What is it?
The Kelly Criterion is a mathematical formula that calculates the optimal amount to risk on each bet/trade to maximize long-term growth while avoiding ruin.
Formula:
If you know your:
-
Win Probability p
-
Loss Probability q = 1 - p
-
**Reward-to-Risk Ratio (b) = reward / risk
Then:
🎯 Let’s Apply it to a Case
-
You have $100.
-
The game has:
-
High Risk
-
Reward range: 1x to 100x
-
Let’s assume average reward = 10x
-
Let’s say win probability p = 0.1 (10%)
-
Then q = 0.9 , and b = 10
-
So you should risk only 1% of your capital on each bet.
Why? Because risking more (e.g., 10%, 20%) in a high-variance system will eventually blow your account. Kelly ensures long-term compounding with minimal risk of ruin.
Should You Keep Risk Constant?
Not always. Here's the logic:
Situation | Action | Reason |
---|---|---|
You’re winning | Increase slightly | Capital grows → bigger % dollar-wise, keep % stable or increase slightly. |
You’re losing | Reduce risk | Avoid drawdowns turning into ruin. Compounding in reverse is deadly. |
Game edge changes | Recalculate Kelly | As probability or payout changes, so does optimal risk. |
Real-World Traders Use This:
-
Edward Thorp (inventor of Kelly) turned blackjack profits into a hedge fund empire.
-
Renaissance Technologies, Soros, Druckenmiller, and many quant funds use Kelly-like models.
-
Crypto fund managers scale positions dynamically based on edge + volatility.
Conclusion: Strategy Summary
Metric | Value / Logic |
---|---|
Capital | $100 |
Average Win % | 10% |
Reward/Risk | 10:1 |
Risk per Bet | 1% (Kelly) |
Adjust per outcome? | Yes, adapt slightly |
Goal | Avoid ruin, grow exponentially over time |