Calculator

Kelly Criterion Calculator: Optimal Bet Size

About this calculator

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

You found an edge. Now the harder question: how much do you actually put on it?

Animated derivation and joint sizing for several bets: open the Kelly tool in the app →

A Kelly criterion calculator returns the share of your bankroll to stake at a given price and win chance: the size that grows a bankroll fastest over the long run. With no edge, the right stake is $0, and that is what it prints.

Why not just bet more

Because losing 50% and then gaining 50% does not get you back to where you started. It gets you to 75 cents. Big bets have to climb out of that hole every time, and past a certain size no edge is big enough.

Kelly is the stake that grows a bankroll fastest over the long run. Bet more than it says and you grow slower and risk more. That is not a trade-off, it is just worse.

The default here is half Kelly. Full Kelly assumes you know your win probability exactly, and you do not. Half gives up about a quarter of the growth and cuts the swings roughly in half, which is a deal most people should take.

No edge, no stake. When the price is fair or worse the answer is $0, and that clamp lives in the math library rather than the display, so nothing downstream can round it up.

Want more math?the Nerd Corner

f^{*} = \dfrac{b\,p - q}{b}, \qquad q = 1 - p, \qquad f_{\text{used}} = \lambda\, f^{*}

where:

$b$ : net decimal payout, in dollars of profit per dollar risked. −152 gives $b = 100/152 = 0.658$ ; +138 gives $b = 1.38$ .
$p$ : your estimate of the win probability, between 0 and 1. Not the book’s implied probability (that one returns exactly zero).
$q = 1 - p$ : the chance the stake is lost.
$f^{*}$ : the full-Kelly stake, as a fraction of current bankroll.
$\lambda$ : the fraction of full Kelly used, $\tfrac12$ (half, the default here) or $\tfrac14$ (quarter).

Side A’s price and side A’s win chance size the stake. Side B’s price is there only so the panel can de-vig the market and show how far the estimate sits from fair.

Worked example: the numbers in the form below

-152 \Rightarrow b = \tfrac{100}{152} = 0.6579, \qquad p = 0.65,\quad q = 0.35

f^{*} = \dfrac{0.6579 \times 0.65 - 0.35}{0.6579} = \dfrac{0.07763}{0.6579} = 11.80\%

f_{\text{used}} = \tfrac{1}{2} \times 11.80\% = 5.90\% \;\Rightarrow\; \$59.00\ \text{on a}\ \$1{,}000\ \text{bankroll}

The price alone implies 60.32%; the de-vigged fair line says 58.94%. A 65% estimate is 6.06 points above fair, worth +7.76¢ of expected value per dollar. Full Kelly would stake $118; half Kelly puts down $59.

How the Kelly criterion calculation works

Kelly maximizes the expected growth rate of a bankroll: not profit on any one bet, but how fast money compounds when the same edge is bet repeatedly. The numerator b·p − q is the edge in odds terms, the same per-dollar figure the EV calculator reports; dividing by b turns it into a share of bankroll. That fraction is the peak of the expected-log-wealth curve:

g(f) = p\,\ln(1 + b f) + q\,\ln(1 - f)

Log wealth is the right thing to maximize because betting compounds: a drawdown costs more than a same-sized win gives back.

Why half Kelly is the default

Full Kelly assumes p is exactly right. It never is, and the curve is flat near its peak, so a fraction of full Kelly keeps most of the growth for much smaller swings. Priced out on the example above ( $b = 0.658$ , $p = 0.65$ , $1,000 bankroll), with growth per bet read off $g(f)$ :

Kelly fraction	Stake	On $1,000	Growth per bet	Share of full growth
Quarter (λ = 0.25)	2.95%	$29.50	+0.201%	43%
Half (λ = 0.5, default)	5.90%	$59.00	+0.347%	75%
Full (λ = 1)	11.80%	$118.00	+0.465%	100%
Double (λ = 2)	23.60%	$236.00	−0.040%	−9%

Half the stake buys three quarters of the growth. Double the stake buys negative growth on a real edge. The cost of being under is small; the cost of being over is not.

The honest zero

Kelly’s break-even is exactly the probability the price implies. A −152 price implies 152/252 = 60.3175%, and there the numerator vanishes:

p = \tfrac{152}{252} \;\Rightarrow\; b\,p - q = \tfrac{100}{152}\cdot\tfrac{152}{252} - \tfrac{100}{252} = 0 \;\Rightarrow\; f^{*} = 0

Below that the fraction goes negative: the arithmetic saying the price is worse than the estimate justifies. The panel prints $0 and labels it “no edge”; it does not round a non-edge up into a small stake. The sign of the Kelly fraction is just the sign of your disagreement with the price, so everything hard about this calculation lives upstream, in p.

Limits and common mistakes

Kelly answers how much, never whether. The sign has to be settled first: strip the vig to get the fair line, then measure expected value.
p has to be your own number. The book’s implied probability is the break-even by definition, so f* is exactly 0; the de-vigged fair probability on a favorite sits below the price and returns a negative fraction. Side A’s win chance also has to go with side A’s price.
The fraction is of the current balance. Sizing off January’s bankroll is flat betting with extra steps; the self-shrinking property after losses is what makes ruin impossible in the idealized model.
One bet at a time. Six simultaneous 11.8% stakes put 70% of the bankroll at risk, which is nothing like what the single-bet formula assumed. Joint sizing is in the app and the Kelly criterion guide.
The output is a calculation, not advice. It is the growth-maximizing fraction under the estimate supplied. Wrong estimate, wrong stake, and the error is not symmetric.

Check this number yourself

The page runs the same math as the MIT-licensed teachersbettextbook package: kelly_fraction(p, b) and fractional_kelly(p, b, fraction) with DEFAULT_FRACTION = 0.5, plus growth_rate(p, b, f) for the growth column.

pip install teachersbettextbook

>>> from teachersbettextbook import kelly_fraction, fractional_kelly, moneyline_to_odds
>>> b = moneyline_to_odds(-152)
>>> kelly_fraction(0.65, b)
0.1180000000000001
>>> fractional_kelly(0.65, b, 0.5) * 1000
59.00000000000005

Same inputs, same digits: the trailing float tail is what the panel rounds to 11.80% and $59.00. No account required. More on what is open and what is not: open source.

Frequently asked questions

What is a Kelly criterion calculator?

A Kelly criterion calculator returns the share of a bankroll to stake that maximizes the bankroll’s long-run growth rate. Enter the odds, your estimated win chance and your bankroll; it computes f* = (b·p − q)/b and scales it by the Kelly fraction you choose.

Why use fractional (half) Kelly?

Full Kelly assumes p is exactly right. Real edge estimates are noisy, and overestimating p makes full Kelly overstake. Half Kelly keeps about 75% of the growth for half the stake and far smaller drawdowns, which is why a half is the default here.

How much should I bet according to Kelly?

Kelly’s answer is f* = (b·p − q)/b of the current bankroll, where b is decimal odds minus one, p is your win probability and q = 1 − p. If f* is zero or negative there is no edge and the stake is nothing.

Why does the calculator sometimes return $0?

Because the inputs contain no edge. Kelly’s break-even is exactly the probability the price implies (−152 implies 152/252 = 60.3175%), so an estimate at or below that gives a fraction of zero or less. The panel prints $0 rather than rounding a non-edge up into a stake.

How much growth does half Kelly give up?

About a quarter of it. On the 11.80% full-Kelly edge above, full Kelly compounds at roughly 0.465% per bet and half Kelly at 0.347%, around 75% of the growth. Quarter Kelly keeps about 43%; double Kelly drives growth to about zero.