Understanding Value in Betting

Value. You can’t eat value, they say. A 2/1 winner is better than a 22/1 loser.

Value can be a lonely place.

But value is the single most important element in the determination of the profitability or non-profitability of any betting strategy. Value in anything is about getting something at a price that is more favourable than the true price. Buying a €500 suit for €200. A packet of Jaffa Cakes for a pound. (Check the expiry date.) Same in betting. If you can bet on the outcome of any event at a price that is better than the true price for that outcome occurring, then you are on your way.

Take a roulette wheel for example, a European roulette wheel, numbers 1 to 36, plus the Zero. So, 37 possible outcomes, each (on a fair wheel) with an equal chance of occurring. In a single spin then, each number has one chance in 37 of coming up, that’s true odds of 36/1. But the house only pays 35/1. 

So the true probability of the ball landing in 7 Red is 0.02702, but the player is betting at odds that suggest a higher probability of 0.02778. It’s a bad value bet for the player. In the long term, the player will lose.

There may be short-term wins. It may be that, in any chosen short-term period, 7 Red will come up more often than it should statistically. On average, if you spin the wheel 100 times, 7 Red (and every other number) should come up just over 2.7 times. But it may be that, in any chosen period of 100 spins, 7 Red will come up four or five or six times. In which case, a person who is betting on 7 Red during that period, to level stakes, will show a profit. But spin the wheel a million times, and 7 Red will come up close to 27,000 times, or 27,027 times to be more precise.

So, Roulette is a bad-value bet. Any bet in Roulette. If you bet on Red or on Black, for example, you bet at even money but, because of the Zero, the green one, the true price is slightly bigger than even money. You bet on Black at odds that suggest a probability of 0.5, but the true probability of the ball landing in a black segment is 0.4865, slightly lower than 0.5. In decimal odds terms, you bet at 2.0, but the true price is 2.0555. The Zero gives the house its edge. It’s not a good bet for the player and, in the long run, the player will lose.

Take a deck of cards. If you draw one card at random from a full, fair deck of 52 cards, then the probability of drawing a black card is 0.5, as represented by odds of even money or 2.0. Twenty-six black cards in the deck, 26 red cards (and no Zero), so there is one chance in two that you will draw a black card. Probability 1/2 or 0.5.

There are 13 diamonds in the deck, so the chance of drawing a diamond is one in four, probability of 0.25, represented by odds of 3/1 or 4.0. And there is only one Ace of Hearts, so the chance of drawing that card is one chance in 52, probability of 0.019, and represented by odds of 51/1 or 52.0.

You will obviously draw a black card more often than you will draw a diamond, and you will draw a diamond far more often than you will draw the Ace of Hearts. So, the probability of drawing a black card from the deck is greater than the probability of drawing a diamond, the probability of which, in turn, is far greater than the probability of drawing the Ace of Hearts.

But let’s say, in the draw of a card from a full, fair deck, you are offered odds about each outcome occurring that are different to the true odds. Say, for example, you are offered 4/5 or 1.8 about drawing a black card, and 4/1 or 5.0 about drawing a Diamond, and 80/1 or 81.0 about drawing the Ace of Hearts. How would that impact on the bet(s) that you would be likely to have?

As can be seen from the table, the odds that you are being offered about drawing a black card are worse than the true odds for that outcome occurring. By contrast, the odds that you are being offered about drawing a diamond, and about drawing the Ace of Hearts, are greater than true odds.

So, if you bet on a black card every time a card is drawn, you will win often. On average, you will win once out of every two draws. So, let’s say from 104 draws, on average you will win 52 times. However, because you are betting at 4/5, at 1.8, you will show a net loss. If you bet €10 on a black card on every draw, if you win 52 times, you will bet €1,040 and you will get back €936. So you will show a net loss of €104, or 10% of your total outlay.

If you bet on a diamond every time, on average you will win just once out of every four draws. (A heart, a club and a spade will be drawn, on average, as often as a diamond is drawn.) On average, you will win 26 times out of the 104 draws. However, if you bet €10 on a diamond on every draw, because you are betting at 5.0, not at true odds of 4.0, you will make a profit. You will have a total return of €1,300 (€10 stake x odds of 5.0 x 26 wins) for an outlay of €1040, so you will show a net profit of €260, or 25% of your total outlay.

Even though you will lose more often than you win, even though you will lose three times more often than you will win, because you are betting at better odds than true odds, you will show a profit.

Same with the Ace of Hearts. In 104 draws, on average you will win just twice, but because you are betting at 81.0, your total return will be €1,620, for a total outlay of €1,040. As long as you can weather the long losing runs, that would give you a net profit of €580, or a net return of over 55% on your investment.

Horse racing betting, of course, is not like the spin of a roulette wheel or the draw of a card. Nobody knows what the true odds are for any horse winning any race. Early prices and morning prices and exchange prices and SPs are just a function of opinion, supply and demand, the ebbs and flows of the marketplace. Consequently, in endeavouring to filch out a value bet, to identify a horse that is available at a price that is greater than what you determine to be that horse’s true odds of winning, you will probably be going against popular opinion.

It can be a lonely place: standing there having backed a loser, when all around you are celebrating have backed the, telling you how big a certainty the favourite was. Arguments about odds and value do not wash after the race has been run.

Console yourself, though, with the fact that you can’t back-fit value. Just because a horse has won, it doesn’t mean that it was value at 6/4 beforehand, given the information that you had beforehand. Just because Tails has come up on the toss of a coin, it doesn’t mean that it was value at 4/5.

It’s all about the odds. A horse that you want to back at 6/1, is he still a bet if his odds have contracted to 7/2, if there has been no other material change to the make-up of the race? You want to bet on a diamond at 7/2 or 4/1, but you don’t want to bet on a diamond at 5/2 or 11/4.

Value is the goal though. Always. Because, if you can consistently bet on the outcome of an event at odds that are genuinely greater than the true odds for that outcome occurring, then, in the long run, you will make a profit.