Is there a Gambler's Fallacy at the dog track?

General / Leighton Vaughan Williams / 08 August 2008 / Leave a Comment

The gamblers fallacy is alive and well amongst New Jersey lottery players but what about down the dogs?

Can winning at the dog track really be as simple as betting the greyhound in the starting trap occupied by the previous winner? This was the startling conclusion of a paper published in the Royal Economic Society's flagship publication, the 'Economic Journal', in 1996, authored by Professor Dek Terrell and Amy Farmer. In fact, such a strategy was revealed to yield a 9 per cent profit, and was, according to the authors, "the only strategy yielding positive profits", at least that they could find.

The reason for this so-called 'anomaly' was explained in the paper in term of bettors underestimating the probability of a repeated outcome. This is the classic 'Gambler's Fallacy', i.e. the proposition that bettors, instead of accepting the actual independence of successive outcomes, are influenced in their forecasts of the next possible outcome by the results of the preceding sequence of outcomes, whether that be throws of a die, spins of a wheel, or dogs chasing a 'hare.'

Dek Terrell provided a formal definition of this 'fallacy' in 1994 in the Journal of Risk and Uncertainty. "The gambler's fallacy", he writes, "is the belief that the probability of an event is decreased when the event has occurred recently, even though the probability of the event is objectively known to be independent across trials."

Professor Terrell went further than merely defining the term, he proved its existence in the behaviour of those playing the New Jersey State lottery. In a sample of no fewer than 1,785 daily drawings of the lottery between 1988 and 1993, he found that the expected payout on a number increased by 28 per cent one day after winning, and decreased from that level by about 0.5 per cent for each subsequent day, returning to its base level after a period of about 60 days or so. In other words, the 'gambler's fallacy' was alive and well among players of the New Jersey Lottery, and lasted for about two months.

These findings are not peculiar to New Jersey, however, but echoed a previous study of a Maryland numbers game. The Maryland game was a little different in construction to the New Jersey lottery, however, in that it was characterised by a fixed-odds payout to a unit bet, and so the impact of the gambler's fallacy had no effect on actual returns. In contrast, the New Jersey lottery was based on a standard 'pari-mutuel' (pool) system, with holders of winning tickets sharing the prize fund made up of all entries into the pool. Interestingly, the size of the effect was rather bigger in Maryland than New Jersey. The implication is that while irrational behaviour (i.e. succumbing to the 'gambler's fallacy') exists whether it has a financial impact on returns or not, the extent of the irrationality reduces where the cost of behaving irrationally increases. For those brought up according to the tenets of conventional economic theory this is, of course, very good news.

So, can you make money at the dog track by exploiting the 'Gambler's Fallacy'? Well, there's some evidence that it's worked in the past. Having said that, I wouldn't jump in with both feet! That would be to risk engaging in a very different form of gambler's fallacy.