# Kelly Criterion Calculator

Optimal Investment Size
##### Kelly Simulator
times
Wins: . Losses: . Win Rate: %

## How to use

Kelly Criterion Calculator is a tool for finding the optimal investment size to maximize profits on repeated investments.

• Winning Probability : Enter the probability of earning a profit from investment.
• Gain of Positive Outcome : Enter the potential gain of a positive outcome. For example, if you invest 100 and get 10, the gain is 10%.
• Loss of Negative Outcome : Enter the potential loss of a negative outcome. For example, if you invest 100 and lose 10, the loss is 10%.

Optimal Investment Size means the ideal investment ratio for the capital. For example, if it is 50%, ideally you should invest 50% of your capital each time. On the other hand, 100% or more means leveraged investments.

## What is the Kelly criterion?

The Kelly criterion is a theoretical formula for obtaining the best return when repeatedly investing money. Sizing an investment according to the Kelly criterion can theoretically yield the best results.

## Risks

The Kelly criterion requires clearly the probability and magnitude of a return on an investment. However, in real-world investing, it is impossible to fully predict this. In the Kelly criterion, even a small change in probability can significantly change the size of an investment. Therefore, you should not make investments decision based solely on the Kelly criterion.

## The usefulness of the Kelly criterion

The Kelly criterion shows that when investing in a more volatile asset, you should scale down your investment size to maximize returns. For example, even if you have the same profit/loss ratio, if you invest in [Win: +20%, Loss: -10%], you need to reduce the amount of investment by half compared to [Win: +10%, Loss: -5%] to achieve optimal results.

## Kelly criterion formula • f : Optimal Investment Size
• p : Winning Probability
• q : Losing Probability (q = 1-p)
• a : Loss of Negative Outcome
• b : Gain of Positive Outcome