Calculator

Bet Payout Calculator

About this calculator

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

What comes back if it wins, what the same bet returns at the fair price, and the gap between the two.

Converting price formats alone? The odds converter, with the derivation →

A bet payout calculator turns a stake and a price into the profit if the bet wins and the total return, which is that profit plus your stake back.

Profit and return are different numbers

Profit is what you win. Total return is that plus your stake back. They differ by exactly the stake, and confusing them is the most common arithmetic mistake in betting.

A $100 bet at +150 profits $150 and returns $250. A prediction-market contract always returns $1, so the price you paid is the whole story there.

A bonus bet pays profit only. The token never comes back, which is why it is worth less than the number printed on it.

The page also shows what the same bet returns at the vig-free price. That difference is what the cut costs you, in dollars, on this bet.

Want more math?the Nerd Corner

\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, how much both sides’ implied probabilities exceed 1. It separates the posted payout from the fair one.

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 gap is the house margin in dollars: the 4.76% overround the vig calculator reports, times the money that comes back.

Profit and total return are not the same number

The two differ by the stake, and the 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: 40¢ in, 60¢ of profit.

A slip reading “to win $250” beside “total payout $350” is quoting both. The calculator prints both, labelled.

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: $37 at +250 profits $37 \times 2.50 = \$92.50$ . The implied column is the price’s vig-inclusive probability, 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, and that needs the other side of the market. One price alone cannot say how much margin is in it.

If both sides’ implied probabilities sum to $1 + \rho$ , de-vigging divides each by that sum, which multiplies each 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.

That identity holds for the proportional method only. Power and Shin split the margin unevenly between favourite and longshot: on $50 at +250 against −310, fair profit is $132.32 proportional, $142.47 power, $138.82 Shin. The calculator names the method it used.

Prediction-market contracts pay $1

An event contract settles at $1 or $0, so the price is the cost and the payout is fixed. A 40¢ contract 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, before fees. The book takes its margin in the line; the exchange takes it on the fill, at entry and again on an early exit, so only settlement is free. The Kalshi fee calculator prices that side; prediction-market odds covers the conversion.

Free bets pay profit only

A stake-not-returned token is the one case where profit and total return are the same number: the token is not cash and 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, which is why a token is worth $(d-1)/d$ of its face value: 71.4% at +250, 47.6% at −110. The free bet calculator works it out.

Pushes, voids and cashing out

A push returns the stake. Profit is $0 and total return is $S$ ; graded records drop it from the denominator.
A void does the same, but on a parlay it removes the leg and reprices the rest, changing every remaining combination. The parlay calculator shows the multiplication.
A cash-out is a hedge at the book’s own price, margin included. The hedge calculator prices the same position at a competing venue instead.

Check this number yourself

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

pip install teachersbettextbook

>>> from teachersbettextbook import decimal_odds, overround
>>> S, d = 100.0, decimal_odds(-110)
>>> S * (d - 1), S * d               # profit, total return
(90.909090..., 190.909090...)
>>> S * d * (1 + overround(-110, -110))   # the fair total return
200.0

Same inputs, same digits, no account. More: open source.

A payout is arithmetic on one price. Whether that price is worth taking at all is expected value.

Frequently asked questions

How do you calculate the payout on a bet?

Convert the price to decimal odds and multiply: profit is S × (d − 1) and total return is S × d. 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.

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 and $150 of profit. Decimal odds quote total return; American and fractional odds quote profit. Mixing the two is the most common payout error there is.

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 times (1 + ρ). At −110 on both sides ρ is 4.76%, so a $190.91 return should be $200.00, and that $9.09 is the house margin in dollars.