The Labouchere System (or Cancellation System) For Roulette

If the infamous Martingale system may feel a bit like 'betting by numbers', Labouchere offers a little more stimulation, and has caught the attention of thrill-seeking authors like Ian Fleming - who outlines Labouchere as 'the system' in the Monte Carlo section in his collection of travelogues, Thrilling Cities.

The system itself was the brainchild of the charismatic aristocrat Henry Du Pre Labouchere. Labouchere came from a wealthy Huguenot family who had fled France at the beginning of the 19th century. As a young man, he indulged his whims wherever he could, and mixed stints working for a circus and living in an Chippewa Indian colony, with numerous hours spent betting on horses at Newmarket. He would later gain a certain amount of fame as an MP and journalist, but it's for his fascinating little gambling system that he's now principally known.

How It Works

Like Martingale, Labouchere expects that you'll bet repeatedly on a 50/50 selection - such as Red/Black or Odd/Even. But while Martingale requires nothing more than the ability to double numbers in your head, Labouchere has some intricate sequences that'll require most of us to take a notebook and pen to the casino. Let's say you want to win £20. Split it into five portions, and write all five portions down on a piece of paper. We might, for example, use the following portions:

3 4 6 4 3

The idea is that you take the first and last numbers, add them together, and then bet that amount. In the above example, the first and last numbers will give you a total of 6. So you bet £6 on 'red'. If you win the bet, you simply strike out the first and last numbers. You're now left with

4 6 4

You then repeat the process, once more adding the first and last numbers together. 4 and 4 gives you 8, so you bet £8 on red. If that bet wins, you're left with a single 6. You would thus bet £6 on red. If that wins as well, you've cleared the entire row, and have completed the system. Your winnings will amount to £20.

Losing Bets

But what if one of your bets loses? Well, let's go back to the original row above - 3 4 6 4 3. For our first bet, we've added together the 3 and the 3 to give us a bet of £6. If we lose that, we simply add 6 to the end of the row. We now have a line that reads:

3 4 6 4 3 6

As before, we add the first and last numbers - in this case, 3 and 6, giving us a total of 9. So we bet £9 on red. If that loses, we add the 9 to the row, and now have:

3 4 6 4 3 6 9

And so on. Each time you play Labouchere, you must cross off every number on the list before you have won your cash.

 

Better than Martingale?

As a general system, Labouchere works very well. You might imagine that the lines would sometimes become too long, and would take significant periods to clear. In fact, this isn't as serious a problem as it might be. That's because two numbers are being subtracted when you win, but only one is being added when you lose. That 2 for 1 deal helps keep lines pretty manageable - even if you might find your notebooks becoming rather full. In testing, we rarely experienced lines with more than 10 numbers on them, and lines of 15 or more were very rare indeed.

Another nice aspect of Labouchere is that, generally, the numbers remain pretty modest. Let's start off with the 3 4 6 4 3 line above. Start up with five losses in a row, and you would end up with the following:

3 4 6 4 3 6 9 12 15 18

You would need a minimum of five wins to clear this. And the bets will get bigger and bigger. Nonetheless, initially at least, the numbers remain small. In the example above, the sixth bet would set you back £21. In contrast, were you using Martingale, five losses in a row would leave you needing to put down £32 in order to clear your deficit. Another loss would mean betting £64 - with Labouchere, you'd only be up to £24.

Admittedly, winning one bet on Martingale would allow you to completely clear any deficit. On the other hand, it's also true that you would need to play Martingale 20 times - exposing yourself to extreme runs each time - in order to make £20. Labouchere seems to be more drawn out, and less risky. And generally it is. The problem is that, every now and again, Labouchere has a nasty habit of turning on you...

 

When Good Systems Turn Bad

Labouchere's downfall isn't in long sequences of numbers. It's in the way those sequences can throw up some steep betting amounts. The effect is particularly pronounced when the player hits a long sequence of mostly losing bets, punctuated by the occasional win. At the bottom of this page, we've placed a couple of pretty scary sequences. These aren't typical, but they will happen if you play this system for long periods. (Both were recorded in a simulator of roulette, using a European-style table with one green zero square. The results would be even worse on an American-style table)

Exhibit A, for instance, appears to start well. After the third spin, three of the five numbers have been erased. Sadly, though, the system is about to be sabotaged by a violent run against the player. The sequence is still going after 26 spins, and, by now, the next bet is up to £220 - a far cry from that opening bet of £6. After 39 spins, it's over the £500 mark, and after 45 spins, it's beyond £1,000. Ultimately, the maximum bet gets up to £2,220. Despite these heady heights, it takes just three wins in a row to clear the entire set. Nonetheless, somebody starting out with a bet of £6 would have had to swallow a pretty hefty four figure bet in order to get through.

Exhibit B is even worse. This fearsome sequence of numbers stretches up to a bet of £9,560 at one point. We even saw some five figure bets while testing. We should stress that these aren't typical, but you should expect them to happen if you go long enough. If you play for 10,000 spins, you're likely to catch at least one bet of over £1,500. Play for 50,000 spins, and you have a good chance of seeing an Exhibit B-style horror show. The table or betting limits may well exclude you from successfully navigating such a sequence, even if you have the bank balance behind you.

Variations

One of the nice things about Labouchere is that the basic system is highly adaptable, so you can play around with it to your heart's content. The original £20 3 4 6 4 3 sequence could be turned into a three-part 6 8 6 sequence, for instance. Or it could be lengthened to a longer set - 2 2 2 2 2 2 2 2 2 2, perhaps? The 6 8 6 sequence produced some more eye-watering bets, in practise. And while the longer set resulted in fewer 'big bets', there were still plenty of them - it took us twice as long to complete each set, too, so our win rate halved.

You could also change the size of the portions. That 3 4 6 4 3 sequence can be turned into a more stable 4 4 4 4 4. Or you could have a set that alternated small figures with big ones - 2 5 6 2 5, for example. In testing, neither variation made any significant difference.

If the problem is that the figures get too big, why not break figures down into individual sets once they get past a certain point? For instance, take the following sequence:

6 4 10 16

Rather than adding 6 and 16 together, and betting £22, why not break down the 16 into its own sub-sequence of 3 4 2 4 3. Try and clear that amount. If successful, you would be left with a 6 4 10 sequence instead, and would have 'eliminated' the 16. The problem is that this can make games very long-winded and tedious. We've already seen from Exhibits A and B how a fairly short sequence of three wins can wipe out a seemingly massive deficit. If you're in the middle of a long losing sequence, breaking big numbers down into sub-sets will still result in some big figures being bandied about.

So is Labouchere of any worth?

Well, the sheer quantity of variations makes this a fascinating system to play around with. And Labouchere does create a game within a game, mesmerising onlookers with its falling and rising sequences. Compared to the rather mechanical and joyless Martingale, Labouchere has a lot to offer. However, the bets can get cripplingly high, and there isn't really any jumping-out point. If you're betting a very small amount compared to your budget, it could make sense - although whether this would allow you to make enough to compensate you for your time is open for question. Overall, though, it's a system to be treated with caution.

Pros

Interesting system to play
Lots of variations
Can work indefinitely provided your bank is big enough, and table/betting limits don't come into play

Cons

Bets can become absolutely massive relative to your starting bet
Can get out of control very easily
No obvious jumping out point
Generally needs a big notepad and pen

Exhibit A

Starting Sequence - 3 4 6 4 3

Lost (6): 3 4 6 4 3 6
Won (4): 4 6 4 3
Won (2): 6 4
Lost (3): 6 4 10
Lost (4): 6 4 10 16
Lost (5): 6 4 10 16 22
Lost (6): 6 4 10 16 22 28
Won (4): 4 10 16 22
Lost (5): 4 10 16 22 26
Lost (6): 4 10 16 22 26 30
Won (4): 10 16 22 26
Lost (5): 10 16 22 26 36
Lost (6): 10 16 22 26 36 46
Lost (7): 10 16 22 26 36 46 56
Lost (8): 10 16 22 26 36 46 56 66
Won (6): 16 22 26 36 46 56
Lost (7): 16 22 26 36 46 56 72
Lost (8): 16 22 26 36 46 56 72 88
Won (6): 22 26 36 46 56 72
Lost (7): 22 26 36 46 56 72 94
Lost (8): 22 26 36 46 56 72 94 116
Lost (9): 22 26 36 46 56 72 94 116 138
Won (7): 26 36 46 56 72 94 116
Lost (8): 26 36 46 56 72 94 116 142
Lost (9): 26 36 46 56 72 94 116 142 168
Lost (10): 26 36 46 56 72 94 116 142 168 194
Won (8): 36 46 56 72 94 116 142 168
Lost (9): 36 46 56 72 94 116 142 168 204
Lost (10): 36 46 56 72 94 116 142 168 204 240
Won (8): 46 56 72 94 116 142 168 204
Won (6): 56 72 94 116 142 168
Won (4): 72 94 116 142
Lost (5): 72 94 116 142 214
Lost (6): 72 94 116 142 214 286
Won (4): 94 116 142 214
Lost (5): 94 116 142 214 308
Won (3): 116 142 214
Lost (4): 116 142 214 330
Lost (5): 116 142 214 330 446
Lost (6): 116 142 214 330 446 562
Won (4): 142 214 330 446
Lost (5): 142 214 330 446 588
Lost (6): 142 214 330 446 588 730
Won (4): 214 330 446 588
Lost (5): 214 330 446 588 802
Lost (6): 214 330 446 588 802 1016
Lost (7): 214 330 446 588 802 1016 1230
Lost (8): 214 330 446 588 802 1016 1230 1444
Won (6): 330 446 588 802 1016 1230
Lost (7): 330 446 588 802 1016 1230 1560
Lost (8): 330 446 588 802 1016 1230 1560 1890
Won (6): 446 588 802 1016 1230 1560
Won (4): 588 802 1016 1230
Won (2): 802 1016

Exhibit B

Starting Sequence - 3 4 6 4 33 4 6 4 3

Lost (6): 3 4 6 4 3 6
Lost (7): 3 4 6 4 3 6 9
Lost (8): 3 4 6 4 3 6 9 12
Lost (9): 3 4 6 4 3 6 9 12 15
Lost (10): 3 4 6 4 3 6 9 12 15 18
Won (8): 4 6 4 3 6 9 12 15
Lost (9): 4 6 4 3 6 9 12 15 19
Lost (10): 4 6 4 3 6 9 12 15 19 23
Won (8): 6 4 3 6 9 12 15 19
Lost (9): 6 4 3 6 9 12 15 19 25
Won (7): 4 3 6 9 12 15 19
Lost (8): 4 3 6 9 12 15 19 23
Lost (9): 4 3 6 9 12 15 19 23 27
Won (7): 3 6 9 12 15 19 23
Lost (8): 3 6 9 12 15 19 23 26
Lost (9): 3 6 9 12 15 19 23 26 29
Lost (10): 3 6 9 12 15 19 23 26 29 32
Won (8): 6 9 12 15 19 23 26 29
Lost (9): 6 9 12 15 19 23 26 29 35
Won (7): 9 12 15 19 23 26 29
Lost (8): 9 12 15 19 23 26 29 38
Won (6): 12 15 19 23 26 29
Lost (7): 12 15 19 23 26 29 41
Lost (8): 12 15 19 23 26 29 41 53
Lost (9): 12 15 19 23 26 29 41 53 65
Lost (10): 12 15 19 23 26 29 41 53 65 77
Won (8): 15 19 23 26 29 41 53 65
Lost (9): 15 19 23 26 29 41 53 65 80
Lost (10): 15 19 23 26 29 41 53 65 80 95
Lost (11): 15 19 23 26 29 41 53 65 80 95 110
Lost (12): 15 19 23 26 29 41 53 65 80 95 110 125
Lost (13): 15 19 23 26 29 41 53 65 80 95 110 125 140
Lost (14): 15 19 23 26 29 41 53 65 80 95 110 125 140 155
Lost (15): 15 19 23 26 29 41 53 65 80 95 110 125 140 155 170
Won (13): 19 23 26 29 41 53 65 80 95 110 125 140 155
Won (11): 23 26 29 41 53 65 80 95 110 125 140
Lost (12): 23 26 29 41 53 65 80 95 110 125 140 163
Lost (13): 23 26 29 41 53 65 80 95 110 125 140 163 186
Lost (14): 23 26 29 41 53 65 80 95 110 125 140 163 186 209
Won (12): 26 29 41 53 65 80 95 110 125 140 163 186
Won (10): 29 41 53 65 80 95 110 125 140 163
Won (8): 41 53 65 80 95 110 125 140
Won (6): 53 65 80 95 110 125
Lost (7): 53 65 80 95 110 125 178
Won (5): 65 80 95 110 125
Lost (6): 65 80 95 110 125 190
Lost (7): 65 80 95 110 125 190 255
Won (5): 80 95 110 125 190
Won (3): 95 110 125
Lost (4): 95 110 125 220
Lost (5): 95 110 125 220 315
Lost (6): 95 110 125 220 315 410
Lost (7): 95 110 125 220 315 410 505
Won (5): 110 125 220 315 410
Lost (6): 110 125 220 315 410 520
Won (4): 125 220 315 410
Lost (5): 125 220 315 410 535
Lost (6): 125 220 315 410 535 660
Lost (7): 125 220 315 410 535 660 785
Lost (8): 125 220 315 410 535 660 785 910
Lost (9): 125 220 315 410 535 660 785 910 1035
Won (7): 220 315 410 535 660 785 910
Won (5): 315 410 535 660 785
Won (3): 410 535 660
Lost (4): 410 535 660 1070
Won (2): 535 660
Lost (3): 535 660 1195
Lost (4): 535 660 1195 1730
Won (2): 660 1195
Lost (3): 660 1195 1855
Won (1): 1195
Lost (2): 1195 1195
Lost (3): 1195 1195 2390
Lost (4): 1195 1195 2390 3585
Lost (5): 1195 1195 2390 3585 4780
Lost (6): 1195 1195 2390 3585 4780 5975
Lost (7): 1195 1195 2390 3585 4780 5975 7170
Lost (8): 1195 1195 2390 3585 4780 5975 7170 8365
Won (6): 1195 2390 3585 4780 5975 7170
Won (4): 2390 3585 4780 5975
Won (2): 3585 4780