# Rothstein Betting System

## Introduction

The Rothstein is a betting system closely related to the Martingale. The difference is with the Rothstein, the player increases his bets more aggressively, ensuring one unit of profit for every bet made, as long as he doesn't go broke. This is unlike the Martingale, where the player has a net win of one unit for every bet won. The tradeoff is the player will go broke faster if he doesn't see a win.

## Rules

The only difference between the Rothstein and the Martingale is the Rothstein adds one more unit to each bet after a loss, compared to the Martingale.  In other words, instead of doubling the previous bet after a loss, you double it and then add one more unit.  Following are the details.

1. As with most betting systems, it is best explained and applied on games with even money bets.
2. The player must choose a unit size and a bankroll. The first ten bankroll sizes in units are: 1,4,11,26,57,120,247,502,1013,2036. Note how as they get large they are slightly less than powers of 2. To be specific, they can all be expressed as 2n+1-(n+2), where n is the maximum number of consecutive losses.
3. Player starts by making a one-unit bet.
4. If last bet made wins, quit and walk away with a net win of one unit for every bet made.
5. If last bet made loses, then bet two times the previous bet plus one more unit next time.
6. Repeat until you either win a bet or go bust trying.

Note that the bet sizes (in units) will be powers of 2 minus one:  1, 3, 7, 15, 31, 63, etc..

## Five Step Analysis

The following table shows my analysis based on the pass bet in craps where the player can make up to five bets. The worst case scenario, with five losses, is a loss of 57 units.

### Five Step Analysis — Craps Pass Bet

Loses Net Win Probability Expected Win
0 1 0.492929 0.492929
1 2 0.249950 0.499900
2 3 0.126742 0.380227
3 4 0.064267 0.257069
4 5 0.032588 0.162940
5 -57 0.033523 -1.910810
Total   1.000000 -0.117744

The following is my summary of the table above.

• Expected net win = -0.117744 units
• Expected total bet = 8.326175 units
• Ratio of expected win to expected total bet = -1.41%

The following table shows my analysis based on the don't pass bet in craps where the player can make up to five bets. The worst case scenario, with five losses, is a loss of 57 units. For purposes of my analysis, I don't count pushes (12 on the come out roll) as a bet resolved.

### Five Step Analysis — Craps Don't Pass Bet

Loses Net Win Probability Expected Win
0 1 0.493182 0.493182
1 2 0.249954 0.499907
2 3 0.126681 0.380043
3 4 0.064204 0.256817
4 5 0.032540 0.162699
5 -57 0.033440 -1.906057
Total   1.000000 -0.113409

The following is my summary of the table above.

• Expected net win = -0.113409 units
• Expected total bet = 8.316626 units
• Ratio of expected win to expected total bet = -1.36%

The following table shows my analysis based on any even money bet in single-zero roulette where the player can make up to five bets. The worst case scenario, with five losses, is a loss of 57 units.

### Five Step Analysis — Single-Zero Roulette Even Money Bets

Loses Net Win Probability Expected Win
0 1 0.486486 0.486486
1 2 0.249817 0.499635
2 3 0.128285 0.384854
3 4 0.065876 0.263504
4 5 0.033828 0.169141
5 -57 0.035707 -2.035327
Total   1.000000 -0.231708

The following is my summary of the table above.

• Expected net win = -0.231708 units
• Expected total bet = 8.573191 units
• Ratio of expected win to expected total bet = -2.70%

The following table shows my analysis based on any even money bet in double-zero roulette where the player can make up to five bets. The worst case scenario, with five losses, is a loss of 57 units.

### Five Step Analysis — Double-Zero Roulette Even Money Bets

Loses Net Win Probability Expected Win
0 1 0.473684 0.473684
1 2 0.249307 0.498615
2 3 0.131214 0.393643
3 4 0.069060 0.276241
4 5 0.036347 0.181737
5 -57 0.040386 -2.302008
Total   1.000000 -0.478087

The following is my summary of the table above.

• Expected net win = -0.478087 units
• Expected total bet = 9.083655 units
• Ratio of expected win to expected total bet = -5.26%

The following table shows my analysis based on the Player bet in baccarat where the player can make up to five bets. The worst case scenario, with five losses, is a loss of 57 units. I do not count tie outcomes as a bet resolved.

### Five Step Analysis — Player Bet in Baccarat

Loses Net Win Probability Expected Win
0 1 0.493175 0.493175
1 2 0.249953 0.499907
2 3 0.126683 0.380048
3 4 0.064206 0.256824
4 5 0.032541 0.162706
5 -57 0.033442 -1.906182
Total   1.000000 -0.113523

The following is my summary of the table above.

• Expected net win = -0.113523 units
• Expected total bet = 8.316877 units
• Ratio of expected win to expected total bet = -1.36%

Please note that 1.36% is the house edge on the Player bet if ties are not counted as a bet resolved.

## Ten Step Analysis

The following table shows my analysis based on the pass bet in craps where the player can make up to ten bets. The worst case scenario, with ten losses, is a loss of 2036 units.

### Ten Step Analysis — Craps Pass Bet

Loses Net Win Probability Expected Win
0 1 0.492929 0.492929
1 2 0.249950 0.499900
2 3 0.126742 0.380227
3 4 0.064267 0.257069
4 5 0.032588 0.162940
5 6 0.016524 0.099147
6 7 0.008379 0.058653
7 8 0.004249 0.033990
8 9 0.002154 0.019390
9 10 0.001092 0.010924
10 -2036 0.001124 -2.288037
Total   1.000000 -0.272866

The following is my summary of the table above.

• Expected net win = -0.272866 units
• Expected total bet = 19.295522 units
• Ratio of expected win to expected total bet = -1.41%

The following table shows my analysis based on the don't pass bet in craps where the player can make up to ten bets. The worst case scenario, with ten losses, is a loss of 2036 units. For purposes of my analysis, I don't count pushes (12 on the come out roll) as a bet resolved.

### Ten Step Analysis — Craps Don't Pass Bet

Loses Net Win Probability Expected Win
0 1 0.493182 0.493182
1 2 0.249954 0.499907
2 3 0.126681 0.380043
3 4 0.064204 0.256817
4 5 0.032540 0.162699
5 6 0.016492 0.098951
6 7 0.008358 0.058508
7 8 0.004236 0.033889
8 9 0.002147 0.019323
9 10 0.001088 0.010881
10 -2036 0.001118 -2.276668
Total   1.000000 -0.262467

The following is my summary of the table above.

• Expected net win = -0.262467 units
• Expected total bet = 19.247601
• Ratio of expected win to expected total bet = -1.36%

The following table shows my analysis based on any even money bet in single-zero roulette where the player can make up to ten bets. The worst case scenario, with ten losses, is a loss of 2036 units.

### Ten Step Analysis — Single-Zero Roulette Even Money Bets

Loses Net Win Probability Expected Win
0 1 0.486486 0.486486
1 2 0.249817 0.499635
2 3 0.128285 0.384854
3 4 0.065876 0.263504
4 5 0.033828 0.169141
5 6 0.017371 0.104227
6 7 0.008920 0.062442
7 8 0.004581 0.036646
8 9 0.002352 0.021170
9 10 0.001208 0.012079
10 -2036 0.001275 -2.595951
Total   1.000000 -0.555767

The following is my summary of the table above.

• Expected net win = -0.555767 units
• Expected total bet = 20.563375 units
• Ratio of expected win to expected total bet = -2.70%

The following table shows my analysis based on any even money bet in double-zero roulette where the player can make up to ten bets. The worst case scenario, with ten losses, is a loss of 2036 units.

### Ten Step Analysis — Double-Zero Roulette Even Money Bets

Loses Net Win Probability Expected Win
0 1 0.473684 0.473684
1 2 0.249307 0.498615
2 3 0.131214 0.393643
3 4 0.069060 0.276241
4 5 0.036347 0.181737
5 6 0.019130 0.114782
6 7 0.010069 0.070480
7 8 0.005299 0.042394
8 9 0.002789 0.025102
9 10 0.001468 0.014679
10 -2036 0.001631 -3.320793
Total   1.000000 -1.229435

The following is my summary of the table above.

• Expected net win = -1.229435 units
• Expected total bet = 23.359270 units
• Ratio of expected win to expected total bet = -5.26%

The following table shows my analysis based on the Player bet in baccarat where the player can make up to ten bets. The worst case scenario, with ten losses, is a loss of 2036 units. I do not count a tie as a bet resolved.

### Ten Step Analysis — Player Bet in Baccarat

Loses Net Win Probability Expected Win
0 1 0.493175 0.493175
1 2 0.249953 0.499907
2 3 0.126683 0.380048
3 4 0.064206 0.256824
4 5 0.032541 0.162706
5 -57 0.033442 -1.906182
Total   1.000000 -0.113523

The following is my summary of the table above.

• Expected net win = -0.262740 units
• Expected total bet = 19.248861 units
• Ratio of expected win to expected total bet = -1.36%

Please note the house edge on the Player bet is 1.36% if ties are not counted as a bet resolved.

## Conclusion

My conclusion is the same as my conclusion for every betting system. The ratio of the expected win to the expected amount bet always equals how much the player can expected to lose on each individual bet. In other words, the product of -1 and the house edge. Measure this way, as how much the player can expect to lose compared to total amount bet, all betting systems are equally worthless.

That said, if you must use a betting system, please use a free one, like the Rothstein, as opposed to paying some quack/con artist for one.

## Video

Please enjoy my video on the Rothstein betting system.