Kelly Criterion
A formula that turns your win probability and payoff odds into the bet fraction that grows your money fastest over the long run — the "how much" problem, even once you have an edge.
Formula
f* = (b × p − q) / b p = win probability q = 1 − p (loss probability) b = payoff odds (amount won per unit staked, if you win)
Say you're confident about which way a stock or coin will move. That still leaves the harder question: how much of your money should ride on the call? Bet everything and one wrong guess can halve your account, after which even a great streak struggles to dig you out. The Kelly criterion answers exactly this — not the direction, but the position size that compounds your money fastest over time.
It comes down to three numbers: your win probability p, the loss probability q (= 1 − p), and b, the odds you get paid on a win relative to what you lose. The intuition is clean. Bet more when your edge (p) is large and the payoff (b) is generous, and bet nothing at all when p times b fails to clear q, because then you have no real edge to press.
The catch is volatility. Wagering the full Kelly fraction is growth-optimal on paper, but the ride is brutal — deep drawdowns where the account routinely falls by half are normal, not rare. Worse, the formula is only as honest as the p you feed it, and most people overrate their own hit rate. That's why practitioners usually bet half of what Kelly says (half-Kelly): you give up a little growth for a far smoother equity curve.
In the end, the hard part of Kelly isn't the arithmetic — it's knowing p honestly. Feed it a guessed win rate and the formula amplifies that error straight into an oversized bet. Kelly only becomes a usable tool once you have a record that's been tested against the real market enough times to trust the number.
Example
With p = 0.55 and an even-money bet (b = 1), f* = (1×0.55 − 0.45) / 1 = 0.10 — stake 10% of the bankroll. Half-Kelly would stake 5%.
How LDBD uses it
LDBD only forecasts direction — up or down — so nothing here sizes a bet or puts real money down. But the one input Kelly needs and nobody can eyeball is p, your true win probability. Because LDBD resolves hundreds of predictions against real market prices, you can read p straight off a predictor's raw correct/total record. Note what the Verified tier actually certifies: with its 95% confidence interval excluding zero, it says a predictor's annualized return edge — not the hit rate — is statistically unlikely to be luck (a Verified predictor can even have a middling win rate but large returns, so keep the two apart). So draw p from that checked correct/total record rather than a hunch, and treat base_rate_up (an asset's historical chance of rising over a horizon) as a reasonable starting prior.
FAQ
Where do you get the win probability p?
That's the hard part, and Kelly is only as good as it. Estimate p from a real, sizable track record — your historical hit rate on similar bets — not from how confident you feel. A tiny sample or a gut number will push Kelly straight into overbetting.
Does Kelly work for stock or crypto direction bets?
Kelly was built for fixed-odds wagers. Market returns are continuous, so there's a variant that sizes by expected return divided by variance, and a direction call has no fixed payoff b, so any application is an approximation. That extra uncertainty is one more reason to lean toward half-Kelly.