# kelly criterion

Position sizing model that calculates the optimal fraction of your bankroll to bet, given your estimated edge.

## The Formula

Classic Kelly:

```
f* = (p * b - q) / b
```

Where:

* `f*` = fraction of bankroll to bet
* `p` = your estimated probability of winning
* `b` = odds received (payout ratio)
* `q` = probability of losing (1 - p)

## Four Variants

The terminal shows four Kelly calculations side by side:

| Variant             | Formula                  | Risk Profile                                                                                     |
| ------------------- | ------------------------ | ------------------------------------------------------------------------------------------------ |
| **Full Kelly**      | `f*`                     | Maximum growth rate. High variance.                                                              |
| **Half Kelly**      | `f* / 2`                 | Standard recommendation for most traders. Cuts variance by 75% while keeping 75% of growth rate. |
| **Quarter Kelly**   | `f* / 4`                 | Conservative. Good for uncertain estimates.                                                      |
| **Empirical Kelly** | Becker (2025) adjustment | Accounts for estimation error in `p`. Most robust variant.                                       |

## Empirical Kelly (Becker 2025)

Standard Kelly assumes you know the true probability. You don't. Becker (2025) adjusts for estimation error:

```
f_empirical = f* * (1 - uncertainty_penalty)
```

The uncertainty penalty increases when:

* Your confidence in `p` is low
* The market is volatile
* The sample size (for your estimate) is small

This makes Empirical Kelly consistently smaller than Full Kelly, which is the point. Overbetting is the most common mistake in Kelly-based sizing.

## How to Read the Output

| Output                   | Meaning                                                         |
| ------------------------ | --------------------------------------------------------------- |
| **Positive f**\*         | You have an edge. The value tells you the optimal bet fraction. |
| **Zero or negative f**\* | No edge detected. Kelly says don't bet.                         |
| *Large f (>20%)*\*       | Strong edge but high risk. Half or Quarter Kelly recommended.   |
| *Small f (<5%)*\*        | Marginal edge. Transaction costs may matter.                    |

## Practical Guidelines

1. **Never bet Full Kelly** unless you are very confident in your probability estimate. Half Kelly is the standard.
2. **Check Taker Cost** before sizing. If your Kelly edge is 5% but taker cost is 3%, your real edge is only 2%.
3. **Multiple positions** should be sized independently. Total portfolio exposure should still feel comfortable.
4. **Kelly assumes no correlation** between bets. In practice, prediction markets in the same sector often correlate.

## Inputs

Kelly uses:

* **Estimated probability**: From the composite probability model (or your manual estimate via the Live Modeler)
* **Market price**: Current YES price as the "odds" offered
* **Calibration**: Empirical Kelly's uncertainty penalty is adjustable


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