Kelly: sizing a bet to the edge
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. The Kelly number 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 the Kelly number 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. Betting the whole Kelly number 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: betting the whole Kelly number, there is about a 1 in 2 chance your bankroll is cut in half at some point.
Hence the usual fix: bet a fixed share of the Kelly number. Betting half of it keeps about three-quarters of the 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 a half of it for exactly these reasons.
How Consensus Edge sizes a stake
Our suggested stake is sized to the edge: like Kelly, it grows with the edge and the payout, and it is zero when there is no edge. It is also deliberately small, smaller than the professional rule of thumb, and never more than one unit, 1% of bankroll. Your risk setting chooses where you sit: Conservative stakes the least, Aggressive the most.
Small 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 keep every stake small.
A small stake 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 share of the Kelly number you bet.
Try it: enter a chance, a price and a bankroll in the calculator below to see the Kelly number 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 the Kelly number is 5.5% of bankroll, $55
| Sizing | Share of the Kelly number | Stake on $1,000 |
|---|---|---|
| The Kelly number | 100% | $55.00 |
| Half of it | 50% | $27.50 |
| A quarter of it | 25% | $13.75 |
Now a claimed 62% at +100: f* = (1 × 0.62 − 0.38) ÷ 1 = 0.24, or 24% of bankroll. An edge that large is far likelier to be an error than a gift, which is why we cap the Kelly number before we size any stake.
Try it
Terms in this lesson
Kelly CriterionRisk ToleranceSmart SizingUnitBankrollEdgeVariance