Calculator

Free Bet & Bonus Bet Calculator

About this calculator

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

A bonus bet is not cash. It pays the profit and keeps the stake, which makes it worth less than its face value.

Hedging a free bet is the same mechanic as an arb: see the arbitrage calculator →

A free bet (or bonus bet) pays only the profit if it wins, never the stake back. That makes its cash value less than its face amount, and longer odds keep more of it.

What it is really worth

Put $100 cash on +300 and you get $400 back. Put a $100 bonus bet on +300 and you get $300, because the token itself does not come back.

So the token is worth (d − 1) / d of its face value: about 75 cents on the dollar at +300, and much less at short prices. At −200 it is worth about 33 cents.

Which is why a free bet gets more out of long odds than short ones. That is the opposite of most people's instinct, and it is the single most useful thing on this page.

You can also hedge the other side and lock in a smaller, certain number. Whether that beats holding depends on the hedge price, and the form works it out.

Want more math?the Nerd Corner

V = F \cdot \dfrac{d - 1}{d}, \qquad s = \dfrac{F\,(d - 1)}{h}, \qquad G = \dfrac{F\,(d - 1)\,(h - 1)}{h}

where:

$F$ : the face amount of the token, in dollars (the “$100 bonus bet” number).
$d$ : the decimal odds the token is placed at, total return per dollar including stake. American +300 is $d = 4.0$ ; −360 is $d \approx 1.278$ .
$h$ : the decimal odds of the cash hedge on the opposite outcome, at a second venue.
$V$ : the token’s fair cash value in dollars, assuming a zero-vig hedge.
$s$ : the cash stake on the hedge, in dollars, that makes both outcomes pay the same.
$G$ : the equalised return in dollars, what the position pays whichever side lands.

Worked at the form’s defaults, a $100 token at +300 ( $d = 4.0$ ), hedged at −360 ( $h = 1.278$ ):

V = \$100 \times \tfrac{4.0 - 1}{4.0} = \$75.00, \qquad s = \dfrac{\$100 \times 3}{1.278} = \$234.78

G = \dfrac{\$100 \times 3 \times 0.278}{1.278} = \$65.22 \;\Rightarrow\; 65.2\%\text{ of the token, in cash}

What a bonus bet is really worth

Almost every U.S. “bonus bet” or “free bet” is stake-not-returned (SNR): the token is consumed whether or not it wins, so a $100 free bet at decimal odds d pays $100 × (d − 1) or nothing, never $100 × d. A stake-returned promo behaves like cash; this page assumes the SNR form.

Hedged at a fair price the token is worth (d − 1)/d of its face, a fraction that rises with the odds, so the same token converts to more cash at longer prices. On a $100 token:

American odds	Decimal d	(d − 1)/d	Fair value of a $100 token
−500	1.200	16.67%	$16.67
−200	1.500	33.33%	$33.33
−110	1.909	47.62%	$47.62
+100	2.000	50.00%	$50.00
+300	4.000	75.00%	$75.00
+1000	11.000	90.91%	$90.91

The last column is the honest headline: the “$100 free bet” in the promo email is a $100 object only at infinite odds. Books attach a minimum-odds rule (commonly −200 or longer) because the token is cheapest for them at short prices.

The hedge that equalises both outcomes

Bonus on one outcome, real cash on the opposite outcome at a second book: stake s = F(d − 1)/h and the position returns G = F(d − 1)(h − 1)/h either way. Both branches check by hand. Bonus side wins: you collect $F(d-1)$ and lose the hedge stake $s$ ; hedge side wins: you collect $s(h-1)$ and the token is consumed. Substituting $s$ makes the two equal.

At the form’s defaults: $234.78 on the −360 favorite, $65.22 back whichever side wins: 65.2% of the $100 token in cash against a 75% fair value. The missing 9.8 points is the vig paid to the second book.

Why the locked profit is not guaranteed in practice

The arithmetic is exact; realising it is not. The same caveats the arbitrage calculator carries apply here:

Promo terms. Minimum-odds rules, win caps, expiry dates and excluded markets bind before the math does. A cap truncates the win profit and everything downstream of it.
Stake limits and voided legs. The hedge venue may not accept $234.78 at the posted price; a partial fill or a voided leg leaves one side uncovered.
Price movement between placements. The legs are not placed at the same instant. Reach the hedge at −400 instead of −360 and the equalised return falls from $65.22 to $60.00: 5.2 points lost to one line move.
Account limits. Books restrict accounts that work promotions systematically, a business risk the formula cannot price.

The equalised figure is the arithmetic best case on the prices you entered, not a promise about what will settle.

Check this number yourself

One library call: moneyline_to_odds, from the MIT-licensed teachersbettextbook package. The rest is arithmetic:

pip install teachersbettextbook

from teachersbettextbook import moneyline_to_odds
d = 1 + moneyline_to_odds(300)      # 4.0
h = 1 + moneyline_to_odds(-360)     # 1.2777...
win    = 100 * (d - 1)              # 300.0
stake  = win / h                    # 234.78
locked = win * (h - 1) / h          # 65.22

Same inputs, same output, no account required. How the open and hosted halves split →

Weighing an unhedged free-roll against certain cash is a question of expected value and bankroll growth. The full course is free in the Learn guides.

Frequently asked questions

How much is a free bet actually worth?

A stake-not-returned free bet hedged at a fair price is worth (d − 1) / d of its face value, where d is the decimal odds it is placed at. A $100 token at +300 (decimal 4.0) is worth 75% of face, about $75; the same token at −500 (decimal 1.2) is worth 16.7%, about $17.

Is the locked profit from a hedged free bet guaranteed?

No. The arithmetic holds only if both legs land at the prices shown and both stakes are accepted in full. Promo terms cap the win, a voided leg leaves one side uncovered, and the hedge price can move between the two placements. The figure is the best case, not a promise.

Is converting a bonus bet gambling?

This page performs arithmetic on the numbers you type. It is not betting advice and does not place, hold or facilitate any wager. The hedged conversion is a mathematical property of the two prices, shown so a promotion can be valued in dollars.