Flat Betting vs the Kelly Criterion

Both are staking rules. Neither finds an edge; they only decide how much to put on a price once you believe it has one.

Flat betting stakes the same unit on every bet: either a fixed amount, or a fixed share of bankroll (often 1 to 2 percent) recalculated occasionally. The stake ignores how large the estimated edge is.

The Kelly criterion, from John Kelly's 1956 paper on information rates, stakes the fraction f = (bp - q) / b of current bankroll, where b is decimal odds minus one, p is the estimated win probability and q is 1 minus p. The stake rises with the estimated edge and falls with longer odds, and is zero when there is no edge.

Take two illustrative bets. Bet A is at 2.10 with an estimated 52 percent chance: full Kelly is about 8.4 percent of bankroll. Bet B is at 3.00 with an estimated 36 percent chance: b is 2, so f is (0.72 - 0.64) / 2, or 4 percent. A flat bettor using 2 percent units stakes 2 percent on each.

Kelly puts twice as much on A as on B because A's estimated edge is larger relative to its odds. Flat staking treats them identically. If both estimates are exact, Kelly's allocation grows the bankroll faster. The risk is in the estimate: A breaks even at 1/2.10, or 47.6 percent, so if its true probability is 48 percent the bet is still barely positive at plus 0.8 percent, but the correct Kelly stake collapses to 0.7 percent of bankroll. Staking the 8.4 percent the 52 percent estimate implied is then about eleven times Kelly, and expected growth turns negative even though expected value has not. Overbetting a real edge is the more common way to go broke than backing a negative one.

Kelly maximises the expected logarithm of bankroll, which means the fastest long-run growth rate, on the condition that the probabilities are right. Flat betting with edges that vary from bet to bet is below that optimum because it underweights the best opportunities and overweights the marginal ones.

The growth curve around the Kelly stake is flat near the top and steep beyond it. In the standard approximation, half Kelly keeps about 75 percent of full Kelly's growth rate with a quarter of the variance, while staking twice the Kelly fraction drives the growth rate to roughly zero. Underbetting costs a little; overbetting costs a lot.

Full Kelly is volatile even with perfect inputs. In the idealised continuous model described in Ed Thorp's work on Kelly, the probability that bankroll ever falls to a fraction x of its starting value is x raised to the power (2/c - 1), where c is the fraction of Kelly staked. At full Kelly that gives about a 50 percent chance of halving at some point. At half Kelly it is x cubed, about 12.5 percent.

Flat drawdowns are governed by unit size. With fixed amounts, the worst case is easy to reason about but does not scale: a run of losses leaves the same stake against a smaller bankroll, raising risk exactly when it should fall.

Every staking comparison that favours Kelly assumes p is known. In sports models it never is. Worse, errors are not random with respect to stake: the bets where a model shows the largest edges are disproportionately the ones where it is most wrong, because extreme estimates are more often noise than signal. Kelly gives those bets the largest stakes.

Flat betting is robust to this because stake size ignores the estimate. It still loses money on bad estimates, but it does not amplify them. This is why the practical choice is rarely pure Kelly versus pure flat. Most quantitative bettors use fractional Kelly (a quarter or half) with a hard cap on any single stake, which behaves like flat staking on large estimated edges and like Kelly on small ones.

Flat staking makes results easy to interpret: return on investment treats every bet equally, so it measures the average quality of the selections. Kelly-weighted profit and loss is dominated by the largest stakes, which are the least reliable estimates. Whichever rule is used for staking, it is worth recording what flat staking would have returned, alongside calibration and closing line value, so the quality of the estimates can be judged separately from the sizing.

This page compares staking rules and is not betting advice.