# Expected Value in Betting: Do the Maths Yourself

Source: https://cricketin.org/guides/expected-value-explained

[By Nikhil Varma](/authors/betting-analyst), Betting and Odds Analyst. [Reviewed by Rajeev Sathe](/authors/editor-in-chief), Editor-in-Chief. Updated 25 Aug 2026. Editorial policy: https://cricketin.org/editorial-policy

18+ Betting money on cricket carries a direct risk of financial loss, and it can become an addiction. Real-money online gaming is banned across India under the PROG Act 2025, which came into force on 1 May 2026.

If betting is already costing you money you need, or sleep, or people close to you, the free Tele-MANAS helpline is **14416**, and it runs in 20 languages. Our [page on help for gambling harm](/guides/help-for-gambling-harm-india) lists what else exists.

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Expected value is the average result of a bet over many repeats. Learn the formula, follow four worked cricket examples, and see why it runs negative.

Expected value is what a bet averages if you could repeat it endlessly. It equals the chance of winning times the profit, minus the chance of losing times the stake. A ₹1,000 bet at 1.90 on a true 50-50 outcome has an expected value of minus ₹50, which is minus 5% of the stake.

This page gives the formula, four worked calculations, the reason the fee makes the answer negative by design, and a plain explanation of the law of large numbers and the urge to win losses back.

## Expected value in one plain sentence

Expected value is the average result of a bet if you could make it again and again. Statisticians call it the expectation or the mean, and it is a weighted average of the outcomes with their probabilities as weights ([Wikipedia on expected value](https://en.wikipedia.org/wiki/Expected_value)).

For a bet there are two outcomes. You win a profit, or you lose the stake. Weight each by its chance, add them, and you have the expected value.

The number is not a prediction of one bet. One bet gives you a win or a loss, never an average. The average shows up over many repeats, which is what the law of large numbers describes ([Wikipedia on the law of large numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers)).

One legal note before the sums. Real-money online gaming is banned in India under the PROG Act 2025, in force since 1 May 2026, offshore apps included ([Nishith Desai](https://nishithdesai.com/research-and-articles/hotline/gaming-law-wrap/setting-the-rules-of-the-game-indias-online-gaming-law-comes-into-force-15586)). We are teaching arithmetic, not access.

## The formula, written out

Use this form and nothing else is needed.

Expected value = (chance of winning × profit if you win) − (chance of losing × stake).

Two inputs, both easy. Profit if you win is stake × (decimal odds − 1), which our [page on reading odds](/guides/how-cricket-odds-work) covers. The chance of winning is your own estimate, not the price.

That second point is the whole game. If you use the price as your probability, the answer is roughly the fee, every time. You have to bring a view of your own.

## Worked example one: the ordinary bet

**Inputs.** Stake ₹1,000. Price 1.90. Your honest view: a 50-50 match.

**Formula.** Profit if win = 1,000 × (1.90 − 1) = ₹900. EV = (0.50 × 900) − (0.50 × 1,000).

**Result.** EV = 450 − 500 = −₹50. That is −5.00% of the stake.

**Assumptions.** The 50% is your estimate and it might be wrong. The price is one you were actually offered. Tax is not included, and tax makes the figure worse. Nothing here is a measurement of any operator.

Read the result carefully. A fair coin at 1.90 loses you fifty rupees per thousand, on average. The bet is not unlucky. It is priced to lose.

## Worked example two: when EV turns to zero

**Inputs.** Stake ₹1,000. Your view: the outcome happens 40% of the time. Price 2.50.

**Formula.** Profit if win = 1,000 × 1.50 = ₹1,500. EV = (0.40 × 1,500) − (0.60 × 1,000).

**Result.** EV = 600 − 600 = ₹0. The bet breaks even on average.

**Assumptions.** 2.50 is the fair price for a 40% chance, because 1 ÷ 0.40 = 2.50. Break-even is the ceiling a fee-free market offers, not a profit.

Now shave the price a little, the way a real market does.

**Inputs.** Same 40% view. Same ₹1,000 stake. Price cut to 2.35.

**Formula.** Profit if win = 1,000 × 1.35 = ₹1,350. EV = (0.40 × 1,350) − (0.60 × 1,000).

**Result.** EV = 540 − 600 = −₹60, which is −6.00% of the stake.

**Assumptions.** The cut from 2.50 to 2.35 is the seller's fee in visible form. You were right about the chance and still lost value.

That is the lesson of the page. Being right is not enough. You have to be right by more than the fee.

The table gathers several combinations of view and price. All of it uses a ₹1,000 stake, and every row was worked with the formula above.

**Table 1. Expected value on a ₹1,000 bet at different prices and different honest estimates**

| Your estimate | Price taken | Profit if it wins | Expected value | Share of stake |
|---|---|---|---|---|
| 50% | 1.80 | ₹800 | −₹100 | −10.00% |
| 50% | 1.90 | ₹900 | −₹50 | −5.00% |
| 50% | 2.00 | ₹1,000 | ₹0 | 0.00% |
| 50% | 2.10 | ₹1,100 | +₹50 | +5.00% |
| 40% | 2.35 | ₹1,350 | −₹60 | −6.00% |
| 40% | 2.50 | ₹1,500 | ₹0 | 0.00% |
| 40% | 2.60 | ₹1,600 | +₹40 | +4.00% |
| 60% | 1.80 | ₹800 | +₹80 | +8.00% |

Look at the positive rows. Each one needs your estimate to beat the price by a clear margin. Two of them need you to be right about a 60% or 40% chance that the market has mispriced.

## Why the maths runs negative by design

Prices in a market add to more than 100%. Two sides at 1.90 imply 52.63% each, so the book is 105.26% and the excess of 5.26% is the seller's fee, the overround ([Whelan, Estimating Expected Loss Rates in Betting Markets](https://www.karlwhelan.com/Papers/Overround.pdf)).

Feed that fee into the EV formula and it appears as a minus sign. The expected payout on a stake is 1 divided by the book, which is below 1 whenever the book is above 100% ([Whelan](https://www.karlwhelan.com/Papers/Overround.pdf)).

**Inputs.** A market where the price is exactly right. Price 1.90, true chance equal to the implied 52.63%. Stake ₹1,000.

**Formula.** EV = (0.5263 × 900) − (0.4737 × 1,000).

**Result.** EV = 473.67 − 473.70, which is zero within rounding.

**Assumptions.** This is the only way a priced bet reaches zero: your view must match the price exactly. Since both sides cannot be priced at their true chance while the book totals 105.26%, at least one side must be negative, and in practice both usually are.

So a positive EV bet needs one of two things. A price mistake by the seller, or better information than the market has. Neither is available to a casual bettor, and prices are corrected as money arrives.

The rupee scale of the fee across markets is on our [overround page](/guides/what-is-overround). Where prices come from is on our [page on how odds are set](/guides/how-bookmakers-set-odds).

## What a hundred bets look like

A single −₹50 bet feels like nothing. Repeat it and the arithmetic gets loud.

**Inputs.** 100 bets. ₹1,000 each. EV of −₹50 per bet.

**Formula.** Total turnover = 100 × 1,000. Total EV = 100 × (−50).

**Result.** Turnover ₹100,000. Expected loss ₹5,000, which is 5% of everything staked.

**Assumptions.** Every bet carries the same fee, which is optimistic: smaller markets cost more. Results in a real run swing above and below this line. The line itself does not move.

Now recycle a balance instead of adding new money. The same percentage is shaved each time round.

**Inputs.** Bankroll ₹10,000. Fee 5.26% per bet. Whole balance staked each time.

**Formula.** Balance left = 10,000 × (1 − 0.0526) raised to the number of bets.

**Result.** After 10 bets, ₹5,826. After 20 bets, ₹3,394. After 50 bets, ₹671.

**Assumptions.** This is the average path only. It ignores tax, which lands on winnings at a flat 30% under Section 115BBJ ([Income Tax Department](https://www.incometaxindia.gov.in/w/section-115bbj)), with no set-off for losses ([Income Tax Department](https://www.incometaxindia.gov.in/w/winnings-from-online-games)).

Fifty bets is one busy evening for an in-play bettor. Our [fancy bets page](/guides/fancy-bets-explained) shows how quickly that count is reached.

## The law of large numbers, in plain words

Toss a coin ten times and you might see seven heads. Toss it ten thousand times and the share of heads sits very near half.

That is the law of large numbers. The average of many independent repeats moves towards the true expected value, and it gets tighter as the count grows ([Wikipedia on the law of large numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers)). The standard example is a die: the expected roll is (1+2+3+4+5+6) ÷ 6 = 3.5, and the average of many rolls approaches 3.5 ([Wikipedia](https://en.wikipedia.org/wiki/Law_of_large_numbers)).

Apply that to betting and the news is bad for the bettor. The law does not promise your luck will turn. It promises the average will win, and the average has a minus sign in front of it.

There is a second trap here. Small samples are not representative, and treating them as if they were is a known error ([Wikipedia on the gambler's fallacy](https://en.wikipedia.org/wiki/Gambler%27s_fallacy)). A good week proves nothing about your edge.

## Why trying to win it back makes it worse

After a loss, the urge is to bet bigger and get level. The maths gives that plan no support.

Each bet is a fresh event with the same negative expected value. Doubling the stake doubles the expected loss. It does not buy back the last one.

The belief that a loss makes a win due is the gambler's fallacy. An independent outcome is not more likely because it has been missing, and each die roll stays at one chance in six ([Wikipedia](https://en.wikipedia.org/wiki/Gambler%27s_fallacy)). Runs of the same result are ordinary, and five heads in a row has a chance of 1 in 32, a little over 3% ([Wikipedia](https://en.wikipedia.org/wiki/Gambler%27s_fallacy)).

Chasing has a name in clinical research too. It means continuing to gamble in order to win back losses, and it is treated as a core feature of problem gambling, seen both within a session and across days ([peer-reviewed review of chasing behaviour](https://pmc.ncbi.nlm.nih.gov/articles/PMC11331606/)).

If any of that sounds familiar, our page on [signs of gambling addiction](/guides/signs-of-gambling-addiction) and our list of [help for gambling harm in India](/guides/help-for-gambling-harm-india) are the right next reads.

## Do the sum yourself, in four steps

- Write your own chance for the outcome, as a percentage, before you look at the price.
- Work out the profit if you win: stake × (price − 1).
- Put both into the formula and get the expected value in rupees.
- Multiply by the number of bets you expect to place this month.

Step four is the honest one. It converts a small negative into the figure you will actually pay.

Two habits make the exercise real. Write your probability down before seeing the price, so the price cannot anchor you. And use the same stake in the sum that you truly place, not a modest example.

Every term used here appears in our [betting glossary](/guides/cricket-betting-glossary). The full library sits on the [guides hub](/guides), and the legal picture is in our [PROG Act explainer](/legal/prog-act-2025-explained).

## Questions people ask

### Can expected value ever be positive for a normal bettor?

Only if the price is wrong and you know why. Because the two sides of a market add to more than 100%, at least one side must carry negative value ([Whelan](https://www.karlwhelan.com/Papers/Overround.pdf)), and prices get corrected as money arrives.

### Does a positive run mean my method works?

Not by itself. Small samples are not representative ([Wikipedia](https://en.wikipedia.org/wiki/Gambler%27s_fallacy)). The average only shows through over many repeats, which is what the law of large numbers describes ([Wikipedia](https://en.wikipedia.org/wiki/Law_of_large_numbers)).

### Should I use the price as my probability?

No. If you do, the answer will simply be the fee. Write your own estimate first, then compare it with what the price implies.

### Does raising my stake improve expected value?

No. The percentage stays the same and the rupee loss grows with the stake. Doubling the stake doubles the expected loss.

### Where does tax fit into the expected value sum?

After the maths, and against you. Winnings are taxed at a flat 30% under Section 115BBJ ([Income Tax Department](https://www.incometaxindia.gov.in/w/section-115bbj)) and losses cannot be set off ([Income Tax Department](https://www.incometaxindia.gov.in/w/winnings-from-online-games)).

## More from the guides

- [Fancy Bets in Cricket Explained](/guides/fancy-bets-explained)
- [Help for Gambling Harm in India](/guides/help-for-gambling-harm-india)
- [How Bookmakers Set Cricket Odds](/guides/how-bookmakers-set-odds)
- [How Cricket Odds Work](/guides/how-cricket-odds-work)
- [How DRS Works in Cricket](/guides/how-drs-works)
- [How Net Run Rate Works](/guides/how-net-run-rate-works)
- [How Pitch Conditions Change a Cricket Match](/guides/how-pitch-conditions-work)
- [How to Spot a Fake Cricket App](/guides/how-to-spot-a-fake-cricket-app)
- [KYC for Online Gaming in India](/guides/kyc-in-online-gaming-india)
- [Supreme Court on Online Gaming](/legal/supreme-court-online-gaming-cases)
- [TDS on Online Gaming Winnings](/legal/tds-on-winnings-india)
- [Caribbean Premier League 2026 — live schedule and table](/leagues/cpl)