One of the most interesting things about betting is that nobody knows the true probability of the outcome of an event (other than a coin toss). Bookmakers set odds based on their assumptions and the state of the market. A value bettor will attempt to capitalise on the probabilities implied by odds they believe to be incorrect.
In order to find value a bettor needs to determine their own probability of an event occurring. In simple terms, if a bettor is able to correctly identify events where the probability of the event occurring is higher than that implied by the bookmaker’s odds then they will win in the long run.
Bet offers value when:
probability of outcome > probability implied by odds
Let’s use the example of a fair coin toss. Ignoring the chance the coin lands on its side we know that the chance of a head is 50%. This implies fair odds of 2.00. Once the bookmaker adds their margin the odds could be (depending upon the bookmaker) around 1.91 implying a 52.4% chance of the toss resulting in heads.
We know that this bet offers poor value since we are receiving odds on a 50% likelihood as if there was a 52.4% chance of heads.
Now imagine there is some uncertainty as to the percentage chance of heads. We have calculated that the chance of heads is 50% but the market is uncertain. The bookmaker is now offering odds of 2.2 on heads.
This now offers the opportunity to take a bet with 50% odds as if the event had only a 45.5% chance of occurring. This is a value bet.
We can determine the profitability of a bet by using the expected value formula:
So with our coin toss example the expected value calculation from a €10 stake is:
0.5 x €12 – 0.5 x €10 = +€1
For each €10 bet the expected return is €11 (a profit of €1).
For each coin flip we can expect to win €11 for every €10 staked. This would become very lucrative in the long run.
A good way to find value bets is to look at differences in bookmaker odds. Where bookmakers disagree about the chance of an event occurring may be where value is present.
Building a superior model or taking advantage of information asymmetrycan also be a good way to find value. If a model or inside information gives the bettor a clearer grasp of true probability than the bookmaker then profits are available.
When value betting it is important to bet for the long-term. Even with the clear edge on the coin toss at 2.2 odds there is still a 50% chance that the bettor loses. This is when a staking strategy becomes important as bankrolls can be decimated by over staking, even on bets that offer value.
In the long run this strategy pays off. After 100 coin flips staking €10 the bettor would expect to have €1100 from the €1000 wagered.
In a similar way, if a sports bettor can find enough value bets they will win in the long run.