Expected value and the Kelly criterion
What a bet is worth on average, where the probability comes from, and how much of a bankroll Kelly says to stake.
Two ideas sit under almost every serious betting method: expected value (is this bet worth more than it costs?) and the Kelly criterion (how much of the bankroll should go on it?). Surebets avoid the first question; most other approaches live on it.
Expected value
The expected value of a bet is what it returns on average, per unit staked, if you could place it many times.
EV = p × odds - 1
where p is the real probability of winning and odds are decimal.
A positive EV bet can still lose, and usually does over a short run. EV only shows up over many bets.
Where the probability comes from
Nobody hands you p. The two usual sources:
- A model of your own: ratings, simulations, statistics.
- The market: a sharp book's price with its margin taken out. The no-vig calculator does that. If another book pays more than those fair odds, the bet has positive EV against the market's estimate.
Both can be wrong, and a small error in p changes everything downstream.
The Kelly criterion
John Kelly (1956) answered a different question: given an edge, what share of the bankroll grows it fastest over many bets?
f = (p × odds - 1) / (odds - 1)
The top is the edge (the EV per unit); the bottom is the net odds. No edge, f is zero or negative: don't bet.
Why people bet a fraction of Kelly
Full Kelly assumes p is exact. Overestimate it by a few points and the stakes are too big; the swings get large and a bad run takes a big share of the bankroll. Half Kelly keeps about three quarters of the long-run growth with half the volatility. Quarter Kelly is common for people who know their estimates are rough. The Kelly criterion calculator shows all of them.
How surebets differ
A surebet needs no probability at all. If every outcome is covered at prices whose implied probabilities add up to less than 1, the result is fixed by arithmetic, as long as every leg stands at the price you got. The risks move elsewhere: prices moving between legs, voids, rule mismatches and limits. See The real risks and Arbitrage, value betting and matched betting compared.
See it on real data
A free account shows up to 3 live surebets, each 0.99% or less, every leg re-checked at its book. No card needed.