Kelly and fractional Kelly
Level 1 said to keep stakes small and steady. This lesson shows where Consensus Edge's suggested stake comes from, and why it is a small slice of what the textbook formula says.
The Kelly formula
The Kelly criterion sizes a bet from two things: your edge and the payout. Full Kelly is f* = (bp − q) ÷ b, where:
- b is the profit per $1 staked: 0.909 at −110, 1.5 at +150;
- p is your chance of winning;
- q = 1 − p, your chance of losing.
f* is the share of your bankroll to bet. No edge, no bet: when bp is no bigger than q, the answer is zero. Bigger edges get more, and so do shorter prices for the same edge. Over a very long run, betting exactly full Kelly on exactly correct chances grows a bankroll faster than any other fixed-fraction rule.
The catch: your chance is an estimate
That promise holds only when p is the true probability, and nobody's is. Full Kelly punishes overconfidence hard. Bet about twice the right Kelly size and your expected long-run growth falls to roughly zero; bet more and you shrink even with a real edge. Even with perfect chances, the ride is rough: at full Kelly there is about a 1 in 2 chance your bankroll is cut in half at some point.
Hence fractional Kelly: bet a fixed share of the Kelly number. Half Kelly keeps about three-quarters of full Kelly's growth with half the swings, cuts that halving chance to about 1 in 8, and forgives an overstated edge. Many professionals bet a quarter to half Kelly for exactly these reasons.
Why Consensus Edge stakes a tenth
Our suggested stake is at most a tenth of full Kelly, and full Kelly itself is capped at 10% of bankroll first. So the largest stake we ever suggest is 1% of bankroll: one unit. Your risk setting chooses where you sit: Conservative stakes 2.5% of full Kelly, Moderate 5%, Standard 7.5% and Aggressive 10%.
That is smaller than the professional rule of thumb on purpose, and the reason was measured, not guessed. When we checked our own graded bets against their results, our estimated edges had run well above the edges the results showed, and the biggest stakes, the bets where Kelly said to bet most, carried no measured edge at all. That is the classic Kelly failure: an overstated edge oversizes exactly the bets that deserve it least. So we lowered the cap and kept the stakes at a tenth.
A tenth of Kelly gives up some growth if our numbers are right. It protects you if they are not, and with sports probabilities that is the risk worth insuring. If you size your own bets, the same lesson applies: the less sure you are of your chance, the smaller the fraction.
Try it: enter a chance, a price and a bankroll in the calculator below to see full Kelly and our suggested stake at a risk setting.
Example. Our chance is 55% on a side priced −110, and your bankroll is $1,000 (illustrative, not live data).
- b = 100 ÷ 110 = 0.909, p = 0.55, q = 0.45
- bp = 0.909 × 0.55 = 0.500
- f* = (0.500 − 0.45) ÷ 0.909 = 0.055, so full Kelly is 5.5% of bankroll, $55
| Sizing | Share of full Kelly | Stake on $1,000 |
|---|---|---|
| Full Kelly | 100% | $55.00 |
| Half Kelly | 50% | $27.50 |
| Quarter Kelly | 25% | $13.75 |
| Consensus Edge, Aggressive | 10% | $5.50 (0.55u, shown as 0.6u) |
| Consensus Edge, Standard | 7.5% | $4.13 |
| Consensus Edge, Moderate | 5% | $2.75 |
| Consensus Edge, Conservative | 2.5% | $1.38 |
Now a claimed 62% at +100: f* = (1 × 0.62 − 0.38) ÷ 1 = 0.24, or 24% of bankroll. The cap holds full Kelly at 10%, so even Aggressive stakes 10% × 10% = 1%, $10. An edge that large is far likelier to be an error than a gift.
Try it
Terms in this lesson
Kelly CriterionRisk ToleranceSmart SizingUnitBankrollEdgeVariance