# 1-3-2-6 Betting System

## Introduction

The 1-3-2-6 is a simple progressive betting system. It will tend to amplify wins in a good session, but increases losses in a bad or choppy session. I do not know who created it or any history behind it. I've been asked about it so present my explanation and analysis below.

## Rules

Like most betting systems, the 1-3-2-6 is best played in blackjack or any game offering an even money bet. This is a quick system, lasting at most four hands. The player may repeat it as often as desired.

1. Start by defining your unit size. This should be about 1/6 of what you're comfortable losing in a single hand.
2. After any tie, repeat the previous bet.
3. Bet one unit.
4. If the outcome from the first bet is a loss, quit one unit down.
5. If the outcome from the first bet is a win, bet three units on the second hand.
6. If the outcome from the second bet is a loss, quit two units down.
7. If the outcome from the second bet is a win, bet two units on the third hand.
8. If the outcome from the third bet is a loss, quit two units up.
9. If the outcome from the third bet is a win, bet six units on the fourth hand.
10. If the outcome from the fourth bet is a loss, quit breaking even.
11. If the outcome from the fourth bet is a win, quit 12 units up.

Following is my flowchart of how to play. Start in the frame on the left that says "establish unit size." Click on image for larger version.

## Analysis

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on the Player bet in baccarat. The lower right cell shows an expected loss of 0.050308 units per session. The average number of bets per session is 4.073271. The ratio of expected money lost to money bet per session is 0.012351.

### Baccarat Player Bet

Wins Net Win Probability Return
0 -1 0.506825 -0.506825
1 -2 0.249953 -0.499907
2 2 0.123271 0.246542
3 0 0.060794 0.000000
4 12 0.059157 0.709882
Total   1.000000 -0.050308

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on the Banker bet in baccarat. The lower right cell shows an expected loss of 0.044607 units per session. The average number of bets per session is 3.815350. The ratio of expected money lost to money bet per session is 0.010579.

### Baccarat Banker Bet

Wins Net Win Probability Return
0 -1 0.493175 -0.493175
1 -2.05 0.249953 -0.512405
2 1.8 0.126683 0.228029
3 -0.3 0.064206 -0.019262
4 11.4 0.065983 0.752205
Total   1.000000 -0.044607

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on the pass bet in craps. The lower right cell shows an expected loss of 0.052088 units per session. The average number of bets per session is 3.683376.The ratio of expected money lost to money bet per session is 0.014141.

### Craps Pass Bet

Wins Net Win Probability Return
0 -1 0.507071 -0.507071
1 -2 0.249950 -0.499900
2 2 0.123208 0.246415
3 0 0.060733 0.000000
4 12 0.059039 0.708467
Total   1.000000 -0.052088

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on the don't pass bet in craps. The lower right cell shows an expected loss of 0.051671 units per session. The average number of bets per session is 3.789170. The ratio of expected money lost to money bet per session is 0.014026.

### Craps Don't Pass Bet

Wins Net Win Probability Return
0 -1 0.507013 -0.507013
1 -2 0.249951 -0.499902
2 2 0.123223 0.246445
3 0 0.060747 0.000000
4 12 0.059067 0.708799
Total   1.000000 -0.051671

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on any even money bet in single-zero roulette. The lower right cell shows an expected loss of 0.097936 units per session. The average number of bets per session is 3.623616. The ratio of expected money lost to money bet per session is 0.027027.

### Single-Zero Roulette

Wins Net Win Probability Return
0 -1 0.513514 -0.513514
1 -2 0.249817 -0.499635
2 2 0.121533 0.243066
3 0 0.059124 0.000000
4 12 0.056012 0.672147
Total   1.000000 -0.097936

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on any even money bet in double-zero roulette. The lower right cell shows an expected loss of 0.184606 units per session. The average number of bets per session is 3.507508. The ratio of expected money lost to money bet per session is 0.052632.

### Double-Zero Roulette

Wins Net Win Probability Return
0 -1 0.526316 -0.526316
1 -2 0.249307 -0.498615
2 2 0.118093 0.236186
3 0 0.055939 0.000000
4 12 0.050345 0.604139
Total   1.000000 -0.184606

The following table shows the net win, probability, and contribution to the return by following the 1-3-2-6 system on any even money bet in triple-zero roulette. The lower right cell shows an expected loss of 0.261580 units per session. The average number of bets per session is 3.400546. The ratio of expected money lost to money bet per session is 0.076923.

### Triple-Zero Roulette

Wins Net Win Probability Return
0 -1 0.538462 -0.538462
1 -2 0.248521 -0.497041
2 2 0.114702 0.229404
3 0 0.052939 0.000000
4 12 0.045377 0.544519
Total   1.000000 -0.261580

## Video

Please enjoy my video on the 1-3-2-6 betting system.

Direct link: www.youtube.com/watch?v=X_C8LlEKmvY

## Internal Links

Here are some other betting systems I have analyzed.