LEARN · KELLY SIZING

How big each trade is matters as much as the edge.

The same edge can grow an account, stall it, or wipe it out, depending only on how much rides on each trade. This page shows how, with a textbook bet, and how the engine picks its own size.

GENERAL EDUCATION, NOT A RECOMMENDATION

The chart below simulates textbook bets, not Synapse's results, and nothing here says how much anyone should trade. Read the full disclaimer.

WHAT KELLY SIZING IS

The bet size that grows an account fastest.

In 1956 John Kelly, a scientist at Bell Labs, worked out how much of a bankroll to put on each bet when the odds are in your favor. His answer is a share of the account, recalculated every bet, that makes the account grow fastest over many bets. Ed Thorp later carried it from the blackjack table to the stock market.

The formula, for a simple bet

Kelly share = win rate − (loss rate ÷ payoff), where the payoff is how big a win is next to a loss. A bet that wins 55% at even money: 0.55 − (0.45 ÷ 1) = 10% of the account at risk on each bet. No edge, and the formula says zero.

Why most people bet a fraction of it

Kelly assumes the edge is known exactly. Real edges are estimates, real outcomes have fatter tails than a coin, and full Kelly's swings are brutal. So the common practice is a fraction of it, often half, which the chart below shows gives up a little growth for much smaller drawdowns.

BET SIZE AGAINST RUIN

Growth peaks, then turns. Risk only climbs.

Pick an example edge. The green line is how fast the account grows at each size, the amber line how deep the worst drop usually gets, and the red line the chance of losing 90% along the way.

Example: wins 55%, wins and losses the same size. The size that grows this bet fastest (Kelly) is 10% of the account at risk per trade. Each point is 1,000 simulated runs of 250 trades.

Growth, as a share of the best this bet can doTypical worst drawdownChance of losing 90% of the account

SizingGrowthWorst drawdownRuin

Same dollars every trade · 5% of the start (half Kelly), never resized61%-31.7%2.9%

Quarter Kelly · 2.5%43%-24.4%0%

Half Kelly · 5%74%-44.1%0.1%

Full Kelly · 10%100%-73%3.5%

Twice Kelly · 20%13%-96.8%45.6%

The whole account · 100%0%-100%100%

There is a best size, and it's smaller than it feels

Growth rises with size up to one point, the Kelly size, and falls after it. Around twice that size a real edge stops growing at all, and past it the account shrinks even though every trade has the odds on its side.

Drawdown and ruin don't peak

They rise the whole way. Betting a little under the best size gives up a little growth and removes a lot of pain: half the Kelly size keeps about three quarters of the growth with a much shallower worst drawdown.

ONE CONTRACT OR A SHARE OF THE ACCOUNT

Same dollars every time, or the same share every time.

A fixed size doesn't compound

One contract every trade means the risk shrinks as a share of the account when it grows, so growth is left on the table. The table's first row shows it: smaller swings, slower growth.

And it doesn't shrink when the account does

After a run of losses, the same one contract is a bigger share of what's left. Sizing as a share of the account cuts the bet after losses on its own, which is why, in the table, half Kelly's chance of ruin comes in below the same size held fixed.

HOW THE ENGINE CALIBRATES ITS OWN SIZE

Growth, worst drawdown and ruin, traded off on purpose.

01Measure the edge. The average result and its spread per contract, measured on the backtest over years of real option prices.

02Find the fastest-growing size. The Kelly size for that edge: the share of the account that maximizes long-run growth, the peak of the green line.

03Bet half of it. A measured edge is an estimate. If the real edge is half what was measured, half Kelly becomes full Kelly and still grows; full Kelly becomes twice Kelly and stops. Half also keeps the worst drawdown far shallower.

04Cap it, floor it. A cap on contracts per trade so orders fit what the market can fill, and a floor of one contract, which means a small account knowingly runs above half Kelly until it grows.

05Check it on the real sequence. Compound the actual backtest day by day under the rule and read the growth rate, the worst drawdown, and the chance of ruin across reshuffled orders of the same trades. A size that wins on growth but fails on drawdown or ruin is rejected.

For its own book, Phoenix runs one SPXW fly per $20,000 of account, capped at 3. Peregrine is the exception: since October 2026 it sizes at full Kelly rather than half, putting 31% of the account into each XSP trade and 35% into each SPXW trade, at least one contract and at most 10 XSP or 3 SPXW. Both books trade XSP (a tenth the size) below $25,000. That is the engine's sizing for itself, not a size for anyone else.

A NOTE TO ANYONE PUTTING A WHOLE ACCOUNT ON ONE TRADE: DON'T.

The table's last row says it plainly: risk the whole account and the first loss ends it, no matter how good the edge is. Around twice the Kelly size a winning strategy stops growing, and past that it shrinks. When the engine's own tests sized every trade to the account's full buying power, the account was gone within 14 trading days. Same-day options can go to zero in hours.

Not financial advice. Synapse shows what its engine sees and does. It does not know your account or your goals, and nothing here is a recommendation to buy or sell anything. The simulated examples are hypothetical two-outcome bets; real trades have fatter tails, which makes oversizing worse, not better. See what a bad stretch looks like. Read the full disclaimer or the terms.