The Gambler’s Fallacy

Programming, Products & Research for Traders

The Gambler’s Fallacy

I thought that I’d write about something known as the “Gambler’s Fallacy” as it’s something that crops up in trading (particularly FX trading) from time to time. The basic idea is that you can make money by betting cleverly and that somehow through doing this you can turn something that has no inherent edge into something that does. The clue as to whether this works is in the second half of the name – of course you can’t do this but it can be packaged up in a very alluring way that can trick the unwary.

 

Here’s how it works. Take any game of chance with a 50-50 win rate such as betting on black or red on roulette. Make a 1 unit bet on either and if you win then you simply collect your winnings and start again. If you lose then your P&L is currently -1 so this time you bet 2 units, one to cover your loss and one is the profit that you’re looking for. Again, if you win you’ve ended up +1 so far on the session but if you lose then you’re now -3 on the session. Once again if you lose you now bet 4 units to try and make back the 3 that you’re down and 1 for your net profit. I’m sure that you can see that pattern here, you keep doubling your bet each time you lose, hoping to make back your losses and your 1 unit profit. Eventually of course you will win and then you pocket your net +1 unit profit and start the whole process again.

 

It sounds fool proof and the appealing thing about it is that most of the time it works. In fact my daughter used this method at a college ball on a play money casino to break the bank, cleaning them out entirely! However, before you start reaching for your wallet and heading to the nearest casino, the downside to the method is that eventually you’ll hit a losing streak so big that you’ll hit either the house limit (the maximum bet size that a casino will accept) or you’ll run out of money. It’s unlikely but of course eventually it will happen just as eventually it will come up ten blacks in a row on roulette.

 

You also have to be aware of how quickly the bet stake grows. Say you come to the table with 100 units.

After 1 loss    you’re left with 99 and betting 2
After 2 losses you’re left with 97 and betting 4
After 3 losses you’re left with 93 and betting 8
After 4 losses you’re left with 85 and betting 16
After 5 losses you’re left with 69 and betting 32
After 6 losses you’re left with 37 and betting 64

… except that you can’t because you don’t have enough money left! So with 100 unit table stake, 6 losses in a row will leave you with only 37 units left and unable to recoup your losses. What’s more, this event will happen 1 in every 64 rolls so it’s more likely than you think!

The Trading Equivalent

So what has all this to do with trading? Well, the other day I came across a “foolproof” way of trading which was basically this concept though package up in a rather elaborate way. You can download the pdf here if you want. It basically involves setting up a breakout strategy. If it wins then you’re done for the day, if it loses you take a trade in the opposite direction and (you’ve guessed it) you double your size. Keep doing this until you’ve made your money for the day or you’ve wiped out your account.

Grid Trading

There is one other area where this sort of concept comes up which is grid trading. This basically involves buying and selling at fixed intervals on a chart usually in a mean reversion way and hoping that the market reverses after trading. Usually these strategies are offered as an EA (Metatrader Expert Advisor) of some kind which promises untold riches. There are all sorts of elaborate variations on this theme, which generally involves doubling your stake size or at least taking on increasingly large positions in order to try and make back your previous losses and a little bit extra for your profit. They all suffer from the same Achille’s Heel that the Gambler’s Fallacy does, namely that eventually the market will keep going against you and will wipe you out.
A client of mine spent quite a lot of time testing out various versions of these, trying to find a combination of parameters that would somehow avoid the inevitable. I kept telling him that no variation on this theme was going to work but that wasn’t what he wanted to hear. I don’t know whether he saw the light in the end, I hope that if he did it wasn’t at the expense of his entire account!