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Bet Sizing Beyond Kelly Depends on Utility and Risk Preferences

Article Quant Q&A · Author: Mining
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Summary

The document asks how to choose a wager for a game with several possible payouts without relying solely on the Kelly criterion. It gives a discrete outcome distribution and raises expected value reasoning, similar to evaluating a poker pot, as a possible alternative. No numerical bet size is calculated.

The response explains that Kelly’s original formulation assumes binary outcomes and logarithmic utility, while the framework can be extended to multiple outcomes and other utility functions. The optimal wager therefore depends on the bettor’s utility, or risk preferences; there is no universally correct amount independent of those preferences. Concave utility is mentioned as a regularity condition that can express aversion to risk. The discussion is conceptual and does not specify a particular utility function, bankroll constraints, or a worked calculation for the example, so it provides a framework for choosing a strategy rather than a numeric recommendation.

Key ideas

  • Kelly sizing can be generalized from binary outcomes to games with multiple possible outcomes.
  • The bettor’s utility function determines how expected outcomes translate into a wager size.
  • Concave utility can represent risk aversion, but it does not select a unique preference for every bettor.
  • The example’s outcome probabilities are not used to calculate a recommended stake.

Tags

Position sizingRisk managementStatistics
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# Alternatives to Kelly Criterion


# Alternatives to Kelly Criterion












I am preparing for Quantitative Trading interviews and I know that they basically require you to solve problems on the probability of winning in a given game and then they would ask you:

> How much would you bet in this game? What would you strategy be if you had 100$?

Now, I know that the Kelly criterion gives you the optimal fraction of capital that you should bet, but I wonder: Isn't there any other method I could use to answer the question above?

For example, in a given game you have $1/216$ probability of winning $30$ times your bet, $15/216$ of winning $2$ times your bet, and $75/216$ of winning your bet, and thus you have $125/216$ of losing your entire bet.

How much should we bet in this game without using Kelly, what would be an optimal strategy?

I am thinking: Couldn't we apply the reasoning that poker players do in estimating the expected value of the pot?

## Answer by Michael Isichenko (score 1)

https://quant.stackexchange.com/a/68158

The original Kelly criterion handles a binary outcome under a log utility. Generalization to multiple, including continuous, outcomes and any other utility is straightforward. A discussion of available options with numeric examples is given, for example, in this book. An important thing to realize is that the optimal betting depends on your utility (aka risk preferences), which is where psychology plugs into the quant process. There is no universal "correct" way to define the player's risk preferences, other than by imposing certain regularity constraints like concavity -- unless the player is into playing a Russian roulette.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.