Good day, everyone.
If you would care to peruse the article on the Labouchere System of Roulette on Wikipedia.org, I wrote the majority of that and it would seem that others viewing that article have felt little need to change it over the years.
I was considering applying the Labouchere System to on-line Blackjack, but have not done so, because it seems that the Terms & Conditions of many casino websites restrict the use of system betting to such an extent that system-betting may void payouts. That is unfortunate because a 3:2 payout on natural Blackjacks would offer an even greater advantage in using the Labouchere System as you could theoretically scratch out three (or more) numbers on your Labouchere list with one natural Blackjack.
Imagine a list of: 2, 2, 2, 2, 2
Let's say you experience two wins, then five losses, then a win, your new list would be:
2, 2, 2,
2, 2, 4
2, 2, 4, 6
2, 2, 4, 6, 8
2, 2, 4, 6, 8, 10
2, 4, 6, 8
The next bet as demanded by the system would be 10, but if you were to hit that for a Natural, the pay would be +15 which would enable you to scratch out the 2, 4, 8 and either reduce the six to a five, or breakdown that five into smaller parts, such as 2, 2, 1.
The advantages are obvious because, given the fact that the player need only prevail 33.34 (or more) percent of the time with the standard Labouchere on an even money bet, the prospect of eliminating more than two numbers for a Natural reduces the necessary winning percentage further. The actual winning percentage completing the line will vary based upon how many Naturals you hit and how you choose to play the remainder.
Why does this not work at a live casino?
Simple: You can't have a pen and paper at a live casino, so it is much more difficult to track your line, and you only have so much space to work with in terms of setting your chips up in a line.
You can generally have a pen and paper at the Roulette Table, but if Labouchere actually worked in practice (in theory works because there are no Limits and an unlimited bankroll) everyone would be doing it. I've tried it live, and you will usually complete 5-10 lines successfully, but the one you lose absolutely clobbers you.
I consider myself a student of Table Game theory, so if anyone is interested in that subject, hit me up via PM oir Chat. I'm strong in mathematics, so I can usually devise a formula to figure out just about anything.
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