Value Betting – Betting Odds with a Positive Expected Value
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Do you think that having perfect knowledge of a particular sport automatically makes you a successful bettor? Wrong! To be successful in the long run and perhaps even make money betting, you first and foremost need to understand odds. It is precisely this expertise that separates the wheat from the chaff—in our case, profitable bettors from losing ones. The profitable ones know that long-term profit can only be achieved by placing bets with a positive expected value, i.e. bets that have a greater chance of winning than the odds suggest. Over a longer time horizon, this eliminates luck, which of course plays its part in betting, and reduces variance to an acceptable minimum. What betting on value odds (also known as value betting) is all about and what it can look like in practice is what we will cover in the following lines.
What the Expected Value of a Bet Tells You
First of all, it is important to understand the term expected value of a bet. Before we get to an illustrative example, let's look at it from a general perspective. The expected value of a bet can be thought of as the average expected return on your stake, most commonly expressed as a percentage. Simply put, it is what we get back from our stake. Unlike slots, roulette and other gambling games you can encounter in a casino, which have a precisely defined value based on how they are programmed, calculating the value expressed by odds is a bit like gazing into a crystal ball, requiring certain knowledge and skills. To be able to calculate the exact value of opportunities, we would need to know the exact probabilities with which an outcome occurs. But if we knew the exact probabilities, we would be able to beat bookmakers regularly and they would go bankrupt. In betting, we can therefore work with the so-called expected value of a bet.
Let's pause for a moment on slots and roulette, where the return on stakes is indicated by the abbreviation RTP (return to player). In all casino games, this figure is less than 100%, which means that in the long run the casino always profits, because it pays players out less than they invested in the game. For slots, the RTP most commonly ranges between 75% and 95%. For French roulette with a single zero, we can easily calculate the return. There are 37 numbers on the roulette wheel including zero, but the payout for hitting a number is only 36 times the amount staked. We calculate the average return expressed as a percentage by dividing the paid-out winnings (36:1) by the probability of winning (37:1) and then multiplying by 100, i.e. (36 / 37) * 100 = 97.3%. In the long run, for every 100 CZK staked, we only get 97.3 CZK back. The casino always has an edge over us. But that is not the case with bookmakers.
The Classic Coin Toss Example
Back to betting. In probability theory, the expected value of a random event is the long-term average value of repeating the experiment it represents. A perfect example is a coin toss. Assuming that the chance of heads or tails coming up is exactly 50%, the fair odds for both outcomes should be 2.00. In that case, the bookmaker would take no margin and it would be a so-called 100% market, where neither side has an edge. The long-term return would be 100%, meaning for every 100 CZK staked on heads, we would get 100 CZK back.
However, to actually make a profit, we need to bet on odds with a positive expected value. So what would happen if the bookmaker listed the odds as follows: 2.20 (heads) – 1.60 (tails)? We use the formula for calculating expected value.
(probability of winning * amount won per bet) – (probability of losing * amount lost per bet)
We know that the probability of winning, as well as losing, is 50%. Probability is expressed on a scale from 0 to 1, so we will use the value 0.50 in our calculation. We have decided to stake 100 CZK on heads, so in the case of a win, the amount won is 120 CZK (stake * odds), while in the case of a loss, we lose 100 CZK. So let's plug these numbers into the formula.
(0.5 * 120 CZK) – (0.5 * 100 CZK) = 10 CZK
We can see that the expected value came out positive. For every 100 CZK staked on heads, we will be 10 CZK in profit (i.e. 10%) over the long run, so our decision to bet on heads is correct in this case, even though we will lose in 50% of cases. Our goal, however, is not to win every bet, but to make decisions that have a positive expected value.
Only place bets with a positive expected value!
The Best Bookmakers
Odds Represent the Probability of an Outcome as Set by the Bookmaker
How does the search for odds with a positive expected value work in practice? It starts with realizing that the listed odds represent nothing other than the probability of an outcome as determined by the bookmaker. It is up to us to assess how much this probability differs from reality, and if the chances of our pick winning are higher than those set by the bookmaker, to bet on that opportunity. By doing so, we place a bet on value odds (a value bet).
Formula for deriving odds from probability: 100 / probability of the outcome
Let's imagine, for example, a tennis match between Nadal and Djokovic, for which the bookmaker listed the odds as follows:
- Odds on Nadal winning: 2.25
- Odds on Djokovic winning: 1.70
To find out whether any of the listed odds hold value, we need to know the real chances of both players winning. This is where the biggest stumbling block comes in, because we can rarely estimate the chances precisely. Purely hypothetically, however, let's assume that based on our knowledge the chances are much more even than the listed odds suggest—specifically, we predict a 49% chance for Nadal and a 51% chance for Djokovic. Using the formula for calculating fair odds—odds that correspond as closely as possible to reality—we find the following:
- Nadal has a 49% chance of winning, so the fair odds are: 100 / 49 = 2.04
- Djokovic has a 51% chance of winning, so the fair odds are: 100 / 51 = 1.96
Now everything is clear. The listed odds of 2.25 on Nadal hold value, because his real chances of winning are expressed by odds of 2.04, whereas the odds of 1.70 on Djokovic do not hold value, because his real chances of winning are expressed by odds of 1.96! Another bettor, however, sees Djokovic's chances of winning at 60%, which is reflected by odds of 1.67, so for them it is the odds on Djokovic that hold value. In the long run, the more successful of us will be the one who can estimate the chances of winning as accurately as possible and find the discrepancy in the listed odds.
Calculating the Expected Value of a Bet
Calculation Using the Expected Value Formula
We already know the formula for calculating expected value, so let's see what it looks like once we plug in the individual values. For all models, we will use a stake of 1,000 CZK.
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- We start with the probabilities listed by the bookmaker.
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- Nadal at odds of 2.25 = 44.4% chance of winning
- Djokovic at odds of 1.70 = 58.8% chance of winning
If you are confused at this point and wondering why their chances add up to 103.2% instead of 100%, remember that bookmakers add a margin to their odds. So on this market, the bookmaker's margin is 3.2%.
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- Expected value of a 1,000 CZK bet on Nadal at odds of 2.25: (0.444 * 1,250 CZK) – (0.588 * 1,000 CZK) = -33 CZK.
- Expected value of a 1,000 CZK bet on Djokovic at odds of 1.70: (0.588 * 700 CZK) – (0.444 * 1,000 CZK) = -32.4 CZK.
Expressed as a percentage: with a 1,000 CZK bet on Nadal, the expected value of the bet is -3.3%, and with a 1,000 CZK bet on Djokovic, the expected value of the bet is -3.2%.
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- Now we use our own probability.
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- Nadal at odds of 2.25; our own probability of winning = 49%
- Djokovic at odds of 1.70; our own probability of winning = 51%
Now let's see how the expected value of the bet changes once we plug these into the formula.
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- Expected value of a 1,000 CZK bet on Nadal at odds of 2.25: (0.49 * 1,250 CZK) – (0.51 * 1,000 CZK) = 102.50 CZK.
- Expected value of a 1,000 CZK bet on Djokovic at odds of 1.70: (0.51 * 700 CZK) – (0.49 * 1,000 CZK) = -133 CZK.
Expressed as a percentage: with a 1,000 CZK bet on Nadal, the expected value of the bet is roughly 10.3%, and with a 1,000 CZK bet on Djokovic, the expected value of the bet is -13.3%.
Calculation Using the Formula Based on the Listed and Fair Odds
To avoid having to calculate the expected value of a bet in an overly complicated way, we can use a simpler calculation, for which we only need to know the odds listed by the bookmaker and the fair odds, which we calculate based on the probability we assign to the given pick. The formula for calculating the percentage value of odds looks like this:
[(listed odds/real odds) – 1] * 100
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- For Nadal, we plug in these values: [(2.25 / 2.04) – 1] * 100 = 10.3%
- For Djokovic, we plug in these values: [(1.70 / 1.96) – 1] * 100 = -13.3%
Value Betting Looks Simple at First Glance, but Appearances Are Deceiving
In conclusion, all that remains is to say that we have at least partially explained how important it is to think about the listed odds. On the other hand, it is important to keep in mind that even though the example we used tempts you into the heretical thought that finding value is easy, the opposite is true. In reality, you are fighting a battle not only against bookmakers, who have computer-modeled odds at their disposal and the advantage of a margin, but also against other bettors, whose bets sharpen the odds into their most efficient form.
Frequently Asked Questions
1️⃣ Does value betting really work?
Not only does it work, it works brilliantly. It is important to realize that it is a long-term strategy which, if you truly place bets with a positive expected value, will lead to consistent long-term profit.
2️⃣ What is the principle behind value betting?
Betting on value odds is essentially the ability to identify an edge in the odds offered by the bookmaker. If the chances of our pick winning are higher than those set by the bookmaker, we have managed to find a value bet.