What the simulation is doing
Position sizing is the difference between a good strategy that compounds and a good strategy that blows up. The Kelly Criterion gives the growth-optimal fraction of capital to stake given your edge — but a single number hides how violent that sizing can be. This simulator makes it concrete. It draws a random run of trades that matches your win rate, then compounds the account at Full, Half, One-Third and Quarter Kelly through the same trades, so the only difference between the four curves is the bet size.
What Full, Half, One-Third and Quarter Kelly mean
The four rows in Your Kelly stake are the same formula scaled down. Full Kelly is the number the math hands you; the fractions trade a little long-run growth for a lot less pain.
- Full Kelly
- The raw formula output, untouched — the fraction that grows the account fastest over the long run. The catch: that only holds if your win rate and payoff are exactly right and stay that way forever, which they never do in real life. Full Kelly's swings are brutal — drawdowns of 50% or more are routine — and if you have overestimated your edge even slightly, it quietly bets too much. Almost nobody should trade it straight.
- Half Kelly
- Exactly half the Full stake, and most traders' home base. You keep roughly three-quarters of the long-run growth for a fraction of the volatility, plus a wide margin for your edge estimate being wrong. When in doubt, this is the default.
- One-Third and Quarter Kelly
- Smaller still. You give up a bit more growth for materially calmer equity and a bigger buffer if your real edge turns out worse than your sample suggested. The honest test: if a Full-Kelly drawdown would scare you out of the strategy, size down to here — a smaller bet you can hold beats a bigger one you panic out of.
How each trade is sized
Each sizing risks a fixed fraction of your current balance, in whole positions that each risk one average loss. Here is the full mechanic on the default numbers, sized at Half Kelly.
Worked example — 60% win rate, $120 average win, $100 average loss, $10,000 account, Half Kelly
- Find the edge. f* = win rate − (1 − win rate) ÷ payoff ratio. The payoff ratio is your average win ÷ average loss = $120 ÷ $100 = 1.2, so f* = 0.60 − 0.40 ÷ 1.2 = 0.27. Full Kelly is about 27% of the account.
- Pick a fraction. Half Kelly is 27% ÷ 2 ≈ 13%. On a $10,000 account that is a $1,333 stake.
- Turn the stake into positions. Each loss costs one average loss, $100, so $1,333 ÷ $100 = 13 positions (the simulator rounds down to whole lots).
- Play the trade. A win adds 13 × $120 = +$1,560, taking the account to $11,560. A loss subtracts 13 × $100 = −$1,300, dropping it to $8,700.
- Re-size and repeat. The next trade sizes off the new balance — that compounding is the entire point. After the win, 13% of $11,560 ≈ $1,541 → 15 positions; after the loss, 13% of $8,700 ≈ $1,160 → 11 positions. The bet rises and falls with the account.
That is exactly what the equity curve and the trade-by-trade table below play out — one trade at a time, with all three sizings facing the same run of wins and losses.
Why fractional Kelly usually wins in practice
Re-roll a few times and a pattern emerges: Full Kelly posts the biggest numbers on the lucky runs and the ugliest drawdowns on the unlucky ones. Its max drawdown is routinely 50–90%+ — a level very few people can actually hold through. Half and Quarter Kelly give up some upside but cut the drawdowns sharply, which is why seasoned traders almost always size down. The growth-optimal bet on paper is rarely the bet you can live with in a real account, and a sizing you abandon mid-drawdown is worse than a smaller one you can keep.
The high-win-rate trap
Try a premium-seller's profile — a 90%+ win rate with an average loss several times the average win. Kelly still returns a positive fraction, and most runs look serene, but the rare losing trades are large and Full Kelly turns them into cliff-edge drawdowns. This is exactly how high-win-rate strategies blow up: the sizing feels safe because losses are rare, until a cluster of them arrives at full size. The simulator lets you feel that risk before the market charges you for the lesson.
How to use it
- Enter your real, fee-adjusted edge from closed trades — not your best-case numbers.
- Re-roll 5–10 times and watch the range of outcomes, not a single run.
- Judge each sizing by its max drawdown, then ask honestly which one you could hold.
- Whatever you land on, remember the formula sizes one independent bet — correlated positions stack into a bigger one.
Frequently asked questions
What does this Kelly simulator show?
It takes your edge — win rate, average win and average loss — computes the Kelly fraction, then compounds your account across a random run of trades at Full, Half, One-Third and Quarter Kelly. All four sizings face the exact same sequence of wins and losses, so you can compare ending balance, total return and the worst drawdown side by side.
Why does Full Kelly swing so wildly?
Full Kelly stakes the growth-optimal fraction, which is large. A loss at that size takes a big bite, and a run of losses compounds into a deep drawdown — 50% or more is normal, and you will often see far worse in the simulation. Half and Quarter Kelly keep most of the long-run growth with a fraction of the volatility, which is why almost everyone trades a fraction of Kelly.
Why do the results change each time I re-roll?
Each run draws a fresh random sequence of wins and losses consistent with your win rate. That is the point: one lucky or unlucky run tells you little, so re-roll several times to see the range of outcomes. Notice how Full Kelly’s ending balance and drawdown vary far more between runs than Quarter Kelly’s.
Is this a backtest of a real strategy?
No. It is a Monte-Carlo illustration driven entirely by the three numbers you enter, assuming every trade is independent with the same fixed win and loss. Real strategies have varying win sizes, correlation between positions and changing edges. Treat it as an intuition builder for position sizing, not a forecast.
How is each trade sized?
At each fraction the simulator risks that share of your current balance in whole positions, each risking one average loss. Example: Half Kelly of 13% on a $10,000 account is a $1,300 stake, and at a $100 average loss that is 13 positions — a win adds 13 × your average win, a loss subtracts 13 × your average loss, then the next trade re-sizes off the new balance. That re-sizing of a fixed fraction against a moving balance is what compounds the account. The "How each trade is sized" section on this page walks through it step by step.
What is the "Contracts" number for?
It is your actual order size — the stake turned into whole contracts (stake ÷ your average loss). A broker takes a number of contracts, not "13% of my account", so this is the number you act on. It also doubles as a feasibility check: if even Full Kelly works out to less than one contract, your account is too small to express that edge at that risk, so trade a cheaper underlying or accept sizing off the Kelly grid. And it shows how lumpy your risk is — a Full Kelly of 2 contracts means each contract is a huge share of the bet with little room to fine-tune, while 40 contracts lets you scale precisely. It is not a count of how many losses you can take.
Related tools
Get your stake from the Kelly Criterion calculator, sanity-check your win rate with the Expected Move Calculator, and see whether premium is rich with the IV Rank Calculator. Browse everything on the tools page.
Educational tool only. Nothing here is financial advice. This is a Monte-Carlo illustration from an edge estimate that is never exact and assumes independent, identically-sized trades — real results differ. Most traders use a fraction of Kelly and size correlated positions well below the sum of their individual stakes.