Math Question: Kelly Criterion for Three outcomes

[NotEnoughHeat]

Excuse me for posting this in the general forum, I'll offer an explanation if anyone truly cares.

I haven't looked too hard through search engines, but after trying two or three different sets of search terms and not finding what I was looking for on the first page I figure I might have a good chance here.


I'm currently trying to calculate kelly sizing for a relatively simple game but the issue is that the formula I keep running into is a simplified formula for two outcomes (win or loss). The game I'm trying to figure out has three outcomes: an even money win, an even money loss or a multiple bet size loss (you could frame it in a different yet mathematically equivalent way, but this description imo most accurately captures the feel of the game).

What I'm looking for is either a tool to calculate kelly for three outcomes (or for whatever relevant features match my game) or the formula itself. The latter is preferable but I'll take either or both.

The most general (unqualified) formula is something that would also be appreciated but I'll take anything I can get, even if it means I put in a bit of extra work to figure it out.


Thanks in advance to anyone who steps forward.

Also, if you guys want. General Kelly thread.

[ZenMaster_Flash]

Two words:

Weighted Outcomes

[NotEnoughHeat]

Two words:

Weighted Outcomes

I just came home from a long day, I'll see if I can figure it out myself tomorrow.

EDIT: I missed the possible relevance of this section when skimming through the article. See paragraph under 'Many Horses'
https://en.wikipedia.org/wiki/Kelly_criterion

[Gronbog]

For more complex games, the estimate of EV/Variance is very good. It gives you an estimate the percentage of bankroll that you should bet for full kelly.

[NotEnoughHeat]

For more complex games, the estimate of EV/Variance is very good. It gives you an estimate the percentage of bankroll that you should bet for full kelly.

Thank you, I find this is very helpful. I've heard of EV/Variance being applied to BJ but I've never known why it was used.