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?

  • 1
    $\begingroup$ The example you give can be solved using the Kelly criterion with more than 2 outcomes math.stackexchange.com/questions/662104/…. It does not have a closed form solution but can be solved iteratively. $\endgroup$
    – noob2
    Sep 30 at 12:13
  • $\begingroup$ thanks @noob2, but what I meant was to look for different approaches besides kelly $\endgroup$
    – Mining
    Sep 30 at 14:38
  • $\begingroup$ The papers and books by Ralph Vince might be of interest, @Mining $\endgroup$
    – user42108
    Sep 30 at 19:54

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.


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