# The Gambler’s Fallacy – Page 2

Thought I would give a little update to this thread. Yes, I count cards. Yes, I incorporate mean regression into my play. If you run 10,000 sims of 100 rounds each (1 million hands) you will see that the occurance of dealer wins greater than 62 (10 hands over ‘expectation’) is pretty infrequent. When the count is in my favor and I am well below my win expection, I ramp more aggresively. In contrast, when I am well above my win expectation and the count goes high… I will be a little more conservative. I know a lot of people think this is pure crap. I have spent a lot of time looking at mean regression and its potential as an added “tool” to the game. I have come to the conclusion that it has some added benefit to my game. I am not suggesting anyone else go out and use this technique. For one thing, it is not easy keeping the count (with conversions), making indices adjustments, and dividing wins by total hands to convert to a % that can be compared to expectations. I am good at math, and it took me over a year to become comfortable with all of those spot calcuations

The bottom line is, mean regression exists and is a mathematical fact. Is it a stand alone system? No way. Is it a viable tool that can be added to a player’s box of toys to help win more money at a faster rate? I believe it can be. I know most of the forum members will disagree. I respect your opinions. I am not trying to convince anyone of anything. I am not selling anything. The only thing that really counts for me is my bankroll and the amount over that that I have been able to pull out to help clean up my personal balance sheet as I approach retirement. To that end, things have been going very well.

Regards to all,

• Sonny
When the count is in my favor and I am well below my win expection, I ramp more aggresively. In contrast, when I am well above my win expectation and the count goes high… I will be a little more conservative.

Those short-term results have no bearing on what will happen in the future. Just because you are below expectation does not mean that you are due for a win. That is the gambler’s fallacy.

The times that you are underbetting are probably offset by the times you are overbetting so it may not affect your EV much, but it will increase your variance and therefore your probability of going broke. You are increasing your risk without increasing your profit. That is something you need to consider. As long as it doesn’t bother you, everything is fine. It’s not something that most people would consider a beneficial tool though.

The bottom line is, mean regression exists and is a mathematical fact.

It is a mathematical fact but it is not what you think it is. The percentages will regress towards the mean but the individual results probably will not. The second post in this thread explains the difference. It’s a very common misconception, which is why I made this a sticky thread in the Voodoo forum.

-Sonny-

• rrwoods

Just to throw yet another way of saying the same thing on the pile (you never know what phrasing will make something “click”) —

If you look at a chart of some number of wins and losses — past wins and losses — it is easy to say that the total number of losses “probably” won’t exceed X over Y hands, or similarly that a streak containing X losses “probably” won’t happen over a Y-hand session. Using that statistical information, it’s also easy to extrapolate this to a future session, and say that if the session is Y hands, your total/maximum-in-a-row losses “probably” won’t exceed X. You can even assign a certainty to those numbers, if you have the mathematical knowledge.

However, the Gambler’s Fallacy is conflating statistical predictions about a large number of hands with statistical predictions about a single hand. Predictions about large numbers of hands are derived from predictions about single hands — *not* the other way around!

When you have lost X hands (in a row, if you so choose), the likelyhood of you losing the next hand is *exactly* the same as it was before you started playing. It is *because* of this — not in spite of it! — that the Law of Large Numbers is true (what is being referred to as “mean regression” in this thread). See Sonny’s example about the number of heads and tails on a series of coin flips, where despite the *number* flips of difference increasing, the *ratio* representing that difference decreases.

I hesitate to keep this going… I don’t want to offend anyone. I will try to wrap up my thoughts with this:

I have spent A LOT of time studying this. It is not only mean regression, but also streak theory, retracement theory, and elliot wave anlysis. A lot of this has applications in the financial markets as well. The people who I have looked at this with are well qualified in their fields (1 phd in statistics and 1 phd in combinatorial mathematics). I say this only to convey that I have given this serious consideration, not to try and change your minds. Some important conclusions we have reached are:

1) From an EV perspective of a straight counter, there is really no harm.

2) As it affects an individual player, Mean regression may not occur, but it certainly may occur. It is more likely than not that it will.

3) Of course no one knows the outcome of the next hand, next stock tick, or next currency pip. Or the next 10 for that matter. However, if after 50 hands you are 10 wins below expectation, it is more likely than not that some regression (or retacement) will take place within the next 50 hands. No guarantee, of course.

Given these statements (taken together), there is no reason not to be more aggresive in good counts if potential mean regession warrants it. If mean regression occurs, as explained, it should give a good boost to earnings. If it does not occur, the downside risks are limited.

Regards

• WRX
It is not only mean regression, but also streak theory, retracement theory, and elliot wave anlysis.

There’s a reason this is in the Voodoo Betting forum.

• muppet
I have spent A LOT of time studying this. It is not only mean regression, but also streak theory, retracement theory, and elliot wave anlysis.

after some quick googles for definitions of these terms, streak theory, retracement theory, and elliot wave analysis simply are not applicable to blackjack. please elaborate on how these concepts are in any way pertinent to this discussion.

2) As it affects an individual player, Mean regression may not occur, but it certainly may occur. It is more likely than not that it will.

3) Of course no one knows the outcome of the next hand, next stock tick, or next currency pip. Or the next 10 for that matter. However, if after 50 hands you are 10 wins below expectation, it is more likely than not that some regression (or retacement) will take place within the next 50 hands. No guarantee, of course.

Given these statements (taken together), there is no reason not to be more aggresive in good counts if potential mean regession warrants it.

your expectation on your next hand is independent of your ’10 wins below expectation’. if your ev was +1% before the bad cards, the next time you sit down to play there it will still be +1%.

it is more likely than not that some regression will happen, but that fact is completely irrelevant to what you should bet – because it does not increase your ev. it’s the same as it was before your bad luck.

and this is completely beside point above, but: anything can happen in the next ’50 hands.’ 50 hands is statistically insignificant. sims are done with millions or billions of hands for a reason.

you may want to reread sonny’s first post on the second page:

Quote: Sonny said:
In theory, the regression is always happening. The problem is that it happens so slowly, and with such high variance, that it is difficult for us to see in the short-term. Here’s how most gamblers think of it: If you have a coin that lands on heads 10 times in a row, how do you know that it isn’t just regressing from 10 tails that happened before? How do you know that the coin isn’t at it’s mean after those 10 heads? Maybe it just “evened out” and now you’re betting on a completely random coin. You don’t know.

In reality, the fact that a coin lands on heads 10 times in a row doesn’t mean that the coin is “uneven” at all. It doesn’t mean anything. As Guynoire said, you would expect it to be 10 heads ahead for the rest of its life. If you flip that coin 100,000 more times it will average 50,010 heads and 50,000 tails. But, as the number of flips increases, those ten flip become less significant. The coin still may exhibit a bias, but the percentages become smaller as the number of flips increases. And don’t forget, the percentages can approach the expected 50/50 results even though the difference between the number of heads/tails is increasing.

This theory works in reverse as well. Imagine that the coin has been flipped 100,000 times before you flipped 10 heads in a row. You would expect 50,000 heads in the past, so now it has 50,010 heads and 50,000 tails. The coin is still at 50/50 and there is no reason to expect it to behave any differently than before.

-Sonny-

• assume_R

Well put, muppet. Sonny’s post clearly indicates the common misconception about streaks. The point is that the average win rate comes about not because the “numerator” of the mean value (total wins / total hands) corrects itself, but rather the “denominator”, if that makes any sense.

• rrwoods

Elliot wave theory has nothing to do with casino gambling. The forces that produce Elliot Waves simply are not present.

“Mean regression”, defined in terms of the gambler’s fallacy, simply does not occur.

“Mean regression”, defined in terms of the Law of Large Numbers, definitely occurs. It is easy to conflate the two and hard to “see the light”.

Quote: rrwoods said:
Elliot wave theory has nothing to do with casino gambling. The forces that produce Elliot Waves simply are not present.

“Mean regression”, defined in terms of the gambler’s fallacy, simply does not occur.

“Mean regression”, defined in terms of the Law of Large Numbers, definitely occurs. It is easy to conflate the two and hard to “see the light”.

Please chart your wins and losses on an x/y axis. The graph produced will look remarkably similar to any stock or forex chart. There are ups, downs, and retracements. If you take the names off the charts, you cannot tell which is which. Elliot Waves are present on all the charts, as are retracements that are correlated to fibonacci numbers. Perhaps when I say mean regression, I should say “regress towards the mean”, as it is surely true that quite often you will never regress back fully to the mean, or expectation. The question is, will you keep progessing away from the mean, or will you have some form of retacement towards it? And what are the probablities of each occuring? I believe that thorough the analysis of the above mentioned elements, I can identify situations when some retacement is more likley than not, thus giving me the opportunity to bet a little more aggresively and increase my earnings. How often do I use it? Not that often. I probably (from my experience playing) see an opportunity once every 2 or 3 hours of play. It is just an added tool in my game. Thus far, it has been a nicely profitable addition. I know this is anecdotal, but my account appreciates it non the less!

Finally, let me say that regression, retracement, elliot waves, and streak theory have ABSOLULTLEY NOTHING to do with counting cards. They are seperate disciplines unto themselves. These tools simply try to give you an idea of when you may be more likley to be a net winner in a series of hands.

I wish I had not updated this thread. The vast majority of folks could never implement this strategy…. and those with the brainpower to do it never will without first seeing for themselves the hard, proveable research. I cannot give out that research, as it is propritarey to the guys (the 2 phd’s) that produced it, and up till now they have chosen not to release it or publish it. So, even if what I am saying has any merit…it is really not doing anybody any good.

Again, I know you all disagree with me and I respect your thoughts. It is posted in the voodoo forum!

Regards,

• muppet

Quote: muppet said:

Yes, I read it. I thought I tried to answer your questions in the post above. If I did not, then I apologize. As to your point that EW, mean regression, retracemnt analysis, and streak theory have nothing to do with blackjack, I obviously disagree. These can be applied to any system (balanced or unbalanced) that is random in nature. The nature of blackjack is similar to stock markets, and remarkably similar to foreign echange markets. I fear that I will not be able to adequatley answer your questions. However, as long as the discourse is civil, I will try if that is what you wish.

Regards,

• QFIT
Yes, I read it. I thought I tried to answer your questions in the post above. If I did not, then I apologize. As to your point that EW, mean regression, retracemnt analysis, and streak theory have nothing to do with blackjack, I obviously disagree. These can be applied to any system (balanced or unbalanced) that is random in nature. The nature of blackjack is similar to stock markets, and remarkably similar to foreign echange markets. I fear that I will not be able to adequatley answer your questions. However, as long as the discourse is civil, I will try if that is what you wish.

Regards,

Sorry, but this is incorrect. Financial markets include moderating pressures. Kind of like fluids and gasses. If you swing to one direction, there are pressures that increase the probability of a swing in the other direction. No such pressures exist in an independent trials system.

• assume_R

Yeah, the point seems to be whether or not adventureboy believes there are “pressures” which are “pushing” the system back towards the mean. pressures reacting to the current state of the system assumes that they aren’t truly independent trials. random in the independent trials sense will regress towards the mean, but not because of a corrective pressure

Also, I’m kind of surprised, and mildly impressed, that this discussion has remained civil! kudos to all

Quote: QFIT said:
Sorry, but this is incorrect. Financial markets include moderating pressures. Kind of like fluids and gasses. If you swing to one direction, there are pressures that increase the probability of a swing in the other direction. No such pressures exist in an independent trials system.

Yes, you are correct in that the pressures exerted on each are different. However, what is interesting is that they move in very similar ways. I don’t care why something happens or about the forces that bring it about. I just care if I can predict it and make money on it. In that sense, I am a “technical”, not “fundamental” trader of stocks and player of blackjack. If you graph 10,000 hands of blackjack, you will see that the graph lookes remarkably like a foreign exhange graph. Move and retrace, move and retrace, move and retrace. Those retracements can, at times, be explotied. Not always, but at times.

REgards

• QFIT
Those retracements can, at times, be explotied. Not always, but at times.

REgards

Well, you’re on the right page. This is pure voodoo. And, it is the very definition of “gambler’s fallacy.” There exists no force to cause “retracements.” Cards have no memory, no emotions and no support levels. They’re just cards.

Quote: QFIT said:
Well, you’re on the right page. This is pure voodoo. And, it is the very definition of “gambler’s fallacy.” There exists no force to cause “retracements.” Cards have no memory, no emotions and no support levels. They’re just cards.

Then let’s just agree to leave it there. As I said earlier, I know that the vast majority of posters here will have no use for this line of reasoning. My degree is in mathematics eduacation, but it seems that explaining this to a point of satisfaction is going to be beyond my capablities. If anyone wants to discuss this any further, and how I believe this benefits my game, feel free to pm me. For forum postings, I will continue to add trip reports and chime in from time to time on counting issues, to which I am fully committed.

Regards to all, and I wish you well.

• StandardDeviant
If you graph 10,000 hands of blackjack, you will see that the graph lookes remarkably like a foreign exchange graph.

This, of course, proves nothing. It is easy to create a graph, based on a random number generator, that looks just like an FX graph. There have been many, many serious academic studies that demonstrate that the “patterns” we think we see in securities data have no predictive power.

Man has been seeing patterns where there aren’t any for many thousands of years B.C.E., and will no doubt continue many years into the future. Just ask any shaman who’s read the cracks on a tortoise shell.

• rrwoods
beyond my capablities

No offense, but proving something that is provably false is beyond most peoples capabilities, no matter their background.

• blackjack101
Quote: Canceler said:
Thank you, Sonny! Now I’m finally getting it.

(The worst part is that in college I got a 4.0 in Statistics, but that was 30 years ago.)

Daaammmm, I had to read this to understand that too, and I also Aced Statistics, but it was like a year ago….lol

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