 is a mathematical formula used to determine the optimal size of a series of bets to maximize the long-term growth of capital. In trading, it’s the bridge between having a "winning strategy" and actually growing an account without blowing it up.

The Kelly Criterion tells you what percentage of your equity ($f^*$) you should risk on a single trade based on your historical performance.

For trading, we use the version that accounts for varying win/loss ratios:

If you define W as your win rate and R as your risk/reward ratio (Average Win / Average Loss):

You cannot use Kelly without a backtest or trading journal. You need:

Standard Kelly is mathematically aggressive. It assumes your win rate and payoff are perfectly stable—which they never are in trading. Most professionals use 

This script calculates the Kelly fraction and simulates equity growth compared to a fixed-risk strategy.

import numpy as np
import matplotlib.pyplot as plt

def calculate_kelly(win_rate, avg_win, avg_loss):
    """
    Calculates the Kelly Criterion fraction.
    """
    reward_risk_ratio = avg_win / abs(avg_loss)
    kelly_f = (win_rate * (reward_risk_ratio + 1) - 1) / reward_risk_ratio
    return max(0, kelly_f) # Return 0 if the edge is negative

# Strategy Parameters
win_rate = 0.55       # 55% Win Rate
avg_win = 1000        # Average profit
avg_loss = 800        # Average loss
initial_capital = 10000

# 1. Calculate Fractions
f_star = calculate_kelly(win_rate, avg_win, avg_loss)
half_kelly = f_star * 0.5

print(f"Full Kelly Fraction: {f_star:.2%}")
print(f"Half Kelly Fraction: {half_kelly:.2%}")

# 2. Simulation
trades = np.random.choice([avg_win, -avg_loss], size=100, p=[win_rate, 1-win_rate])
equity_curve = [initial_capital]

for trade in trades:
    # Use Half-Kelly for the simulation
    risk_amount = equity_curve[-1] * half_kelly
    
    # Calculate gain/loss relative to the amount risked
    # (Simplified: trade result is scaled by how much of a 'unit' we bet)
    actual_result = (trade / avg_loss) * risk_amount
    equity_curve.append(equity_curve[-1] + actual_result)

plt.figure(figsize=(10, 5))
plt.plot(equity_curve)
plt.title("Equity Growth using Half-Kelly Strategy")
plt.xlabel("Number of Trades")
plt.ylabel("Account Balance")
plt.grid(True)
plt.show()


 ($f^* \times 0.25$). It provides a much smoother equity curve and allows for "errors" in your estimated win/loss statistics.