Value Bets and Expected Value: How to Calculate Them and Why They Are Hard to Prove

The term value bet is often used in promotions and tip groups as if it were a secret. This article opens it up as it is: a calculation anyone can check.

The definition is simple: a value bet is a bet whose chance of winning, in someone’s estimate, is larger than the chance implied by the odds. If that estimate is right, the bet’s expected value is positive.

Note the two key phrases: “in someone’s estimate” and “if right”. The whole concept depends on a number that is never known for sure, the true probability. That is why it is better called an expected-value calculation than a secret to profit.

All numbers here are made up for learning. This article recommends no bet and assesses no site or provider. Readers are free to judge the calculation themselves, and the tool in section 4 shows every number it uses.

The calculation compares two numbers.

• The probability implied by the odds. For decimal odds d it is 1 ÷ d. Odds of 2.00 imply 50%, and odds of 1.90 imply about 52.6%. The basics are in the (Indonesian) Panduan Sportsbook.
• Your estimate of the probability. This comes from a model, data, or personal judgement. Its source is not the odds.

“Value” exists only if your estimate is higher than the implied probability. The difference is the edge, the claimed advantage.

Example: odds of 2.00 imply 50%. If someone estimates the true probability at 55%, the edge is 5 percentage points. The question worth asking is not “how big is the edge” but “how sure is that 55%, and what is the evidence?”

Expected value (EV) per 1 unit staked comes from one formula:

At odds of 2.00 with a true probability of 55%, the expected value is +10%: on a stake of 100,000, an average of +10,000 per bet if that situation were repeated very many times. At 45% the result is −10%. Notice that a 10-point difference in the estimate changes the result from +10% to −10%.

Expected value is a long-run average, not the result of one bet. A single bet simply ends in a full win or a full loss.

Because the true probability is unknown, the most important part of this calculation is how fragile the result is to errors in the estimate.

At odds of 2.00 and an estimate of 55%, the expected value is +10%. If the true probability is only 52%, it falls to +4%. At 50% it is zero. At 48% it is −4%. A small error is enough to erase or flip the “value”.

The tool below shows this. Enter the odds and your probability estimate, then look at the “If your estimate is off” table at the bottom. It does not search for matches and does not recommend bets; it only calculates from the two numbers you enter.

The tool runs in your browser and neither stores nor sends data. Every result depends on the numbers you enter.

The odds on offer already include the provider’s margin. In a balanced two-way market the fair price for each side is 2.00, yet the offer is often about 1.90 for both sides.

As a result the break-even point shifts. At odds of 1.90 the implied probability is about 52.6%, not 50%. An estimate of 50% at odds of 1.90 gives an expected value of −5.0%: a 5% loss of the stake on average, not break-even.

So to win on average, a person’s estimate must be more accurate than a price that has already been corrected for the margin, not just more accurate than a guess. The margin is explained in the (Indonesian) Panduan Sportsbook, its accumulation across many selections in Mix Parlay, and its relation to the provider’s advantage in House Edge.

Suppose someone really does have an advantage. How can they prove it, and how can others check it? The answer: with a great many results.

A rough sample-size illustration: the number of similar bets at which the 95% margin of error is about the size of the gap. It is not a test design with a stated power, so the number needed for convincing proof can be larger:

By this illustrative formula, an edge of 5 points needs hundreds of similar bets for the margin of error to shrink to the size of the gap, and an edge of 1 point almost ten thousand; for convincing proof the number can be larger. This kind of evidence does not come from a week or two, or from screenshots. The statistical reason is covered in Sample Size and Uncertainty.

So profit in the short run does not prove an advantage, and loss in the short run does not prove its absence. All that can be checked is a complete record, including every bet that lost.

An expected-value calculation looks tidy, but there are things no model can see.

• The true probability is never known. There are only estimates, and an estimate can be wrong without anyone noticing.
• Late or incomplete information. Injuries, line-ups and team condition are often known to the market before outside observers.
• The market already contains a lot of information. A price that looks “wrong” often reflects something you do not yet know.
• Results that are not purely random. Match-fixing by criminal networks has been proven in many countries and sports. A simple model like the calculators on this blog has no way to tell a fixed result from ordinary competition. Integrity bodies use statistical and market analysis as a filter, but still need investigation and other evidence. It is discussed in Match-Fixing Is Real.

So an expected value that looks positive on paper is a statement about an estimate, not about reality.

Exercise without betting

Odds of 1.80 and an estimated probability of winning of 58%. Compute the implied probability, the edge, the expected value per unit, and an illustrative number of similar bets using the formula in section 6.

Five things to remember

1. A value bet is a calculation: the estimated probability compared with the probability implied by the odds.
2. Expected value = probability × odds − 1, and it is a long-run average.
3. The result is very fragile to estimation errors, which can flip it from positive to negative.
4. Odds contain a margin, so break-even is not 50%.
5. Proving an advantage takes a very large, fully recorded body of results, not a few outcomes.

Laws differ in every country. In Indonesia, gambling, including online, is prohibited by law. This article is written to open up how the calculation works, not as an invitation to bet.