The mathematical formula used by the greatest traders and investors to maximize long-term growth while minimizing the risk of ruin.
Percentage of winning trades over your last 100 trades minimum
In $ or R (risk units)
Average amount lost per losing trade
2.00:1
+65.00$
Full Kelly is mathematically optimal but extremely volatile in practice. Most professionals use Half Kelly (50%) or Quarter Kelly (25%) to reduce psychologically difficult drawdowns. Past results do not guarantee future performance.
Everything you need to know to master scientific money management
Imagine you have discovered a trading strategy with a 60% success rate and a 2:1 win/loss ratio. On paper, it's excellent. But here's the million-dollar question: what percentage of your capital should you risk on each trade?
Risk 1% and you'll have stable but slow growth, perhaps too slow to reach your financial goals before retirement. Risk 50% and you'll maximize your potential gains, but a series of 3-4 consecutive losses (statistically inevitable) will completely wipe you out. Between these two extremes exists an optimal point, mathematically provable, that maximizes your long-term growth while minimizing your risk of ruin.
This optimal point is called the Kelly Criterion, and it is probably the most important formula you will ever learn as a trader or investor. Used by finance legends such as Edward Thorp, Warren Buffett and Jim Simons, this formula has been proven over more than six decades of real-world application.
John Larry Kelly Jr. was not a trader. He was a Texan physicist working at AT&T Bell Labs, the legendary research laboratory that gave birth to innovations like the transistor, the laser, and the C programming language. Kelly was working on a technical problem: how to transmit information optimally through a noisy telephone line?
In solving this problem, Kelly discovered something much more profound. He published his paper "A New Interpretation of Information Rate" in the Bell System Technical Journal, mathematically demonstrating that there existed an optimal fraction of resources to allocate to maximize the exponential growth of a system.
Edward O. Thorp, a mathematics professor at MIT, was fascinated by games of chance. He had developed the first card counting system for Blackjack and was looking for a method to manage his bankroll optimally. When he discovered Kelly's paper, it was a revelation.
Thorp applied the Kelly criterion in the casinos of Las Vegas and documented his results in his bestseller "Beat the Dealer" (1962), which became the first book to mathematically prove that a player could beat the house. Casinos had to modify the rules of Blackjack in response to his methods.
Building on his success at the casinos, Thorp turned to Wall Street. He founded Princeton Newport Partners in 1969, one of the first quantitative hedge funds in history. Using the Kelly criterion to size positions on convertible arbitrage strategies, the fund generated an annualized return of 19.1% over 19 years, with remarkably low volatility and no losing years.
This extraordinary performance attracted the attention of the financial community. Warren Buffett himself became friends with Thorp and admitted to using similar principles to size his investments at Berkshire Hathaway. Jim Simons, founder of Renaissance Technologies (the best-performing fund in history), also cites Kelly as a major influence.
1956
Kelly's publication at Bell Labs
1962
Thorp's Beat the Dealer
1969
Creation of Princeton Newport
Today
Industry standard
The Original Formula
Let's take a realistic example. You have analyzed your last 200 trades and you have:
// Step-by-step calculation
p = 55 / 100 = 0.55
q = 1 - 0.55 = 0.45
r = 300 / 150 = 2.0
f* = 0.55 - (0.45 / 2.0) = 0.55 - 0.225 = 0.325
→ Optimal size = 32.5% of capital per trade
This result of 32.5% may seem aggressive, and it is. That's why in practice, most professional traders use a fraction of Kelly (Half Kelly at 16.25% or Quarter Kelly at 8.125%). We'll explain why in the next section.
The Kelly formula maximizes the geometric growth rate of your capital. It is mathematically optimal in the long run. But "optimal" does not mean "comfortable". Here is why professionals almost always reduce their Kelly:
At Full Kelly, you can expect drawdowns (temporary declines) of 50% or more on a regular basis. Imagine watching your $100,000 account drop to $50,000, then climb back to $80,000, then drop again to $40,000... all while knowing that in the long run you will win. Few traders have the psychological discipline to endure this roller coaster.
Recommended for: Nobody (in practice)
Recommended for: Experienced traders
Recommended for: Beginners & Prop Firms
Edward Thorp himself revealed in interviews that he never used Full Kelly in his career. At Princeton Newport Partners, he typically used between 20% and 40% of the suggested Kelly. His philosophy: "It is better to slightly underperform than to risk ruin. You cannot recover from zero."
You trade a funded account (FTMO, The Funded Trader, etc.) with strict drawdown rules to follow.
Recommendation
Use Quarter Kelly maximum. Calculate on your max drawdown, not the account size. A $100k account with 10% max drawdown = calculate on $10k.
You trade cryptocurrencies with your own capital and seek aggressive growth.
Recommendation
Half Kelly is ideal. Crypto volatility amplifies drawdowns, so never exceed Half Kelly even if you are confident.
You invest long-term and prioritize capital preservation over explosive growth.
Recommendation
Use Kelly as an upper limit never to exceed. A Quarter Kelly or less better matches your risk profile.
Context: Thomas just passed an FTMO challenge. He now has access to a $100,000 funded account with the following rules:
Thomas has an excellent track record: 60% Win Rate and 1.5:1 Ratio.
He uses the Kelly calculator above and gets: 33% optimal risk.
Excited, Thomas opens a trade risking $33,000 of his $100,000 account.
ACCOUNT LOST
The market moved only 15% against his position before reversing. But that 15% on $33k = $4,950 floating loss. This triggered the 5% daily drawdown rule. Account automatically closed.
In Prop Firms, your "real capital" is not the account size. It is your Maximum Allowed Drawdown.
By calculating Kelly on $10,000 instead of $100,000:
Using the Win Rate from your last 20 trades instead of 100+. Small samples are misleading. Always use a minimum of 100 trades for a reliable estimate.
Kelly assumes perfect executions. In reality, commissions, spreads and slippage reduce your edge. Subtract these costs from your average win before calculating.
Your stats change with time and market conditions. Recalculate your Kelly at minimum every month, or after 50 new trades.
If you trade multiple strategies, each has its own Kelly. Adding them up can put you at over-risk. Use fractional Kelly for the total portfolio.
If you have multiple positions open simultaneously on correlated assets, your real risk is greater than the sum of individual risks.
Even though mathematically optimal, Full Kelly is too volatile to use in practice. Use Half Kelly or less for a better return/comfort ratio.
Kelly assumes a normal distribution. If your gains have a fat tail (a few very large wins), the standard Kelly may underestimate your optimal size.
Here is the step-by-step process to correctly implement the Kelly criterion in your trading:
Export the history of your last 100+ trades. You need: the result (win/loss) and the amount of each trade. Use a trading journal or your broker's export.
Win Rate = (Winning trades / Total trades) x 100. Average Win = Sum of wins / Number of winning trades. Average Loss = Sum of losses / Number of losing trades.
Use our calculator above or the formula f* = p - (q/r). Note the Full Kelly, Half Kelly and Quarter Kelly results.
Beginner or Prop Firm: Quarter Kelly. Experienced with own capital: Half Kelly. Full Kelly: Avoid unless you have nerves of steel and absolute confidence in your stats.
Multiply your capital (or max drawdown for Prop Firms) by your chosen Kelly. Example: $50,000 x 8% (Quarter Kelly) = $4,000 maximum per trade.
Divide your risk in dollars by your stop loss in dollars. Example: $4,000 risk / $50 stop loss per unit = 80 units maximum.
Your statistics evolve. Recalculate your Kelly every month or every 50 trades. Adjust downward if your performance degrades.
Yes, but with caution. If Kelly gives you 250% (f* = 2.5), this theoretically suggests 2.5x leverage. However, leverage also amplifies liquidation risk. In crypto or forex with leverage, slippage and liquidations can exit you from a position before it turns around. Always divide the suggested Kelly by at least 2 when using leverage.
A negative Kelly means you have no statistical advantage (edge). Mathematically, the best decision is not to trade this strategy at all. Either your win rate is too low or your win/loss ratio is insufficient. Work on your strategy before risking real money.
The principle is identical, but you have the advantage of having more data. With 500+ trades, your statistics are very reliable. However, watch out for transaction fees that can significantly erode your edge on low-profit trades. Subtract fees from your average win before calculating.
Yes, but it's more complex. Options have asymmetric win/loss profiles. For buying calls/puts, classic Kelly works if you clearly define your maximum loss (premium paid) and your historical average win. For options selling strategies, consult a professional as the risk can be theoretically unlimited.
Each strategy has its own Kelly. For the total portfolio, you must consider correlations between strategies. A conservative approach: calculate the Kelly for each strategy, then divide by the number of active strategies. Example: 3 strategies with Kelly of 20%, 15% and 25% → use ~6-8% per strategy instead of the sum.
No, that's excessive and can create instability. Recalculate monthly or every 50-100 trades. That said, if you have a significant losing streak (5+ consecutive losses), temporarily reduce your position size by 25-50% as a precaution, then re-evaluate.
No. Kelly minimizes the probability of ruin in the long term, but does not eliminate it. An exceptionally long losing streak (statistically rare but possible) can still ruin you. This is why professionals use Half Kelly or less, and diversify their strategies and assets.
The 1-2% rule is a simple heuristic that ignores your actual statistics. Kelly is a mathematical formula that optimizes based on YOUR specific edge. A trader with 70% win rate and 3:1 ratio should risk well above 2%. A trader with 52% win rate and 1:1 ratio should risk less than 1%. Kelly personalizes the optimal risk to your situation.
The Kelly criterion is not just a mathematical formula. It is a risk management philosophy that separates amateurs from professionals. Casinos learned this the hard way facing Edward Thorp. Financial markets saw it in action with Princeton Newport Partners.
Now, you have access to the same tool. The question is not whether Kelly works -- six decades of results have proven its effectiveness. The question is: will you use it correctly?
Remember these three fundamental principles:
Trading is a marathon, not a sprint. The Kelly criterion is your compass to navigate this marathon optimally. Use our calculator above, respect your limits, and let the mathematics work for you.
Use our other trading tools to complete your arsenal: position size calculator, Monte Carlo simulator, trading journal and more.
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