{"id":48,"date":"2026-05-28T00:39:13","date_gmt":"2026-05-28T00:39:13","guid":{"rendered":"http:\/\/docs.traderis.me\/en\/docs\/kelly-criterion\/"},"modified":"2026-06-06T04:34:01","modified_gmt":"2026-06-06T04:34:01","password":"","slug":"kelly-criterion","status":"publish","type":"docs","link":"https:\/\/docs.traderis.me\/en\/docs\/kelly-criterion\/","title":{"rendered":"The Kelly Criterion and Optimal Lot Size \u2014 Finding the Mathematically Optimal Risk %"},"content":{"rendered":"\n
\n

\ud83d\udccc Key Takeaway<\/p>\n\n\n\n

The Kelly Criterion shows that the mathematically optimal risk % (e.g. 25% for a 50% win rate \/ RR 2.0 strategy) is far too large to use directly \u2014 apply only 1\/10 to 1\/25 of full Kelly in practice. The 1% rule is an ultra-conservative Kelly that prioritizes survival over maximum growth, and that trade-off is entirely rational.<\/p>\n<\/div><\/div>\n\n\n\n

“What’s the optimal risk % per trade?” The Kelly Criterion<\/strong> gives this question a mathematical answer<\/strong>. From your win rate and risk-reward ratio, you can compute the “optimal fraction to bet” that theoretically maximizes long-term capital growth.<\/p>\n\n\n\n

This article covers the Kelly formula, worked examples, why full Kelly is dangerous, and how the practical “half Kelly” relates to the 1% rule<\/a>. Reading Risk-Reward Ratio<\/a> and Risk-Percent Position Sizing<\/a> first will deepen your understanding.<\/p>\n\n\n\n

What Is the Kelly Criterion?<\/h2>\n\n\n\n

The Kelly Criterion, proposed by physicist John Kelly in 1956, is a formula for the bet fraction that maximizes long-term capital growth rate<\/strong>. It’s widely applied to position sizing in gambling and investing.<\/p>\n\n\n\n

f* = (b \u00d7 p \u2212 q) \u00f7 b<\/strong>\n\nf* = fraction of capital to bet (optimal risk %)\np  = win rate\nq  = loss rate (= 1 \u2212 p)\nb  = payoff ratio when you win (risk-reward ratio)<\/pre>\n\n\n\n
This can also be written f* = p \u2212 (q \u00f7 b)<\/strong>. It means “the higher the win rate and the larger the RR, the bigger the optimal risk %.”<\/p>\n\n\n\n
Example: 50% win rate, RR 2.0<\/h3>\n\n\n\n
p = 0.5, q = 0.5, b = 2.0\nf* = (2.0 \u00d7 0.5 \u2212 0.5) \u00f7 2.0\n   = (1.0 \u2212 0.5) \u00f7 2.0\n   = 0.5 \u00f7 2.0\n   = 0.25 \u2192 25%<\/pre>\n\n\n\n
So in theory, a 50%-win-rate \/ RR-2.0 method grows fastest by risking 25% of the account<\/strong>. That’s surely bigger than you expected \u2014 and that very magnitude is why you must not use Kelly as-is.<\/p>\n\n\n\n
Full Kelly by Win Rate and RR<\/h2>\n\n\n\n
\n\n
Win rate<\/th>RR 1.0<\/th>RR 1.5<\/th>RR 2.0<\/th>RR 3.0<\/th><\/tr><\/thead>\n
40%<\/td>\u221220% (don’t bet)<\/td>0%<\/td>10%<\/td>20%<\/td><\/tr>\n
50%<\/td>0%<\/td>16.7%<\/td>25%<\/td>33.3%<\/td><\/tr>\n
60%<\/td>20%<\/td>33.3%<\/td>40%<\/td>46.7%<\/td><\/tr>\n
70%<\/td>40%<\/td>50%<\/td>55%<\/td>60%<\/td><\/tr>\n<\/tbody>\n<\/table><\/figure>\n\n\n\n
A negative f* (e.g. 40% win rate, RR 1.0) means the edge is negative and you shouldn’t bet at all<\/strong>. This is the same “break-even win rate” idea from the Risk-Reward Ratio article<\/a>.<\/p>\n\n\n\n
Why Full Kelly Is Dangerous<\/h2>\n\n\n\n
The f* (full Kelly) maximizes growth rate, but using it as-is in live trading is extremely dangerous<\/strong>, for three reasons.<\/p>\n\n\n\n
Reason 1: Extreme drawdowns<\/h3>\n\n\n\n
Full Kelly optimizes only growth rate and ignores intermediate drawdown<\/a> entirely. At 25% risk, losing 50-70% of the account over a few consecutive losses isn’t unusual. Even if it grows fastest in theory, real human psychology can’t withstand that volatility<\/strong>.<\/p>\n\n\n\n
Reason 2: Estimation error easily causes overbetting<\/h3>\n\n\n\n
Kelly assumes you know win rate and RR exactly. But real values are past measurements that may not hold in the future<\/strong>. If you estimate a 55% win rate but it’s actually 48%, full Kelly becomes a severe overbet and Risk of Ruin spikes. The slightest optimism in your estimate makes full Kelly fatal<\/strong>.<\/p>\n\n\n\n
Reason 3: The overbetting penalty is asymmetric<\/h3>\n\n\n\n
Betting below Kelly (underbetting) only slows growth slightly, but betting above Kelly (overbetting) degrades growth rate sharply, and betting too much can even make expected growth negative<\/strong>. So “betting less” is far safer.<\/p>\n\n\n\n
The Practical Answer: Half Kelly and Fractional Kelly<\/h2>\n\n\n\n
For these reasons, pros use “fractional Kelly” \u2014 only a portion of full Kelly<\/strong>. The classic choice is half Kelly (1\/2 of full Kelly)<\/strong>.<\/p>\n\n\n\n
Half Kelly has an excellent property: in theory, it retains about 75% of full Kelly’s expected growth rate while cutting volatility (drawdown) roughly in half<\/strong>. Sacrificing a little growth to greatly reduce risk is an extremely favorable trade-off.<\/p>\n\n\n\n
\n\n
Method<\/th>For 50% win \/ RR 2.0<\/th>Expected growth<\/th>Drawdown<\/th><\/tr><\/thead>\n
Full Kelly<\/td>25%<\/td>Maximum (100%)<\/td>Extremely large<\/td><\/tr>\n
Half Kelly<\/td>12.5%<\/td>~75%<\/td>~half<\/td><\/tr>\n
1\/5 Kelly<\/td>5%<\/td>~36%<\/td>Quite small<\/td><\/tr>\n
1% rule<\/td>1%<\/td>Low but stable<\/td>Very small<\/td><\/tr>\n<\/tbody>\n<\/table><\/figure>\n\n\n\n
The 1% Rule Is an Ultra-Conservative Kelly<\/h2>\n\n\n\n
In the example above, against full Kelly of 25%, the 1% rule<\/a> is 1\/25 of full Kelly (about 0.04 Kelly)<\/strong> \u2014 extremely conservative. Why go so small?<\/p>\n\n\n\n