The Search for Value

Almost any serious article about gambling will mention "value" at some point. Not many of them explain neatly what value is. They will generally give a few examples, assume you've got the point, and move on. So here, once and for all, is the definition of value: the value of the bet is the "real" probability of the result happening divided by the implied probability of the bookmaker's odds. If this number is greater than one, the bet constitutes value.

That seems simple enough. The implied probability might look a bit tricky, but it's not too bad. In decimal odds, the implied probability is simply one divided by the odds - so a team available at 2.00 to win have an implied probability of 0.50, or 50%. If the odds were 1.5, the implied probability would be two-thirds, or about 67%. Odds of 10.00 represent a 10% chance.

All well and good, if you're using decimal odds. What if you prefer the old-fashioned, 100-to-30 style favoured by men in cloth caps making odd gestures? Well, you're going to need to do a little more maths, I'm afraid. Odds in the style x-to-y against simply mean that the bookies imply the selection will lose x races for every y they win. X-to-y on is the other way around - they'll win x for every y they lose. Evens, or 1/1, means wins and losses are (implicitly) equally probable, 2/1 on* represents an implied probability of 2/3, and 9/1 against corresponds to a one in ten chance.

To convert fractional odds like these into implied probabilities, you take the number on the right (left if it's in the style of 2/1 on) and divide it by the sum of the two numbers - so it's the number of races you'd expect to win divided by the total number of races. You can easily see that 9/1 corresponds to 1/10 = 10%. (If you divide one by that, you get the decimal odds, 10.00.)

So much for the maths involved in working out implied probability. There are two burning questions that I can see I haven't answered. One, how do you compute the probability of winning? And two, why is value important? The first is one of the main things The Martingale will be looking into. The short answer is I don't know, but I hope to find out. I can answer the second, though:

A value bet is one where, if you repeated it often enough, you would win more money from winners than you lost from losing. For instance, if a horse was at 10.00 and you figured it had a one-in-eight chance of winning**, over a hundred races you'd expect it to win about 12 or 13 times. Each time, you'd be returned $10 for a $1 stake. So you'd get, let's say $125 back from the bookie after giving him only $100 - a profit of $25. The value (minus one) is the return (here, 0.25 or 25%) you'd expect on your money over the long term if you made bets at that value.

In the next article, I'd better talk about the gambler's fallacy and the law of large numbers.

* This also gets written as 1/2, in which case the first definition is correct - the selection loses one race for every two it wins.

** (1/8) / (1/10) = 10/8 = 1.25, so this is value.