Bet Payout Calculator

By Alex Thornton · author of the MIT-licensed teachersbettextbook library · Last reviewed 24 July 2026

Stake and price in; profit and total return out, with the price restated in every notation — American, decimal, fractional, percentage, contract cents. Then the part no other payout calculator prints: what the same bet would return at the vig-free price.

A bet payout calculator turns a stake and a price into two numbers: the profit if the bet wins, and the total return, which is that profit plus the stake coming back. Profit is S × (d − 1) and total return is S × d, where S is the stake and d is the decimal form of the price.

\text{profit} = S\,(d - 1) = S\,b, \qquad \text{return} = S\,d, \qquad d = 1 + b

where:

$S$ — the stake, in dollars: the amount at risk if the bet loses.
$d$ — decimal odds: total return per dollar staked, including the dollar back. −110 is $d = 1.9091$ ; +250 is $d = 3.50$ .
$b = d - 1$ — net profit per dollar staked. This is what American and fractional odds quote.
$\text{ml}$ — the American moneyline: $b = \text{ml}/100$ when positive, $b = 100/|\text{ml}|$ when negative.
$\rho$ — the market’s overround, the amount both sides’ implied probabilities exceed 1. It is what separates the posted payout from the fair one.

And the comparison that makes this page worth more than a multiplication. Under proportional de-vigging, the fair payout is the posted payout scaled by the overround:

\text{return}_{\text{fair}} = S\,d\,(1 + \rho), \qquad \text{cost of the vig} = S\,d\,\rho

Worked example — the numbers in the form below

$100 at −110, with the other side of the market also at −110:

d = 1 + \tfrac{100}{110} = 1.9091 \Rightarrow \text{profit} = \$90.91, \quad \text{return} = \$190.91

\rho = 0.5238 + 0.5238 - 1 = 4.76\% \Rightarrow \text{fair } d = 2.000

\text{return}_{\text{fair}} = \$190.91 \times 1.0476 = \$200.00, \qquad \text{gap} = \$9.09

A coin flip priced at −110 pays $90.91 where the fair price pays $100.00. The $9.09 is the house margin, in dollars, on this single bet — the same 4.76% overround the vig calculator reports, multiplied by the money that comes back.

Converting between price formats on their own? The odds converter does the five-way conversion with the derivation →

Profit and total return are not the same number

Most payout arguments are this confusion wearing a disguise. The two quantities differ by the stake, and the odds formats disagree about which one they quote:

American quotes profit. +250 means $250 of profit per $100 staked; −110 means $110 staked to profit $100.
Fractional quotes profit. 5/2 is $5 of profit for every $2 staked.
Decimal quotes total return. 3.50 means $3.50 comes back per $1 staked — $2.50 of it profit.
Contract cents quote cost. A 40¢ contract pays $1 at settlement, so it costs 40¢ and returns 60¢ of profit.

Same price, four conventions, and a bet slip that shows “to win $250” next to “total payout $350” is showing both. The calculator above prints both every time, labelled, so there is nothing to infer.

Payout table on a $100 stake

American	Decimal	Fractional	Implied	Profit	Total return
−200	1.500	1/2	66.67%	$50.00	$150.00
−150	1.667	2/3	60.00%	$66.67	$166.67
−110	1.909	10/11	52.38%	$90.91	$190.91
+100	2.000	1/1	50.00%	$100.00	$200.00
+120	2.200	6/5	45.45%	$120.00	$220.00
+150	2.500	3/2	40.00%	$150.00	$250.00
+250	3.500	5/2	28.57%	$250.00	$350.00
+400	5.000	4/1	20.00%	$400.00	$500.00

Payouts scale linearly in the stake, so this table works for any amount: $37 at +250 profits $37 \times 2.50 = \$92.50$ . The implied column is the price’s vig-inclusive probability, which is also its break-even win rate.

The same payout at the fair price

A payout is arithmetic; whether it is a good payout is a comparison. The comparison needs the other side of the market, because one price alone cannot say how much margin is in it.

Under proportional de-vigging the answer is unusually tidy. If both sides’ implied probabilities sum to $1 + \rho$ , then de-vigging divides every implied probability by that sum, which multiplies every decimal price by it:

p_i = \dfrac{q_i}{1 + \rho} \quad\Longrightarrow\quad d_i^{\text{fair}} = \dfrac{1}{p_i} = d_i\,(1 + \rho)

So the fair payout is the posted payout times the overround factor, whatever the price. At −110 / −110 that factor is 1.0476, turning a $190.91 return into $200.00. The $9.09 difference is not an opinion about the teams; it is the margin, converted from percent into money.

That identity is exact for the proportional method only. The power and Shin methods split the margin unevenly between favourite and longshot, so on a lopsided market they produce a different fair payout for each side. The calculator names the method it used, and the example below shows how much it can matter.

Second example: $50 at +250, other side −310

d = 3.50 \Rightarrow \text{profit} = \$125.00, \quad \text{return} = \$175.00

q_A = 28.57\%,\; q_B = 75.61\% \Rightarrow \rho = 4.18\%

\text{proportional: } d^{\text{fair}} = 3.50 \times 1.0418 = 3.6463 \Rightarrow \text{profit}_{\text{fair}} = \$132.32

The posted price pays $125.00 where a zero-margin market pays $132.32 — a $7.32 gap, which is exactly the $175.00 return times the 4.18% overround. Switch the method and the fair figure moves: power puts the underdog’s fair probability at 25.98% and its fair profit at $142.47, Shin at 26.48% and $138.82. On a lopsided market the choice of de-vig method is worth more than $10 on a $50 bet, which is why this page never reports a single fair number without naming how it got there.

Prediction-market contracts pay $1

An event contract settles at $1 if the event happens and $0 if it does not, so the price is the cost and the payout is fixed. A 40¢ contract costs 40¢ and returns $1.00: 60¢ of profit on 40¢ at risk, which is $b = 1.50$ — the same price as +150.

d = \dfrac{1}{P}, \qquad \text{profit per contract} = 1 - P, \qquad \text{contracts for } \$S = \dfrac{S}{P}

$100 at 40¢ buys 250 contracts, returns $250.00 and profits $150.00 — identical to $100 at +150 at a sportsbook, before fees. Fees are where the two diverge: the sportsbook takes its margin in the line, the exchange takes it on the fill. The Kalshi fee calculator prices that side, and prediction-market odds covers the conversion in both directions.

Free bets pay profit only

A stake-not-returned token is the one case where total return and profit collapse into the same number. The token is not cash, so it does not come back:

\text{profit}_{\text{free bet}} = F\,(d - 1), \qquad \text{return} = F\,(d-1)

A $100 free bet at +250 pays $250, not $350. That single missing term is why a token is worth $(d-1)/d$ of its face value rather than all of it — 71.4% at +250, and only 47.6% at −110. The free bet calculator works the conversion out.

Pushes, voids and cashing out

A push returns the stake. Profit is $0 and total return is $S$ . It is not a loss and it is not a win; graded records drop it from the denominator entirely.
A void does the same thing — but on a parlay it removes the leg and reprices the rest, which changes the payout of every remaining combination. The parlay calculator shows the multiplication.
A cash-out is a hedge at the book’s own price. The book offers to buy the position back, and the offer is priced with margin on top of the current line. Running the same position through the hedge calculator at a competing venue’s price prices that difference instead of accepting it.
Odds boosts raise $d$ and nothing else, so the payout arithmetic is unchanged. Whether the boosted price beats fair is a separate question for the expected value calculator.

Common mistakes

Multiplying by decimal odds and calling it profit. $S d$ is the total return. Profit is $S(d-1)$ . On a $500 bet at 1.909 the difference is the entire $500 stake.
Reading a negative American price as a payout. −110 is not $110 of anything won; it is $110 risked per $100 of profit. The profit on $110 is $100, so the profit on $100 is $90.91.
Comparing payouts across formats without converting. 3.50 and +250 are the same price. 3.50 and 5/2 are the same price. The only way to see it is to put them in one column, which the calculator does.
Assuming a bigger payout means a better price. Payout size is a function of the price alone. Whether the price beats fair needs the other side of the market and a de-vig — the section above, then expected value.
Forgetting the exchange fee. A contract’s $1 settlement is gross. The fee comes out of the entry and again out of an early exit; only settlement is free.
Treating a boosted or promotional payout as a fair price. It is still one side of a market, and the fair comparison is the same one this page runs.

Check this number yourself

The payout is one multiplication and the fair payout is one de-vig. Both are in the MIT-licensed teachersbettextbook package, which is the same math this page runs.

pip install teachersbettextbook

>>> from teachersbettextbook import decimal_odds, devig, overround
>>> S, d = 100.0, decimal_odds(-110)
>>> S * (d - 1), S * d               # profit, total return
(90.909090..., 190.909090...)
>>> rho = overround(-110, -110); rho
0.047619047...
>>> S * d * (1 + rho)                # the fair total return
200.0
>>> 1 / devig(-110, -110, 'proportional')[0]   # the same fair decimal
2.0

Same inputs, same digits, no account required. More on what is open and what is not: open source.

A payout is the first number and the least interesting one. The odds converter handles the price formats on their own, implied probability turns a price into a chance, the no-vig calculator removes the margin the fair-payout section subtracts, and expected value answers whether the payout is worth the risk at all.

Frequently asked questions

What is a bet payout calculator?

A bet payout calculator turns a stake and a price into the profit a winning bet returns and the total return, which is that profit plus the stake coming back. Profit is S × (d − 1) and total return is S × d, where S is the stake and d is the decimal form of the price.

How do you calculate the payout on a bet?

Convert the price to decimal odds and multiply. A −110 price is decimal 1.909, so $100 returns $190.91 in total and $90.91 of that is profit. A +250 price is decimal 3.50, so $100 returns $350.00 with $250.00 of profit. American prices already quote the profit on $100 staked, which is why +250 pays $250.

What is the difference between profit and total return?

Total return includes the stake coming back; profit does not. A winning $100 bet at +150 shows a $250 total return in the bet slip and $150 of profit. Decimal odds quote total return per unit staked, American and fractional odds quote profit, and mixing the two conventions is the most common payout error there is.

What does $100 at +250 pay?

$250 of profit and $350 back in total. The decimal form is 3.50 and the fractional form is 5/2, so every dollar staked returns three dollars fifty. The break-even win rate that price implies is 28.57%.

What would the same bet pay at a fair price?

More, by exactly the market’s overround. Under proportional de-vigging the fair total return is the posted total return multiplied by (1 + ρ), where ρ is the sum of both sides’ implied probabilities minus one. At −110 on both sides ρ is 4.76%, so a $190.91 return should be $200.00 and the $9.09 gap is the house margin measured in dollars.