Fallacies and Illusions

If you flip a perfectly fair, two-sided coin 10 times and it comes up heads every time so that you have 10 heads in a row, would you think there’s a greater or lessor chance that it will come up heads the next time you flip the coin?

If you think there’s a lessor chance that heads will come next, that “tails is due,” then you are committing the gambler’s fallacy.

If you think there’s a greater chance that heads will come next, that “the trend is your friend,” then you are committing the inverse gambler’s fallacy.

Both fallacies assume that past results in a fair, 50/50 coin-toss type game affects future outcomes. Both are fallacies because the result of any future decision is still just 50/50, and what has already occurred has absolutely no bearing on what will happen. Random events such as coin-tosses have no memory, and each toss is completely independent from one another.

If you flip a coin 100 times and it comes up heads every time so that you have 100 heads in a row, would you think there’s a greater or lessor chance that it will come up heads the next time you flip the coin?

Well, I think if this really happened, you would suspect the coin is actually one-sided! That is, it appears to have a strong (and possibly exclusive!) bias toward heads. Nevertheless, there is nothing statistically prohibiting a perfectly fair, two-sided coin from coming up heads 101 times in a row. It would be a very rare occurrence, to be sure, but flip a perfectly fair, two-sided coin often enough and it can, does, and will happen.

What are the chances that flipping a fair coin 101 times will result in 101 heads in a row? Exactly 1 in 2^101. That is, you will expect to see a 101 streak of heads for every 2-to-the-101st power number of flips. That’s a lot of flips!

But what are the chances that after 100 heads in a row, another head will occur to make 101 heads in a row? Just 1 in 2, that is 50%.

That’s the difference between perception and reality.

The tendency for humans to commit the gambler’s fallacy and its inverse may arise from the clustering illusion. The clustering illusion occurs when people see apparently non-random sequences in a random series. For example, many people would not characterize the following sequence as a random string of X’s and O’s:


The human eye detects repeating patterns in the above sequence which it interprets as being non-random, ordered, and clustered, and concludes it must be the result of some intelligent construction. If asked to guess what might occur next, one might guess “XO” based on the apparent “choppiness” at the end of the string.

The kind of pattern-seeking which causes the clustering illusion comes naturally to humans, perhaps because it serves as an evolutionary advantage. For example, being able to notice patterns in the behavior of prey helps the hunter formulate an effective strategy to capture it, and this ability gives the hunter a survival advantage over those who cannot discern the pattern. The hunter with the pattern-seeking ability will have a greater chance to survive and reproduce, passing along his ability to his progeny, while his less fortunate counterpart lacking this ability will be more likely to die childless. As descendants of the survivors, we have thus inherited the advantageous ability to find patterns in what we observe. We are so good at it that we notice apparently intelligible patterns where there really should be none, such as pictures in the clouds or stellar constellations. Indeed, the purpose of modern science is to help us objectively determine whether an apparently repeating pattern in nature is based on some more fundamental, reproducible, understandable natural law. When it is, this knowledge gives us the ability to make amazingly accurate predictions of future events, and we gain a sense of confidence that what we know about nature is more true than not.

But when it comes to considering the results of a truly random set of events, our natural ability to seek intelligible patterns makes it easy for us to commit the gambler’s fallacy and its inverse. An expert pattern seeker may even attempt to codify his observations into a systematic methodology for trying to predict the outcome of future events, and he may have enough confidence in his pattern-seeking algorithm to wager real money on a coin-toss type game, such as baccarat. If he meets with early success, he may convince himself that not only will his winnings continue, but that he is able to teach others to use the same system to their own advantage.

Another word used to describe an actionable pattern is a “trigger.” A trigger is a specific pattern which calls the user to take certain actions when it arises. Some strategies are so reliant upon triggers that the player will only bet when the trigger occurs. If using triggers offers any advantage, it is entirely psychological, since the gambler’s chances are in reality exactly the same any time before or after the trigger. Even though the occurrence of triggers makes absolutely no real difference, it makes all the difference in the world to the player. Every time he operates under these guidelines, he is committing the gambler’s fallacy or its inverse.

Casinos love players who use pattern-based systems because casinos know all are fallacious. Casinos actively encourage players to commit these fallacies by setting up tote-boards which openly display a running record of past decisions. If knowledge of past results could truly give players even a fractional edge over the house, you can be sure every casino in the world would dismantle all its tote boards immediately. This does not necessarily mean the information displayed on tote boards is entirely useless to a player; just don’t use them to commit the gambler’s fallacy or its inverse.

We can be assured that any system based solely on seeking apparent patterns in the past history of random, independent events, that is to say, based on the gambler’s fallacy or its inverse, is doomed to eventually fail. Strict money-management and damage-control skills may enable the user of such a system to maximize his winnings and minimize his losses, but over time he will realize that his bet placement strategy is not accurate enough to avoid losing. If anything, an appropriate bet progression will be more important to help keep him profitable, or at the very least, less unprofitable.

Played long enough, the Law of Averages dictates he will eventually run out of bankroll to sustain his drawdowns. They call it a Law for a reason, and it is the gambler’s conceit to believe he can avoid ruin.


11 Responses to “Fallacies and Illusions”

  1. […] Of course, you’ll have to sign up with Mark yourself to learn his methods. Mark’s MU is not the “holy grail,” nor did he ever claim it is. Mark is also the first to say that if you already have a method which consistently nets 10 units per shoe, you don’t need Maverick or MU at all; just keep doing what you’re doing. Maverick and MU are simply ways which he found consistently wins for him, and he is just teaching others what works for him. As I have discovered, though, your own mileage may vary. More objectively, Mark’s Maverick and MU can be categorized as examples of methods which commit the inverse gambler’s fallacy. […]

  2. […] Betting with the disparity is to bet with the trend, based on the assumption that the present disparity will persist, an example of the inverse gambler’s fallacy.  Betting against the disparity is to bet against the trend, based on the assumption that that a reversion to the mean is due, which is an example of the gambler’s fallacy (ref. Fallacies and Illusions). […]

  3. […] method assumes an existing shoe bias will tend to normalize (thus committing the gambler’s fallacy).  It bets only in 3 groups of 5 decisions in the last half of the shoe.  It uses a 5-level […]

  4. Hey Imspirit

    Deal an 8 deck Bac shoe for me and I will flat bet it to the tune of at least 51% to at most 58% or more hand win rate most of the time. Deal another 8 deck shoe and I’ll give you that same range. I will lose a shoe out of 15+ or so played. And no I am not psychic. There is a pattern to every thing in this universe; nothing is random. Note: The Butterfly Effect (not the movie) There is an equation for every “prediction”, however inexplicably complex. And yes, there is an equation to every “50/50” coin flip which only “God”, if one exists, can reasonably come up with. So it’s not complete Fallacies.

    • Well, then, Gushin, you should be the richest man in the world pretty soon! I’m flattered you bothered to waste your time reading the obvious ignorance in my blogs. 😉

  5. […] course, assumptions like reversion to the mean is based on gambler’s fallacy (ref. Fallacies and Illusions), and from mathematical grounds, has absolutely no hope of winning a long term simulation.   But […]

    • Reversion to the mean is not a fallacy but a statistical reality. Reversion to the mean doesn’t expect any corrections after any extreme but it only says that after the most biased data the next sample will be more likely to be closer towards the mean. The problem with practically using RTM is the stretch after which a sample will go closer to the mean is not defined. What is fallacious here?

      • virtuoid Says:

        The fallacy is basing a viable, long-term betting system on the expectation that reversion will occur. For example, your system may succeed 99% of the time, but all the casino needs is that 1% when you fail to stay ahead. The odds are always in their favor over the long run.

  6. […] player’s edge, simply because they commit the Gambler’s Fallacy or its Inverse (ref: Fallacies and Illusions).  The past has no bearing on the future for independent […]

  7. […] negative expectancies in the long run, as of course, it must, since all grid approaches commit the gambler’s fallacy or its inverse, and no money management or bet progression procedures are able to make positive an otherwise […]

  8. Hi, keep up the great work on your site. I found the bacc info quite interesting. You’re doing a great job. Thankx!

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