Expected value calculator: EV per bet, edge and break-even

Expected value calculator

EV per bet: -
EV per $100 staked: -
Break-even chance: -
Your edge: -

Key facts

EV per $1 staked = chance of winning x decimal odds - 1. Multiply by your stake for EV per bet.
Break-even chance = 1 / decimal odds. At $1.90 you need to win 52.63% of the time just to break even.
In our calculation a $50 bet at $1.90 that wins 55% of the time is worth +$2.25 on average, +$4.50 per $100.
A true 50/50 at $1.90 is worth -$5.00 per $100, and every standard single zero roulette bet is worth -$2.70 per $100.
Positive EV does not mean you win: with a 4.5% edge you are still behind after 100 bets about 31% of the time, in our calculation.

How to use the expected value calculator

Enter the decimal odds on offer, your chance of winning as a percentage and your stake. The calculator shows the average result of the bet (EV per bet), the same figure per $100 staked, the break-even chance the price requires and your edge as a percentage of your stake. A positive edge means the price is longer than the chance deserves; a negative one means you are paying for the bet.

The chance is the hard part. For a casino bet it is fixed by the rules: 18 in 37 for red on a single zero wheel, for example. For a sports or racing bet it is your own estimate, and the calculator can only be as good as that number.

The expected value formula

A bet at decimal odds O either returns O per $1 (with probability p) or nothing (with probability 1 - p). Its average profit per $1 is:

EV = p x O - 1

From that one line you get everything else the calculator shows:

EV per bet = stake x (p x O - 1)
EV per $100 = 100 x (p x O - 1)
Break-even chance = 1 / O, the chance at which EV is exactly zero
Edge = p x O - 1, shown as a percentage

The break-even chance is the same number as the implied probability of the price. Our implied probability calculator shows it for a whole market at once, along with the bookmaker's margin.

Worked example: $1.90 with a 55% estimate

You can get $1.90 on a team you rate a 55% chance, and you stake $50.

Break-even chance: 1 / 1.90 = 52.63%.
Edge: 0.55 x 1.90 - 1 = 0.045, or +4.5%.
EV per bet: $50 x 0.045 = +$2.25.
EV per $100: +$4.50.

Now suppose the game is really a coin flip. At 50%, EV = 0.50 x 1.90 - 1 = -0.05, or -$5.00 per $100. That is the cost of the bookmaker's margin. Betfair's guide uses this exact pair of prices: two outcomes at $1.90 each add up to 105.3%, so the market has 5.3% built in above a fair 100%, and at a true 50% chance that costs you 5 cents in every dollar staked. Our guide to bookmaker margin explains how to spot it.

How EV changes with your estimate

At a fixed price, every extra point of probability adds the same amount of EV. In our calculation, per $100 staked:

Your chance	EV at $1.90	Your chance	EV at $3.00
50.00%	-$5.00	30.00%	-$10.00
52.63%	$0.00	33.33%	$0.00
55.00%	+$4.50	35.00%	+$5.00
60.00%	+$14.00	40.00%	+$20.00

Each percentage point is worth $1.90 per $100 at $1.90 and $3.00 per $100 at $3.00. Longer prices magnify both your skill and your mistakes: misjudge a $3.00 chance by 3 points and you have turned +$5 into -$4.

EV of common casino bets

Casino bets are the cleanest examples, because the chance comes straight from the rules. Every standard roulette bet has the same EV on a given wheel, in our calculation:

Bet	Chance of winning	Decimal odds	EV per $100
Single number, single zero wheel (pays 35 to 1)	1 in 37	36.00	-$2.70
Red, single zero wheel (pays 1 to 1)	18 in 37	2.00	-$2.70
Single number, double zero wheel	1 in 38	36.00	-$5.26
A pokie with a 90% RTP	set by the game	n/a	-$10.00

For a pokie, EV per $100 is simply the RTP minus 100: a 90% RTP game is worth -$10 per $100 turned over, whatever the hit rate. The pokies calculator turns that into a cost per hour, and our house edge guide compares games side by side.

Pundit tip: if you cannot say where your chance estimate comes from, use the market's chance with the margin taken out. At that chance every bet at the bookmaker's own price has a negative EV, which is the honest default.

Positive EV is not the same as winning

EV is an average. Any single bet still wins or loses in full, and a run of bets can stray a long way from its average. Here is the chance of being ahead after flat $1 bets at $1.90, in our calculation:

Number of bets	True chance 55% (+4.5% EV)	True chance 50% (-5% EV)
10	50.4%	37.7%
100	69.3%	30.9%
500	84.9%	11.4%
1,000	93.2%	4.7%

Over 10 bets, a genuine edge and a losing bet look much the same. It takes hundreds of bets for EV to show through, which is why short winning runs prove very little about a value betting approach. If you do have an edge, the Kelly criterion calculator sizes your stake so a bad run does not wipe out your bank.

Most bets most people make have negative EV, and that includes every casino game. Online casino games such as roulette and pokies cannot legally be offered to people in Australia under the Interactive Gambling Act 2001, although it is not an offence for you to play, and ACMA blocks illegal sites. Treat any gambling as paid entertainment, and if the cost stops feeling like entertainment, free help is available.

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Frequently asked questions

How do you calculate expected value in betting?

Multiply your chance of winning by the decimal odds and subtract 1. That is the average profit per $1 staked. At $1.90 with a 55% chance: 0.55 x 1.90 - 1 = 0.045, so +4.5 cents per dollar or +$4.50 per $100.

What is a positive EV bet?

A bet where your chance of winning is higher than the break-even chance of 1 divided by the odds. At $3.00 that means a chance above 33.33%. It is only positive if your estimate of the chance is right.

What does EV mean for casino games?

In a casino the chances are fixed by the rules, so EV is just the house edge with a minus sign. A $100 bet on red at single zero roulette is worth -$2.70 on average; on double zero it is -$5.26.

Is a positive EV bet guaranteed to make money?

No. EV is an average over many bets. In our calculation, flat bets at $1.90 with a true 55% chance are still behind after 100 bets about 31% of the time, and after 10 bets about half the time.

How is EV different from the Kelly criterion?

EV tells you whether a bet is worth making at all. Kelly takes the same edge and turns it into a stake size as a share of your bank. A bet with zero or negative EV gets a Kelly stake of zero.