✨ Money math, explained like you're five

How big should your money scoop be?

Kelly Criterion is a rule for choosing how much of your money to risk when you have a repeatable advantage. Not too much. Not too little. The scoop that aims for the fastest long-run growth.

Start the tiny story ↓Try the calculator
Grow, don't explode! 🌱
The right-size scoop
$$$$
01 · The tiny story

You own a jar of 100 jellybeans.

A friendly game appears again and again. When you win, the jellybeans you risk are doubled. When you lose, the jellybeans you risk disappear. You need to choose a scoop size.

1

You have a small edge

Your chance of winning is 60%. That is better than a fair coin's 50%. The game can be good for you.

🎲
2

A giant scoop is scary

Risk all 100 jellybeans and one loss leaves zero. Once you have zero, you cannot play again.

3

A tiny scoop grows slowly

Risk only one jellybean and you stay safe—but your useful advantage barely gets to work.

🌱
Kelly asks: “What fraction can grow my jar fastest over many games—without one ordinary loss wiping me out?”

For the 60%-win game that pays one-for-one, the full Kelly answer is 20% of the current jar. If the jar has 100, risk 20. If it later has 150, risk 30. The amount changes because the rule uses a fraction, not a fixed number.

02 · The grown-up symbols

The formula has only three ingredients.

This is the classic version: a loss loses the full amount you risk, and a win earns a known multiple of it.

f* = (b × p − q) / bSame thing: f* = p − q / b
f* = fraction of your bankroll to risk
p = probability of winning
q = probability of losing = 1 − p
b = net profit per $1 risked. Win $1 → b=1. Win $2 → b=2.
Win chance60%p = 0.60
Lose chance40%q = 0.40
Net win1×b = 1
Kelly scoop20%(1×.6−.4)/1
03 · Touch the math

Build your own game.

Move the sliders. The scoop, gauge, advice, and example dollar amount update immediately.

Full Kelly fraction
20.0%
That is $200 from a $1,000 jar.
A positive edge exists. Many real users choose half Kelly—10.0% here—to reduce the bumps caused by imperfect estimates.
04 · Watch the scoops race

Same luck. Different bet sizes.

Every runner sees the exact same wins and losses. Only the fraction risked changes. Press race again for a new path. One path is an illustration, not a promise.

Round 0 / 100
All-in 100%Full KellyHalf KellyTiny 2%
05 · The rules that matter

Kelly is smart math, not a crystal ball.

The formula is only as good as the numbers fed into it. These six ideas prevent the most common mistakes.

✂️

Half Kelly is calmer

Full Kelly maximizes theoretical long-run log growth. Half Kelly gives up some expected growth in exchange for smaller drawdowns and less sensitivity to estimation errors.

🚫

Negative means “no bet”

If the result is zero or negative, the stated game has no favorable edge. Do not turn a negative answer into a positive bet just because you want action.

🔍

Garbage in, garbage out

If you guess a 60% win rate but reality is 48%, Kelly confidently sizes the wrong edge. Use robust data, uncertainty ranges, and out-of-sample testing.

🧾

Count every cost

Fees, spreads, slippage, taxes, and financing reduce the true payoff. Use net returns after realistic costs, not the shiny number before them.

🧺

Connected bets share risk

Five trades that all depend on the same market move are not five independent bets. A portfolio Kelly model must include correlations and covariance.

🌪️

Real losses can be weird

Gaps, fat tails, changing regimes, and leverage can make losses larger than the model assumes. Hard exposure limits still matter.

06 · Why it works

Kelly cares about compounding.

A 50% loss needs a 100% gain to recover. That asymmetry is why “highest average profit per bet” is not enough.

The secret score: logarithmic growth

Kelly chooses the fraction that maximizes the expected logarithm of wealth. Logs turn repeated multiplication into addition and punish paths that approach zero.

maximize: p·ln(1+b·f) + q·ln(1−f)

The assumptions under the toy version

The same known probabilities repeat, the payoff is known, you can resize every round, capital is divisible, and there are no hidden costs or constraints. Real markets violate several of these.

growth after n rounds = W₀ × ∏(1 + returnᵢ)
Why not always bet 100% when the game is favorable?

Because a single full-loss outcome makes wealth zero. Zero multiplied by any future gain stays zero. Kelly balances the reward from pressing an edge against the permanent damage caused by betting too much.

Does Kelly promise I will make money?

No. It is a long-run sizing rule under assumed probabilities and payoffs. Any finite sequence can lose. If the inputs are wrong, the suggested size is wrong. Kelly manages size; it does not manufacture an edge.

Why does the bet use current bankroll?

Fractional sizing automatically risks fewer dollars after losses and more dollars after gains. This keeps the risk proportional and is central to compounding.

What is “overbetting”?

Betting more than full Kelly. Growth becomes less efficient, drawdowns get much larger, and at a sufficiently high fraction the expected log-growth becomes negative—even though the game still has positive expected value.

Can I use this exact calculator for trading?

Only as an educational starting point. Trading returns are not usually a clean win/lose game with fixed odds. A serious implementation models the full return distribution, estimation uncertainty, transaction costs, correlation, leverage, and risk limits.

Pocket summary

Remember the scoop.

✅ Edge first: no reliable advantage, no Kelly bet.
✅ Size is a fraction of current bankroll.
✅ Full Kelly targets maximum long-run log growth.
✅ Half Kelly is often more robust in messy reality.
✅ Never ignore costs, correlation, or extreme losses.
✅ Simulation shows possibilities—not forecasts.