Gambler’s Fallacy

Mar 7, 2008: 9:50 AM CST

What is the “Gambler’s Fallacy” and how might it describe why you may not be achieving the trading results you’ve been expecting?

According to The Skeptic’s Dictionary, the Gambler’s Fallacy is the incorrect notion that the odds for something with a fixed probability increase or decrease upon observing the most recent occurrences.

The classic fallacy plays itself out on the Roulette wheel, when the ball has landed on a red number 4 or 5 times in a row, and gamblers believe that red is now “hot” and so they place their bets more frequently on red, even though the fixed chance of red coming up is 47.5%.

Roulette wheels take advantage of this fallacy by posting the most recent numbers and colors on flashy boards near the roulette wheel.  It causes gamblers either to say a certain number or color is hot or cold, and so they irrationally adjust their betting strategies to accommodate this perceived (though false) edge.

Similarly, if a fair coin has been tossed numerous times and the last 4 throws have been heads, then a better commits this fallacy one of two ways:

1)  By betting heads because he expects heads to come up because it has come up the last 4 times in a row

2)  By betting tails because he expects tails to come up because it has NOT come up in the last 4 throws and he feels it is “due”

Notice that expectation plays a major role in committing the fallacy.  In reality, the outcome of the probability is 50%.

In trading, there are plenty of chances to commit this fallacy, but note that the odds and probabilities in trading are not actually fixed, but often change, which complicates the situation.

However, if your strategy has a certain, discerned edge, then you can create this fallacy the same way if you adjust trading size or expectations significantly based on the results of your last three or four trades.

If you know your trade set-up (or strategy) has a 60% win rate, and you have just experienced 7 winning trades in a row, you would commit the error by doubling your position size because you expect the next trade also to be a big win, or cutting your size in half because you expect the next trade to be a loser because 7 trades in a row is just too good to be true.

The key is to know your probabilities, stick to a certain ‘betting style’ or method of selecting trades (that you know have an edge), and continuing to let the probabilities play themselves out naturally, rather than trying to step in and tweak them whenever you feel either frightened or unstoppable.

12 Comments

12 Responses to “Gambler’s Fallacy”

  1. Tyro Says:

    At the risk of opposing you, I’m gonna say this is a really difficult issue and I’m not sure you nailed it like you’ve done in other posts.

    You say it’s an error to change position size after a series of winners or losers and to one extent I agree that there’s a danger of thinking we’re on a “hot streak” (so doubling-up) or “bound to fail” (so reducing size). I recall reading about someone (Dr Wiseman?) who studied streaks in basketball and found they did not occur with any greater probability than would be predicted if shots were random. Flip a coin, and you will get 4, 5, 9 heads in a row. It gets worse, if we try to make up random heads/tails, you can generally spot the fakes because they don’t have enough streaks, so it seems we really believe that streaks must be caused and not appear through randomness.

    So yes, we definitely have some powerful cognitive biases which are impairing our judgement and we must be aware of this and try to ensure that it doesn’t affect our trading.

    Buuuuut…

    But trades do not have such an objectively quantifiable risk, and the odds of working do vary depending on the market or other factors such as our ability to identify setups. In a strong bull market, almost everything goes up so it would be perfectly justified to increase your size to take advantage. In a volatile market, some trades may not work out so well so maybe you should reduce your size or stop trading entirely. Some strategies work very well for a while and then stop.

    Or worse, after a series of wins or losses, your ability to objectively evaluate trades may suffer and you will enter trades with much poorer risk/reward ratios. The “Going on Tilt” phenomenon, “Revenge Trading”, and “Euphoria Trading”. People who are strongly influenced by their emotions may really be due for losses after a string of winners, not due to chance or fate, but because they self-sabotage.

    Worst of all, we may all experience some levels of emotion after a string of winners or losers which means it is probably the worst time for us to sort out these issues.

    When you’re playing a game with fixed, predictable odds then I agree with you wholeheartedly, but it’s not clear to me that trading fits this model.

    (PS: love the blog, not trying to diss you, just trying for a broader conversation about a difficult subject.)

  2. Corey Rosenbloom Says:

    Hey Tyro! This is what blogs are for! I appreciate the feedback, as everything allows me to consider a new perspective.

    I was aware of the debate between those who advocate variable position sizing and those who advocate fixed sizing. I tried to walk a fine line and draw a distinction by saying that you are changing your size solely because of your expectation. I did this by saying a trader adjusts only because of the last few trades, and that (implied) he/she is not taking into account market conditions. I also drew a distinction by saying that the trader doubled the size, or cut it in half, which was a radical change caused far more by psychology, than by written strategy.

    I also mentioned that trading doesn’t have the fixed odds that a coin flip does, and this is absolutely true, but describing it in detail is very difficult in a brief blog post.

    I guess my point in the post was to indicate that you shouldn’t radically change your strategy based on your feelings or the last few trades alone. I was warning specifically against that. I didn’t mention that it is very important to adjust size based on market condition, or through your predetermined plan. I may follow this post up with a caveat that describes when it is appropriate to change size due to a significant change in broad market conditions, or whether your strategy has entered the “payout” portion of the “Pay-out, pay-back” cycle as described by Bo Yoder.

    It’s so hard to address all the components I want to in a singular, short blog post 🙂 There’s so much to say!

    Thank you for taking the time to respond and share your thoughts.

  3. NTH Says:

    Hi again Corey,

    I agree with Tyro’s comments. The markets are not like a known-odds system, such as roulette or flipping a coin. There is randomness, but it is not complete and within the market itself, it is very much human driven. That’s plain to see as when there is some good financial or economic news, stock prices go up across the board. So prices can be news and hence subjectively driven rather than objectively like the tossing of the coin.

    But with a tossing of a coin and a close-to-random market, there is an approach which I call 1-3-9, which allows a betting person/investor to win on a regular basis. eg: if its a red last time, bet 1 unit black, if you lose, bet 3 units black next time, etc, if you lose again, bet 9 units black, etc, keep going until you win. There is only one catch. You need a deep pool/fund to cover those long streaks that will occur, even if rarely, although a stop-loss strategy could also be applied.

    NTH

  4. Ryan Says:

    Hey Corey,

    Have you read “Trading in the Zone” by Mark Douglas? He touches on this exact subject. I have personally been using his 20 sample size rule for some time with great success. I revaluate or recess my trading results after every 20 trades. Depending on the time frame you use this size will vary.

    BTW, I like the new look!

    Ryan
    http://www.evolvedtrader.com

  5. Corey Rosenbloom Says:

    Ryan, I have read that book and love it immensely.
    I have benefited greatly from Douglas’s work. We’re in a game of probabilities where edge matters over time, rather than on a couple of trades.

    Thank you for the comment and compliment 🙂

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