Bet Less Than the Formula Says
Published 2026-07-27 · By Drew Shelem
The Kelly criterion, fractional Kelly, and why every uncertainty the whole cycle was about forces you to shrink the bet
Article 8 of the cycle. Every earlier article answered one question — is your edge real. This one answers the next, the one that decides whether you keep your money: given a real edge, how much do you bet per trade? And here everything the cycle taught you to fear converges on a single conclusion — you have to bet less than the textbook formula says.
Where this topic even comes from
Suppose you’ve done everything the cycle was about. You checked your sample size, separated the edge from the win rate, counted your trials, measured the gap with live trading, ran the out-of-sample fan, accounted for inertia. And you really do have an edge — a real one, confirmed. There remains a question almost everyone rushes past: what fraction of your account do you put on each trade?
It’s not an idle question. Bet too much and you go broke even with a winning strategy, because a few losses in a row zero out the account. Bet too little and you grow so slowly the edge isn’t worth having. Somewhere in between is the right size.
There’s a famous answer to this — the Kelly criterion: a formula that hands you the “optimal” fraction to bet. And here’s the trap the whole article is written for. The bet that maximizes growth on paper will, with high probability, ruin you before you ever reach that growth. And once you account for the fact that you don’t know your edge exactly and your trades aren’t independent, it ruins you even more surely. Let’s work through why — and, more importantly, by how much you should bet less.
What this is about — briefly
Three things follow, and all of them lead to one conclusion.
First: full Kelly is a trap. Even when the edge is estimated perfectly, it produces a drawdown so deep that most people never survive to the growth it promises.
Second: fractional Kelly — a half or a quarter of the formula — buys you enormous safety for a small loss of growth. This isn’t caution for its own sake, it’s a bargain, and I’ll show it in numbers.
Third: the Kelly formula leans on two assumptions that are false on these markets — that you know your edge exactly, and that trades are independent. Both are wrong, and both err in the same direction: the real bet has to be smaller still. And a small overestimate of the edge, multiplied by an aggressive formula, turns a winning strategy into ruin — which is exactly where all the validation work of the earlier articles pays off.
All the numbers come from synthetic data, where I set the edge and the inertia myself and hold them under control, so the pure mechanism is visible. Your numbers will be your own, but the direction is the same everywhere.
Let’s break it down step by step
Step 1. What Kelly says — and why full Kelly is already a trap
First, how the bet works, without formulas. You buy a share of a contract at a price — say, 50 cents. If you’re right, the share settles at a dollar, and you make 50 cents on the 50 you put in. If you’re wrong, you lose your 50 cents. A price of 50 cents means the market rates the outcome at 50%. Your edge is when you rate the same outcome higher than the market does: say, at 53%.
The Kelly criterion needs exactly two numbers to compute how much to bet: the contract’s market price (which is also the market’s implied probability of the outcome) and your own estimate of that outcome’s probability. It works like this — subtract the market price from your probability (that’s your edge) and divide by one minus the market price:
bet fraction = (your probability − market price) ÷ (1 − market price)
Plug in our example. The market rates the outcome at 50% (price 50 cents), you rate it at 53%. Your edge is the difference, three points: 0.53 − 0.50 = 0.03. Divide by one minus the price, 1 − 0.50 = 0.50. That gives 0.03 ÷ 0.50 = 0.06 — that is, 6% of your bankroll on each trade. That’s where the number comes from. And the whole meaning of the formula fits in one sentence: the more your estimate beats the market, the bigger the bet. Six percent sounds modest.
Now let’s run it. You start with $100, bet 6% of your current account each time, your edge is estimated perfectly correctly, and you do this for 1,000 trades (that’s weeks of work on 5-minute markets). Here’s what comes out:
| What we look at | Value | What it means in practice |
|---|---|---|
| How much the account grew (median) | ×6.06 | $100 became about $600 |
| How deep the account sank (median) | 79% | at some point the account typically fell 79% from its peak |
| How often the account lost half its start | 43% | in almost one run out of two, the account at some point fell to half of the starting $100 |
Read the second and third rows carefully. The sixfold growth is real. But to get it, you’d have had to sit through a 79% fall of the account from its peak, and in nearly half the cases a loss of half of all your money at some point along the way. Full Kelly maximizes growth on the assumption that you can stomach any drawdown, never panic, and never get knocked out. For a real human with a real stop, that assumption is false: you most likely just won’t sit through to the ×6. The formula for maximum growth turns out to be a formula that, with high probability, ruins you.
Step 2. Fractional Kelly — a lot of safety for a little growth
Since full Kelly is unbearable, it’s natural to bet a fraction of it — a half or a quarter of what the formula says. Let’s see what that changes, on the same data and the same correct edge:
| How much of Kelly we bet | Fraction of bankroll | Account growth | Median drawdown | Chance of losing half |
|---|---|---|---|---|
| Full Kelly | 6.0% | ×6.06 | 79% | 43% |
| Half Kelly | 3.0% | ×3.86 | 50% | 11% |
| Quarter Kelly | 1.5% | ×2.20 | 28% | ~0% |
Here’s the point, and it’s worth saying out loud. As you shrink the bet, growth falls slowly, but risk falls fast. Going from full Kelly to half, you give up about a third of the growth (from ×6 to ×3.9) — but the risk of losing half the account drops fourfold, from 43% to 11%. Quarter Kelly gives up a little more growth but takes the risk of ruin down to almost nothing. That’s the bargain: you pay a little in growth and buy yourself survival. This is exactly why serious bettors almost never bet full Kelly — usually a half, and the cautious a quarter.
Step 3. The formula thinks you know your edge. You don’t
This is where the whole cycle converges. To compute the bet, Kelly needs your true win probability. But everything the earlier articles were about showed the opposite: the edge you measured is known imprecisely and is most likely inflated. The sample is noisy (article 1). The best of the variants you searched over is inflated by the search (article 3). One out-of-sample run is a random draw (article 6). You feed the formula not the truth, but your overestimate.
Let’s see how that ends. Suppose you think your win probability is 56%, when it’s really 53% — an overestimate of just three points. Plug 56% into the same formula: the edge is now 0.56 − 0.50 = 0.06, twice the previous three points; divide by the same 0.50 and you get 0.12, that is 12% of your bankroll. Watch what happened: a three-point overestimate of the edge doubled the numerator of the formula, and with it the bet — from 6% to 12%. Now we run that inflated bet, but with the true edge of 53%:
| What we look at | Value | What it means |
|---|---|---|
| How much the account grew | ×0.98 | no growth — the account ends slightly below where it started |
| Median drawdown | 99% | the account was all but wiped out |
| Chance of losing half | 85% | near-certain ruin |
Stop here. An overestimate of three points — a trifle, easily produced by a noisy sample — turned ×6 growth into ×0.98. That is, into ruin. Not because the error is large, but because it landed in an aggressive formula that doubled the bet. This is why all the validation work of the earlier articles isn’t academic nitpicking: an inflated edge estimate blows up the account precisely through the bet size. From which comes a direct rule: since you don’t know your edge exactly, bet as if it were smaller than what you measured. How much smaller — by the lower bound of your confidence (the very one computed in the first article): if the edge could turn out to be half as strong, bet as if it’s half.
Step 4. The formula thinks your trades are independent. They’re not
Kelly’s second false assumption is that each trade is a fresh independent draw. The previous article showed that losses clump into runs. Let’s check what that does to the same bet: take half Kelly and compare independent trades with trades in runs.
| Half Kelly | Median drawdown | Chance of losing half |
|---|---|---|
| Independent trades | 50% | 11% |
| In runs (inertia) | 65% | 28% |
Same bet, same edge — but inertia raises the risk of ruin from 11% to 28%. The reason is the one from the previous article: clumped losses dig the pit deeper, and on a deep pit you get knocked out at a bet the independent data thought was safe. So inertia is another reason to bet below the formula.
Put the three steps together and you have the spine of the article. Full Kelly is unbearable on its own. On top of that you don’t know your edge exactly — so bet even less. On top of that your trades aren’t independent — so less still. All three corrections pull the same way: the right bet is noticeably smaller than the one the formula hands you.
The order of operations: first the edge with an interval, then Kelly
Here a fair question comes up, one it’s easy to stumble on. Kelly needs the edge — but you learn the edge from the backtest, so what bet do you set in the backtest itself, when there’s no edge yet? These are two different tasks, and confusing them is the very mistake that ruins the account. Let me lay out the order.
First the backtest measures the edge — and the bet size barely matters for that. The edge is a property of a single trade: how much you make on average per unit staked, after costs. Bet a dollar, ten, or a hundred in the backtest — that percentage is the same. So for measuring, use a small fixed bet (say, those same $10 per trade, not changing it as the account grows) and look not at the final dollar figure but at the per-trade numbers: edge after costs, the confidence interval of the win rate, the spread. Don’t pick a percentage of capital at this stage at all — it’s too early. The capital (a notional thousand) matters here for one thing: is it enough that a realistic run of losses doesn’t cut the test short. With a small fixed bet — by a huge margin, yes.
One caveat about the backtester itself. If it doesn’t fix the bet but reinvests (betting a fraction of the running account), then the final dollar figure, the shape of the curve, and the drawdown in percent become an artifact of your arbitrary choice of “$10 on $1,000,” not a property of the strategy: switch to “$50 on $1,000” and you get a different result out of the same strategy. So you can’t judge a strategy by its dollar result — read the per-trade percentages.
Then validation — not “tweak until it looks good.” Here’s the main trap, and it comes straight from the earlier articles. If you turn the parameters until the picture starts to please you, you didn’t measure the edge — you fit yourself to noise (article 3), and the figure that “pleases” is the upper bound, not the truth (article 6). The result of honest validation is not one pretty number, but an edge with an interval: “the edge is somewhere between 1 and 4 points,” not “the edge is 4.”
The go-live decision — by the lower bound, not by beauty. Ask not “do I like the result,” but “does the lower bound of the interval exclude zero after costs.” Lower bound in the positive — the strategy is alive. It touches zero — there are too few trades or no edge, and no bet size will save that.
And only now Kelly — and it’s not a second run, it’s one line of arithmetic. You don’t “run it on Kelly” again. You take the edge you already have and plug it into the formula — but not the pretty center of the interval, its lower bound. Then you take a fraction (a half or a quarter) and cut it further for inertia. One line of arithmetic on top of an honest result, with no second pass over the data.
Assemble it into a chain: a small fixed bet in the backtest → honest validation down to an edge-with-an-interval → go live only if the lower bound is positive → fractional Kelly on the lower bound. Swap any link for “tweak until I like it, then bet on the pretty number” and you get exactly the edge overestimate from Step 3 that turns growth into ruin.
What would refute this — and where the limits are
The condition on which the article would collapse (and didn’t). If fractional Kelly cut growth as fast as it cut risk, “bet fractional” would be empty. But it cuts risk fourfold while giving up only a third of the growth. And if overestimating the edge didn’t blow up the bet, “shrink for uncertainty” would be empty. But three extra points of edge turned ×6 into ×0.98. Both attempts to kill the conclusion I made; both failed in my favor.
The honest boundary. All of this math assumes you reinvest — that you bet a fraction of the running account, which compounds up and down. If you bet a fixed sum regardless of account size, the picture is different: you can still go broke, but the growth formula is no longer this one. And the specific fractions — 6%, a half, a quarter — are from my example with a 3-point edge at a price of 50 cents. Your edge and price are different, so your numbers are different. What’s fixed isn’t the figures, it’s the direction and the bargain: growth falls slowly, risk fast, and every uncertainty pushes the bet down.
What I don’t know, and where the limits are
- All the numbers are from synthetic data. I set the edge and the inertia myself. This is a demonstration of the mechanism, not a calculation for your strategy.
- The size of the effect is your own. The twofold drawdown and threefold sample shrinkage are at the inertia I set. Weaker inertia, weaker effect.
- I defined “ruin” as losing half the starting account. That’s a vivid threshold, not the only right one; with your threshold you’ll get your own percentages.
- The Kelly formula assumes a known, fixed edge and independent trades. Both assumptions are broken on these markets — that’s the whole article — so use the formula itself as a ceiling, not a recipe.
- The exact uncertainty of the edge is hard to measure. “Bet by the lower bound of your confidence” is the right direction, but you estimate that lower bound imprecisely too; better to err on the low side.
- Reinvesting. If you don’t fold profit back into the bet but withdraw it, recompute for your regime.
What to do tomorrow
- Never bet full Kelly. Even at a correct edge it’s a 79% drawdown and nearly a one-in-two chance of losing half the account. Take a half; the cautious take a quarter.
- Shrink the bet for edge uncertainty. You don’t know the edge exactly and have most likely overestimated it. Bet as if the edge equals the lower bound of your confidence, not the measured center. A small overestimate at an aggressive bet is ruin, not a shortfall.
- Shrink it further for inertia. If your losses clump (how to check — in the previous article), the same bet is more dangerous than the formula thinks. Reduce it.
- Compute the bet from the distribution of the edge, not from a single figure. A point estimate of “my edge is 3 points” hides that it might be one. Take the position size from the whole spread of possible edges, not from its middle.
- Know your risk of ruin in advance and set a hard stop. You can feel the drawdown before you risk money, in paper mode — free, before any subscription: the same signal engine as in live trading, so the drawdown and the runs of losses are reproduced honestly rather than smoothed away.
FAQ
Isn’t Kelly optimal? That’s what all the textbooks say. It’s optimal for growth — but under three conditions: you know your edge exactly, you can stomach any drawdown, and nothing knocks you out. On real markets none of the three holds. So Kelly is a ceiling on the bet, not a recommendation.
What fraction of Kelly should I take? A half is common, a quarter for the cautious. The less sure you are of the edge and the more your losses clump, the smaller the fraction. Erring low is cheap (slightly slower growth), erring high is expensive (ruin).
Why is such a small overestimate of the edge so dangerous? Because the edge feeds an aggressive formula. Three extra points of estimate doubled the bet — and a doubled bet at the same real edge turns growth into ruin. The error is small, but the lever under it is large.
First I run the backtest, then I run it separately on Kelly? No. Kelly isn’t a second pass over the data, it’s one line of arithmetic on top of a finished result. A backtest at a small fixed bet gives you an edge with an interval; from that interval you compute fractional Kelly — but on the lower bound, not the pretty center. And “a result that pleases me” is a dangerous phrase: if you turned the parameters until it pleased you, you got an inflated edge, and Kelly will amplify that error into ruin. First honest validation, then the bet computed on the lower bound.
I bet a fixed sum, not a fraction of the account. Does this matter to me? The ruin logic — yes, it matters: a run of losses can still zero you out. But the growth formula for a fixed bet is different, so recompute the specific numbers for your regime.
How do I account for edge uncertainty in practice? Don’t plug the measured center into the bet size. Take the lower bound of your confidence from the first article (the edge’s confidence interval) and bet as if for that. If the edge could turn out half as strong — bet as if it’s half.
Disclaimer
This material is educational and is not financial advice. Past results do not predict future results. Trading on prediction markets carries real risk, up to and including the total loss of capital. Access to Polymarket is restricted or prohibited in some jurisdictions — verify legality where you live before trading.