In a recent post, I discussed the importance of defining events clearly when discussing the chance of their occurrence. I also explained that even once that is done, different people might still come up with different assessments of that chance. The example given was of the chance of twins being born in different years, which had been described in the media as one-in-two-million, but for which a back-of-the-envelope calculation suggested it is actually over 100 times more likely than that. This fact that different analysts might obtain quite different estimates of probabilities is what makes gambling a serious investment opportunity.
On the other hand…
Gambling: The sure way of getting nothing for something.
This quote is attributed to Wilson Mizner, an American playwright born at the end of the 19th century. It’s not strictly true, of course. One way you can avoid getting nothing when gambling is by being lucky and winning more than you lose. But the various laws of probability imply that luck balances out in the long run, so if you’re relying on luck to make a profit when gambling, this will only last so long, and you will indeed eventually end up with nothing.
The other way to avoid getting nothing when gambling is by being clever. We’ll come to that in a minute. But the gist of Wilson Mizner’s quote is correct – if you gamble without method, you will eventually lose everything you started with. This is also mathematically guaranteed.
So what does it require to be clever enough to win at gambling? A bookmaker – or an exchange market – provides prices on the possible outcomes of an event. For argument’s sake, let’s suppose it’s a football match, and we’re focusing on match outcome, which will be one of home win, draw or away win. As I’m writing this post, the price given on Liverpool winning tonight away to Inter in the Champions League is 2.05. So if I place a bet for $1 on Liverpool to win and they do win, I’ll get $2.05 back (including my $1 stake); if they don’t win, I’ll lose my $1. So, if the probability of Liverpool winning is P, then my average (or expected) winnings are
2.05 × P − 1
It follows that if
P > 1 ÷ 2.05
my expected profit is positive. This leads to the following betting strategy
- Calculate P;
- If P > 1 ÷ 2.05 place a bet on Liverpool winning; otherwise don’t.
This strategy will have positive expected profit as long as my assumptions about P are correct.
In reality, things are a little more complicated. Our calculation of P will always be an estimate, and we may wish to allow for this uncertainty incorporating some leeway in the process; perhaps place the bet only if P > 1 ÷ 2, for example. But in any case, the principle is that the bookmaker prices will lead to a criterion for placing a bet that depends on our estimate of the probability of Liverpool winning, and the more accurate the estimate, the more certain we can be that our strategy will be a winning one.
The accurate calculation of probabilities like P is really what Smartodds is all about (“Smart – Odds”, after all). The basic recipe is to get as much relevant information as possible – for example, recent Inter results, recent Liverpool results, measures of the strength of the teams they’ve played against, the referee, the weather and anything else that seems useful – and combine all of that information to get the best possible estimate of P. If we do that well across many bets, and apply the same sort of decision-making procedure about when to make bets as described above for the Liverpool bet, we’re bound to make money in the long run. Again, it’s a mathematical certainty. But the challenge is getting the equivalent value of P for all fixtures, making sure that it does better at describing the randomness in match results than the prices provided by the market.
Things weren’t always this sophisticated. One famous instance of punters cleaning up against bookmakers is the so-called ‘Hole-in-One-Gang’. This was back in 1991, when there were still a large number of independent bookmakers and Google searches weren’t much of a thing. To cut a long story short, a pair of gamblers from Essex researched data from a number of the major golf tournaments and found that in several, the chances of there being a hole-in-one was at least 50%. That’s to say, historically, there had been at least one hole-in-one every other tournament or so. So if they could get bookmakers to offer prices on such an event that was at least as good as evens, they had a bet with positive value. The major bookmakers were equally wise to the fact that hole-in-ones were not especially uncommon in the major tournaments, and so their prices were no better than evens. But many of the smaller outlets offered much higher prices – as much as 100-1 in one case. Moreover, the gang were able to place doubles and accumulator bets for up to five Open tournaments, meaning even higher returns if there were hole-in-ones at more than one of the tournaments that year. Again, small bookmakers considerably underestimated the chances of such events occurring, meaning the prices offered for these events were massively over-generous.
Then the gang got lucky. If the probability of a hole-in-one at any one event was genuinely evens, say, then the probability that all five Open events would have a hole-in-one would be just one-in-thirty-two. Yet that’s what happened, there was a hole-in-one at all five events, meaning that every single, double and accumulator bet won. Given the prices the gang were offered, they’d have turned a smaller profit even if there’d been just one or two hole-in-ones; the fact that there were five meant that their win was huge.
Most of the individual bets were for relatively small amounts – just a few hundreds of pounds – but the very large prices meant that the overall return was very large. In total around half a million pounds, though not all of that was received, with several bookmakers either refusing to pay or only paying at much lower prices than those stated at the time of the bet.
It’s unlikely, of course, that bookmakers these days would be so naive as to mis-specify prices so badly that bets with such high value would be offered for any sporting event. But even slight mis-specifications by bookmakers imply profit potential, and the better the calculation of probabilities to gamble with, the more reliable the returns.
In summary, the ambition of “Smartodds” is always “Smarter-odds”.
An even longer version of the Hole-in-One-Gang story is given in this book. I have a copy available if anyone’s interested. (Spoiler: the literary quality is not quite up to Pulitzer Prize standard).
