.044017
Loss on bet 10 9 27.10 0.001088 0.029491
Loss on bet 11 10 34.65 0.000552 0.019111
Loss on bet 12 11 43.15 0.000280 0.012062
Loss on bet 13 12 52.60 0.000142 0.007452
Loss on bet 14 13 63.00 0.000072 0.004524
Loss on bet 15 14 74.35 0.000036 0.002706
Loss on bet 16 15 86.65 0.000018 0.001598
Loss on bet 17 16 99.90 0.000009 0.000934
Loss on bet 18 17 114.10 0.000005 0.000541
Loss on bet 19 18 129.25 0.000002 0.000310
Loss on bet 20 19 145.35 0.000001 0.000177
Loss on bet 21 20 162.40 0.000001 0.000100
Win 21 bets 20 201.40 0.000001 0.000128
Total     1.000000 -0.047746

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on any even money bet in single-zero roulette. The lower right cell shows an expected loss of 0.103915 units per session. The average number of bets per session is 3.844864. The ratio of expected money lost to money bet per session is 0.027027, the same as the house edge in this game.

### Single Zero Roulette

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2 0.513514 -1.027027
Loss on bet 2 1 1 0.249817 0.249817
Loss on bet 3 2 1 0.121533 0.121533
Loss on bet 4 3 2 0.059124 0.118248
Loss on bet 5 4 4 0.028763 0.115052
Loss on bet 6 5 7 0.013993 0.097950
Loss on bet 7 6 11 0.006807 0.074881
Loss on bet 8 7 16 0.003312 0.052987
Loss on bet 9 8 22 0.001611 0.035444
Loss on bet 10 9 29 0.000784 0.022729
Loss on bet 11 10 37 0.000381 0.014108
Loss on bet 12 11 46 0.000185 0.008533
Loss on bet 13 12 56 0.000090 0.005053
Loss on bet 14 13 67 0.000044 0.002941
Loss on bet 15 14 79 0.000021 0.001687
Loss on bet 16 15 92 0.000010 0.000956
Loss on bet 17 16 106 0.000005 0.000536
Loss on bet 18 17 121 0.000002 0.000298
Loss on bet 19 18 137 0.000001 0.000164
Loss on bet 20 19 154 0.000001 0.000090
Loss on bet 21 20 172 0.000000 0.000049
Win 21 bets 0 212 0.000000 0.000057
Total     1.000000 -0.103915

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on any even money bet in double-zero roulette. The lower right cell shows an expected loss of 0.195263 units per session. The average number of bets per session is 3.709994. The ratio of expected money lost to money bet per session is 0.052632, the same as the house edge in this game.

### Double Zero Roulette

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2 0.526316 -1.052632
Loss on bet 2 1 1 0.249307 0.249307
Loss on bet 3 2 1 0.118093 0.118093
Loss on bet 4 3 2 0.055939 0.111878
Loss on bet 5 4 4 0.026497 0.105989
Loss on bet 6 5 7 0.012551 0.087860
Loss on bet 7 6 11 0.005945 0.065399
Loss on bet 8 7 16 0.002816 0.045060
Loss on bet 9 8 22 0.001334 0.029348
Loss on bet 10 9 29 0.000632 0.018325
Loss on bet 11 10 37 0.000299 0.011075
Loss on bet 12 11 46 0.000142 0.006522
Loss on bet 13 12 56 0.000067 0.003761
Loss on bet 14 13 67 0.000032 0.002131
Loss on bet 15 14 79 0.000015 0.001190
Loss on bet 16 15 92 0.000007 0.000657
Loss on bet 17 16 106 0.000003 0.000358
Loss on bet 18 17 121 0.000002 0.000194
Loss on bet 19 18 137 0.000001 0.000104
Loss on bet 20 19 154 0.000000 0.000055
Loss on bet 21 20 172 0.000000 0.000029
Win 21 bets 0 212 0.000000 0.000032
Total     1.000000 -0.195263

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on any even money bet in triple-zero roulette. The lower right cell shows an expected loss of 0.276295 units per session. The average number of bets per session is 3.591833. The ratio of expected money lost to money bet per session is 0.076923, the same as the house edge in this game.

### Triple Zero Roulette

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2 0.538462 -1.076923
Loss on bet 2 1 1 0.248521 0.248521
Loss on bet 3 2 1 0.114702 0.114702
Loss on bet 4 3 2 0.052939 0.105879
Loss on bet 5 4 4 0.024434 0.097734
Loss on bet 6 5 7 0.011277 0.078939
Loss on bet 7 6 11 0.005205 0.057253
Loss on bet 8 7 16 0.002402 0.038435
Loss on bet 9 8 22 0.001109 0.024392
Loss on bet 10 9 29 0.000512 0.014840
Loss on bet 11 10 37 0.000236 0.008738
Loss on bet 12 11 46 0.000109 0.005014
Loss on bet 13 12 56 0.000050 0.002817
Loss on bet 14 13 67 0.000023 0.001556
Loss on bet 15 14 79 0.000011 0.000847
Loss on bet 16 15 92 0.000005 0.000455
Loss on bet 17 16 106 0.000002 0.000242
Loss on bet 18 17 121 0.000001 0.000127
Loss on bet 19 18 137 0.000000 0.000067
Loss on bet 20 19 154 0.000000 0.000035
Loss on bet 21 20 172 0.000000 0.000018
Win 21 bets 0 212 0.000000 0.000019
Total     1.000000 -0.276295

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on the pass bet in craps. The lower right cell shows an expected loss of 0.055393 units per session. The average number of bets per session is 3.917097. The ratio of expected money lost to money bet per session is 0.014141, the same as the house edge on this bet.

### Craps — Pass Bet

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2 0.507071 -1.014141
Loss on bet 2 1 1 0.249950 0.249950
Loss on bet 3 2 1 0.123208 0.123208
Loss on bet 4 3 2 0.060733 0.121465
Loss on bet 5 4 4 0.029937 0.119748
Loss on bet 6 5 7 0.014757 0.103297
Loss on bet 7 6 11 0.007274 0.080015
Loss on bet 8 7 16 0.003586 0.057369
Loss on bet 9 8 22 0.001767 0.038884
Loss on bet 10 9 29 0.000871 0.025266
Loss on bet 11 10 37 0.000429 0.015890
Loss on bet 12 11 46 0.000212 0.009738
Loss on bet 13 12 56 0.000104 0.005843
Loss on bet 14 13 67 0.000051 0.003446
Loss on bet 15 14 79 0.000025 0.002003
Loss on bet 16 15 92 0.000012 0.001150
Loss on bet 17 16 106 0.000006 0.000653
Loss on bet 18 17 121 0.000003 0.000367
Loss on bet 19 18 137 0.000001 0.000205
Loss on bet 20 19 154 0.000001 0.000114
Loss on bet 21 20 172 0.000000 0.000063
Win 21 bets 0 212 0.000000 0.000075
Total     1.000000 -0.055393

The following table shows the net win, probability, and contribution to the return by following the 2-1-2 system on the don't pass bet in craps. The lower right cell shows an expected loss of 0.054950 units per session. The average number of bets per session is 4.029694. The ratio of expected money lost to money bet per session is 0.013636, the same as the house edge on this bet.

### Craps — Don't Pass Bet

Event Last Bet Net Win Probability Return
Loss on bet 1 2 -2 0.507013 -1.014026
Loss on bet 2 1 1 0.249951 0.249951
Loss on bet 3 2 1 0.123223 0.123223
Loss on bet 4 3 2 0.060747 0.121494
Loss on bet 5 4 4 0.029948 0.119790
Loss on bet 6 5 7 0.014764 0.103346
Loss on bet 7 6 11 0.007278 0.080062
Loss on bet 8 7 16 0.003588 0.057410
Loss on bet 9 8 22 0.001769 0.038916
Loss on bet 10 9 29 0.000872 0.025289
Loss on bet 11 10 37 0.000430 0.015907
Loss on bet 12 11 46 0.000212 0.009749
Loss on bet 13 12 56 0.000104 0.005851
Loss on bet 14 13 67 0.000052 0.003451
Loss on bet 15 14 79 0.000025 0.002006
Loss on bet 16 15 92 0.000013 0.001152
Loss on bet 17 16 106 0.000006 0.000654
Loss on bet 18 17 121 0.000003 0.000368
Loss on bet 19 18 137 0.000001 0.000205
Loss on bet 20 19 154 0.000001 0.000114
Loss on bet 21 20 172 0.000000 0.000063
Win 21 bets 0 212 0.000000 0.000075
Total     1.000000 -0.054950

## Video

Please enjoy my video on the 2-1-2.

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