Question 1

What is the Kelly Criterion?

Accepted Answer

The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your capital to allocate to a bet or trade in order to maximize the long-term growth rate of your bankroll. The formula is f* = (b×p − q) ÷ b, where b is the win/loss ratio (how much you win per unit risked), p is the probability of winning, and q = 1 − p is the probability of losing. It was developed by John L. Kelly Jr. at Bell Labs in 1956.

Question 2

How do I use the Kelly Criterion for stock trading?

Accepted Answer

For stock trading, enter your win probability (your estimate of the likelihood the trade will be profitable) and your win/loss ratio (the ratio of your profit target to your stop-loss distance — e.g., if your target is $3 and your stop is $1, the ratio is 3.0). The Kelly formula then gives you the optimal percentage of your account to risk on that trade. Most traders use Half Kelly (50% of the full Kelly %) to reduce drawdown risk while capturing approximately 75% of the optimal growth rate.

Question 3

What is the difference between Full Kelly and Half Kelly?

Accepted Answer

Full Kelly (f*) is the mathematically optimal fraction that maximizes long-term log-growth. However, it leads to high volatility and severe drawdowns in practice. Half Kelly (f*/2) uses half the optimal fraction, which gives approximately 75% of Full Kelly's growth rate with significantly lower variance and drawdown risk. Most professional traders and gamblers use Half Kelly or less as their standard position sizing rule.

Question 4

What is the Kelly Criterion formula?

Accepted Answer

The Kelly Criterion formula is f* = (b×p − q) / b, which simplifies to f* = p − q/b. Here, f* is the optimal fraction of your bankroll to bet, b is the net odds (win/loss ratio — how much you win per unit risked), p is the probability of winning (0 to 1), and q = 1 − p is the probability of losing. For example, with a 55% win probability and a 2:1 win/loss ratio: f* = (2×0.55 − 0.45) / 2 = 0.65 / 2 = 32.5%.

Question 5

What does 'edge' mean in the Kelly Criterion context?

Accepted Answer

Edge in the Kelly Criterion context is the expected value per $1 risked, calculated as: Edge = b×p − q = b×p − (1−p). A positive edge means the trade has a positive expected value and Kelly recommends betting. A negative edge means expected value is negative and Kelly says bet $0. For example, with p=0.55 and b=2.0: Edge = 2×0.55 − 0.45 = 0.65, meaning you expect to profit $0.65 per $1 risked on average.

Question 6

What is the break-even win probability in the Kelly Criterion?

Accepted Answer

The break-even win probability is the minimum win rate needed for a trade to have a positive expected value (and therefore a positive Kelly fraction). It is calculated as p_breakeven = 1 / (1 + b), where b is the win/loss ratio. For example, with a 2:1 win/loss ratio, the break-even win probability is 1 / (1+2) = 33.3%. Any win rate above 33.3% at 2:1 odds has a positive edge; any win rate below it has a negative edge and Kelly recommends not betting.

Question 7

Can I use Kelly Criterion for a portfolio of multiple positions?

Accepted Answer

Yes. For independent positions (uncorrelated trades), you can calculate the Kelly fraction for each position separately. The Portfolio tab in this calculator allows you to enter up to 8 positions with different win probabilities and win/loss ratios, and see the per-position Kelly allocation and recommended position size. If the total Kelly allocation across all positions exceeds 100%, it indicates you would need leverage — proceed with caution and consider using a smaller fraction.

Question 8

What does the Growth Simulator show?

Accepted Answer

The Growth Simulator plots the expected median bankroll trajectory over N rounds for four Kelly fractions simultaneously: Full Kelly, Half Kelly, Quarter Kelly, and a custom fraction you define. It uses the log-normal growth formula: Bankroll_n = Bankroll_0 × exp(n × G), where G = p×ln(1+b×f) + q×ln(1−f) is the expected log-growth rate per round. This shows how different position sizing strategies compound over time and illustrates the trade-off between growth rate and drawdown risk at different fractions.

Question 9

Is the Kelly Criterion Calculator free to use?

Accepted Answer

Yes. The Kelly Criterion Calculator Pro on StockToolHub is completely free with no registration, account, or subscription required. All five tabs — Kelly %, Scenarios, Portfolio, Simulator, and Fractions — are fully accessible with no limitations and no sign-up.

Kelly Criterion Calculator Pro

What each tab calculates

Kelly %

Scenarios

Portfolio

Simulator

Fractions