# Kelly criterion

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Canonical: https://novigapi.com/learn/kelly-criterion

The Kelly criterion is a formula for the fraction of your bankroll to stake on a positive EV bet so that long-run bankroll growth is as fast as possible.

```
f* = (b x p - q) / b, where b = decimal odds - 1, p = win probability, q = 1 - p
```

The Kelly criterion, published by John Kelly in 1956, tells you how much of your bankroll to put on a bet with an edge. Stake too little and you leave growth on the table; stake too much and a run of losses can cripple the bankroll even when every bet is positive EV. Kelly finds the fraction that maximizes the long-run growth rate of the bankroll. Most professionals bet a fraction of full Kelly, often a quarter or a half, because their probability estimates are never exact.

## How it works

The formula needs two inputs: the net odds b, which is decimal odds minus 1, and your fair probability of winning p. It returns f*, the share of the current bankroll to stake. If f* is zero or negative the bet has no edge and Kelly says not to bet. The stake scales with the edge and shrinks as odds lengthen, which keeps long shots from draining the bankroll.

## Worked example

Kelly stakes on a $1,000 bankroll

| Bet | Decimal odds | b | Fair p | Full Kelly f* | Full stake | Half Kelly |
| --- | --- | --- | --- | --- | --- | --- |
| Even money | 2.000 | 1.000 | 55% | 10.00% | $100.00 | $50.00 |
| Underdog | 2.500 | 1.500 | 45% | 8.33% | $83.33 | $41.67 |
| Novig Yes at 42% | 2.381 | 1.381 | 47% | 8.62% | $86.21 | $43.10 |
| -110 with 52% fair | 1.909 | 0.909 | 52% | -0.80% | $0.00 | $0.00 |


For the first row: (1 x 0.55 - 0.45) / 1 = 0.10. For the second: (1.5 x 0.45 - 0.55) / 1.5 = 0.125 / 1.5 = 0.0833. The last row is negative, so Kelly says pass: a 52% edge is not enough to beat -110. Try your own numbers in the [Kelly calculator](https://novigapi.com/kelly-criterion-calculator).

## On Novig

On a Novig contract bought at price c, the net odds are b = (1 - c) / c, and the formula simplifies neatly to f* = (p - c) / (1 - c). Buying Yes at 42% with a fair 47% gives (0.47 - 0.42) / 0.58 = 8.62%, the same as the table. When you buy in-game, fold the taker fee into the price: at 42% the fee of 0.06 x 0.42 x 0.58 = $0.0146 per contract raises c to about 43.46%, which cuts full Kelly to about 6.26%. Pregame game-market fills pay no fee per [Novig trading fees](https://docs.novig.com/api/concepts/fees) (checked 12 Nov 2026).

```
f* = (p - c) / (1 - c) for $1 of payout bought at price c
```

## Common mistakes

- Betting full Kelly on uncertain estimates. Overestimating p by a few points can double the right stake; fractional Kelly is the usual cure.
- Staking Kelly on several simultaneous bets as if each were alone. Correlated or simultaneous bets need a smaller combined fraction.
- Forgetting to resize as the bankroll changes. Kelly is a fraction of the current bankroll, not the starting one.

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