Baccarat, Labouchere, and Regression to the Mean

[traynor]

Some of you may find this interesting. It is excerpted from a recent newsletter that stirred up a world of discussion because we referred to "patterns" in events that are not normally considered susceptible to pattern analysis. The excerpt is a fairly complete explanation of the use of the Labouchere method in baccarat.

<snip>
In addition to the areas explained below, there is a lot of confusion about the
statement that "patterns" exist in what are normally considered random-variable events with no cause-and-effect relationships. The classic example is the question, "If you are flipping a (normal) coin and it comes up heads 10 times in a row, what are the odds that it will come up heads in the 11th flip?" The answer, of course, is 50-50, or a 50% probability.

However, that is ONLY for the 11th flip. Because of a phenomena called "regression to the mean" that has written about elsewhere on this site on a number of occasions, it is slightly more likely that in the next sequence, there will be (again, slightly) more tails than heads. The number in the sequence varies; it may be the next 10, or it may be the excess number of heads in the small sample were in fact "regressing to the mean" to even out an excess number of tails in previous flips.

The application of regression to the mean has enabled a number of very sophisticated bettors to turn a number of casinos into "cash cows" using a fairly simple technique that builds on the Labouchere "cancellation" method originally developed for roulette.

The advantage gained by regression to the mean may be slight, but in conjunction with a Labouchere wagering strategy applied to baccarat, chemin-de-fer, punto banco, or Bank Craps, it is sufficient to enable substantial profits to be derived from situations that the casino personnel believe "impossible."

In fact, the belief in the "Gambler's Fallacy" as a sucker theory is so highly-developed that casinos often install colorful "result trackers" on roulette tables, with the outcome of the last 15 or so coups brightly visible to all who care to look. The idea is that the gullible tourist will see that red has won the last half dozen coups, be convinced that black is "due," and wager accordingly.

How It Plays Out In The Real World
The Labouchere wagering strategy attempts to slightly increment wagers after a loss to increase the amount returned on the wins; the variation is slight, in most cases, and many have used it over the years to win modest amounts with grinder play at roulette. Others have modified the method to use at baccarat and Bank Craps, with substantially improved return.

The modification is simple, and can be as effectively used by competent blackjack players as by baccarat or Bank Craps bettors. The Labouchere uses 1-2-3 as a "series" of wagering units. The two outside digits are wagered (4). If the bet wins, the next wager is the remaining digit, (2). If that is won, the series is completed with a net gain of 6 units, and a new series is started. If any wager is lost, the amount wagered is added to the end of the series, and the next wager is again the two outside digits. Wagering continues until the series is "cancelled," with the associated profit of 6 betting units.

Regression to the mean is added to the mix because each series is implemented when there is an "excess" in the oppostie direction; if you are playing baccarat at the minimum level to keep your seat, and playing Banker, your series starts when Player has won three coups in a row. The new series uses your "normal" betting unit, rather than the token wagers used to stay in action. The effect is similar to backcounting in blackjack; the tendency is to bet more in positive expectation situations.

Yes, we are well aware that it is "mathematically impossible" to gain an advantage using a Labouchere. Yes, we are well aware that the Gambler's Fallacy is a belief in another impossibility. We have no interest whatsoever in debating the situation. However, in the real world, outside the theory, and the forums, and the "expert opinion," there are a number of very adept professional bettors who are laughing all the way to the bank with their winnings, and have done so for a number of years with a regularity that would give a casino pit boss a fit of hysteria if known.

Good Luck!

[aslan]

Is what he is saying something like this? If red comes up 10 times in a row, then over the next hundred spins you should expect a slight tendency for black to come up more than red? Is that possible? I know the very next time it is 50/50. But what about the next hundred spins? Hmmm. Experts, can there be any truth to this assertion?

If such were true, a player must be 100% sure he is not playing on a biased wheel, which could cause unusual occurrences (such as ten reds in a row) to reoccur again and again. The Labouchere player would surely go broke in such a case.

[moo321]

No, not possible. This article relies on logical fallacies, such as short-term luck. You can't beat baccarat unless they deal it to the last card, or the cards are marked.

[aslan]

Originally Posted by moo321

No, not possible. This article relies on logical fallacies, such as short-term luck. You can't beat baccarat unless they deal it to the last card, or the cards are marked.

Aside from Baccarat, are you rejecting the notion of patterns of chance occurrences?

[Guynoire]

I disagree. I think your logic is flawed; here’s an example let’s say you are going to flip a coin 100 times and expect it to come out 50 heads and 50 tails, but on this particular sequence the first 10 flips come out to be heads. You now ask yourself what is my expected number of heads, the answer 55. How did I get this number, I just took the remaining 90 and multiplied it by it’s expected value and added it to the previous total. Yes your sequence does regress towards the mean of 50, but guess what you’re never going to be able to make bets on the entire sequence. You’re only going to be able to make bets on that remaining 90 and those bets are still expected to act normally, you haven’t changed the probabilities on the bets you will be making.

[aslan]

Originally Posted by Guynoire

I disagree. I think your logic is flawed; here’s an example let’s say you are going to flip a coin 100 times and expect it to come out 50 heads and 50 tails, but on this particular sequence the first 10 flips come out to be heads. You now ask yourself what is my expected number of heads, the answer 55. How did I get this number, I just took the remaining 90 and multiplied it by it’s expected value and added it to the previous total. Yes your sequence does regress towards the mean of 50, but guess what you’re never going to be able to make bets on the entire sequence. You’re only going to be able to make bets on that remaining 90 and those bets are still expected to act normally, you haven’t changed the probabilities on the bets you will be making.

It's not MY logic. Read back, it's traynor's. I'm just trying to get him a fair hearing, and am interested in the logic pro/con myself. lol It makes perfect sense, what you say. Are there any opposing points of view? Is traynor mistaken when he says, "Because of a phenomena called "regression to the mean" ..., it is slightly more likely that in the next sequence, there will be (again, slightly) more tails than heads," or has Guynoire completely addressed and busted traynor's notion?

[Guynoire]

I wasn't disagreeing with your post aslan, I disagree with the original thread. I think this is just another betting system and this discussion should be in the voodoo section.

[Sonny]

I think Guynoire explained things pretty well. Curiously, Traynor decided to post this message the same day that I posted an explanation of why this type of logic is flawed:

http://www.blackjackinfo.com/bb/show...7906#post67906

-Sonny-

[moo321]

Originally Posted by Guynoire

I disagree. I think your logic is flawed; here’s an example let’s say you are going to flip a coin 100 times and expect it to come out 50 heads and 50 tails, but on this particular sequence the first 10 flips come out to be heads. You now ask yourself what is my expected number of heads, the answer 55. How did I get this number, I just took the remaining 90 and multiplied it by it’s expected value and added it to the previous total. Yes your sequence does regress towards the mean of 50, but guess what you’re never going to be able to make bets on the entire sequence. You’re only going to be able to make bets on that remaining 90 and those bets are still expected to act normally, you haven’t changed the probabilities on the bets you will be making.

Bottom line: it's voodoo, and it doesn't work. If you can't computer sim it, or show it working over the long run by experimentation, it almost certainly doesn't work.

[davidpom]

All I know is this: past events are no accurate predictor of future ones.

Systems like this seem doomed to fail. That's like saying that because 17 black hasn't spun on a roulette wheel for 100 spins that its "due". Standard deviation would say yes, but actual results may differ. It might be 10000 spins until it shows up.

I'm thinking this is why most labouchere, progressive, and martingale systems are ultimately doomed. I once saw 22 blacks come up in a row on a roulette wheel. Statistically possible, yes. Common, no. But a martingale better (for example) would have hit table max at about bet 8, and would have certainly been completely scr**ed after that...