Gambler's fallacy

In my previous post The problem with Betfair "scalping" I mentioned gambler's fallacy. This fallacy is the belief that past events affect future events. In other words the mistaken belief that an abnormal run of the same occurence will be matched in the future by a corresponding number of opposite occurences that will even up the chances of either occurence happening.

Examples of gambler's fallacy can be seen in coin tossing, roulette and scalping on Betfair. Just because someone tosses heads 9 times in a row with a coin or sees the ball fall into a red cup 9 times in a row on a roulette wheel does not mean that the next toss is more likely to be tails or that the ball is more likely to fall into a black cup.

Equally, just because a horse in a betting market suddenly starts rising in price does not mean that it will mean revert and start shortening again. At any time if the price of a horse goes up then the next price move will either be up, down or it will remain stationary with equal probability of each. The only thing that will change the probability of the price movement is the underlying fundamental chances of the horse winning.

We know from Efficient Market Hypothesis that the starting price before the race starts represents the true chance of the horse winning. Before that the price of the horse is an unpredictable random walk. Eventually, the wisdom of the crowd will settle upon the actual price for the horse.

If information enters a horserace betting market that the price on a horse represents good or bad value then that information will be arbitraged out. Such a price move will take time but in how much time and for how long is not predictable.

Occasionally, the mere actions of bettors can make a price move without information entering the market. Such a false signal will create its own momentum. The varying skills and abilities of traders and their technology will cause a price move to cover over a period of time rather than instantaneously and then revert when arbitrageurs step in. But, as in the case of a true price move, the length and duration of the move is not predictable. If it was predicable then the scalpers wouldn't need to have their finger on the scratch button.

In believing the fallacy, a gambler thinks the chances of a coin toss has to be equal at all times. Yes, over the long run the ratio of heads to tails will tend towards 50/50 through the Law of Large Numbers. However, it is unlikely that at any one moment the actual number of heads and tails tossed will be equal. In fact the more you toss the coin the more the number of heads and tails tends towards 50/50 and yet the greater the potential for a gap between the number of heads and tails thrown.

In the case of price moves in horse betting markets we have to take into account the fundamental chances of the horse winning and the perception of all the bettors in the market. The actual chance of the horse winning is already pre-determined. No single bettor knows what that chance is. Only the combined knowledge of all bettors will reveal that price to us just before the off.

The price on a horse exhibits Brownian motion as it moves randomly. Occasionally, the herding of bettors may create short-term movements but that is only through large numbers of speculators jumping on a bandwagon with nobody steering it. The first on the bandwagon gets the biggest profit and the last gets the loss. Maybe new information has entered the market and the price remains at the new value or maybe insider traders push the price back to where it began when they see a value bet.