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The Gambler's Fallacy

August 17th, 2009 at 07:10 am

Not really stock-related talk, but just wanted to say something quick about probabilities.

In an earlier entry, I've talked about the Monty Hall problem. On the flip side of the coin-- gee, aren't I clever-- there is also something called the Gambler's Fallacy.

Anyways, what both of these mathematical fallacies point out is that, in order to understand your true probabilities, you have to have the correct grasp of the problem itself.

For example, if you want to flip a coin three times in a row with heads, then yes, your probability will be 1 in 8. However, if you've already flipped a coin twice and got heads, then your probability of getting a head with your third flip is in fact 1 in 2.

As you can imagine, this sort of thinking is vital when it comes to assessing stock trades, or really, anything in life. Because the fundamental lesson is to make sure we understand the true context of the question before we can ever hope for an answer. Or at the very least, it's fun to talk about. Big Grin

6 Responses to “The Gambler's Fallacy”

  1. ceejay74 Says:

    Phew, glad you posted that link to the "Monty Hall" problem. The way I'd heard it explained before never took into account the fact that he'd avoided the third curtain, just talked about the strict statistics logic, which was too hard for me to grasp. Now it makes much more sense.

  2. creditcardfree Says:

    Ugh...you are making my mind spin with probabilities. The very reason, I had to drop out of the actuary program in college. I do agree it is good to know the problem before looking for an answer!

  3. Broken Arrow Says:

    Hehe, well, I still get tripped up over it as well. Big Grin

    The key element I realized with the Monte Hall problem is Monte KNOWS where the goats are, and once you have chosen a door, he is GOING to show you one of the other losing door.

    In other words, when you start out, you have 1 in 3 chance of choosing the right door. But the other two doors represent 2 in 3 chance of that the right door. And if Monte then reveals the wrong door of the other two, then the probability has not fallen down to 1 in 2 like Gambler's fallacy (where there are only 2 choices), but rather, the probability of 2 in 3 remains (because it's a 3 choice problem where the prize could have been in any of those doors).

    Something like that anyways. Hurts my head just thinking about it. But that's why it's so interesting to me, and why it's such a great illustration of truly grasping the problem.

  4. princessperky Says:

    Ok but has anyone actually set up three doors and a couple 'goat's' to check? I mean I can flip a coin hundreds of times and if I record each flip or series of flips I see the numbers follow the probability. But honestly no matter how often I hear that 3 door thing, I just don't buy it...

    I can follow the math just fine, But I still don't buy it.

  5. princessperky Says:

    Bertrand's box makes more sense though....but only because there are two coins in each box...

  6. Broken Arrow Says:

    Hehe, would be funny to get a couple of goats.

    Actually, you can get your hubby to set up a computer simulation and post results. That's probably the easiest way... but still not as much fun as using real goats. Big Grin

    But if thought experiment is enough, imagine a slight re-wording. First you pick a door. The other two doors represent your two-third probability. You then pick another door, but Monte says, "No no, that one's not it." Well, your odds remain the same with the other two doors, except Monte just cheated for you by telling you which one of those two doors are not it.

    Perhaps the reason it's hard to grasp has in part to do with the wording, because we humans tend to think that this is three separate trials (like making three coin tosses). You pick a door. Monte picks a door. Then you pick your final door. But that's not true.

    The three sequences are in fact parts of one single trial! Even though doors are chosen in all three sequences, in the end, only the third and final choice is official, and only one door is ultimately chosen, not three separate tries to see if you get the prize.

    The wording obfuscates this critical detail through the use of a once-popular TV show with a deceptively simple premise that seems easy to follow.

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