Labouchere progression (in depth analysis)

Main idea
Labouchere (also called cancellation system or split martingale) is one of the most ingenious betting methods for roulette. It was originally created for betting the Even Chances (or Simple Chances [red, black, high, low, odd, even]). The philosophy, the main idea, is that when your successes are just over half of your failures you make a profit and start over again. To put it in another way, when your losing spins are less than twice the winning spis, you're a winner. For example: if you bet on Black and in 100 total spins, Black comes only 37 times, then you finish the progression with a profit (63 losses are less tan 37*2). This is quite amazing if you think about it.

Description
(There are many variations of the Labouchere system. Most of these variations concern the starting betting sequence. Here we will discuss the classic 1-2-3 starting betting sequence)

• You write three numbers in sequence eg 1 2 3 The sum of these numbers (in this case 1 +2 +3 = 6) will be the profit when you finish this session.
• Bet the sum of the first and last number in your sequence
• When you win erase the two numbers you have bet (the first and the last in your sequence)
• When you lose, you add the sum (your bet) at the end

Example
1,2,3
bet: 1+3=4
lose
add 4 to the end
1,2,3,4
bet: 1+4=5
lose
add the 5 to the end
1,2,3,4,5
bet: 1+5 =6
win
erase 1 and 5
2,3,4
bet: 2+4=6
lose
add 6 to the end
2,3,4,6
bet = 2+6=8
lose
add 8 to the end
2,3,4,6,8
bet: 2+8=10
win,
erase 2 and 8
3,4,6
bet: 3+6=9
lose
add 9 to the end
3,4,6,9
bet: 3+9=12
lose
add 12
3,4,6,9,12
bet: 3+12=15
win
erase 3 and 12
4,6,9
bet 4 +9 = 13
win
erase the 4 and 9
6.
bet 6.
win
End game.

Start over again by writing 1,2,3

In 11 spins, with 6 losses and 5 wins, we won 6 units.
Not bad at all.

Comments
The only way to lose using the Labouchere for even chances, is the losing spins to keep outnumber the winning spins by roughly 2 to 1. In this (rare) case though, your losses can be quite dramatic. They are not as dramatic as say with the Martingale, but still, quite high.

One solution to avoid high bets and high possible losses is to split the sequence into “lighter”, less dangerous sequences. This done like this:
Say after 24 spins your sequence looks like this:
22, 26, 35, 41, 46, 55, 66, 79

You can transform this sequence into 3 separate sequences. The new sequences can be whatever we like. The only requirement is that if added together, they must have a total that equals the total of the original sequence 22+26+35+…+79=340

A: 10, 15, 20, 25, 30, 35, 40, 45 (=220)
B: 15, 15, 15, 15 (=60)
C: 15, 15, 15, 15 (=60)
Total=340

In this case we continue the betting with sequence A, which is much less aggressive and dangerous than the original sequence. Furthermore, after this sequence is completed, we will begin our next 2 sessions with sequences B and C instead of the original “1, 2, 3” sequence. After all these 3 sessions are terminated we start our next attack with the original “1, 2, 3” sequence as usual.

Bet selection
Theoretically, it makes no difference for which even chance bet selection you use the Labouchere progression for. However "Follow the Last" is Kavouras' preferred bet selection on even chances. Follow the Last means betting on the repetition of the last outcome (after red we bet on red etc.). With this bet selection you hope for long strings of the same outcome (ie. same color) and you loose when the outcomes alternate (Red-Black-Red-Black etc.)

The basic idea and progression method of Labouchere - with some modifications - can be applied not only to even chances, but also to other bet selections, (ie. Dozens, streets etc.)