Three stack problem

Here is a problem resembling Pai Gow Poker. The graph of symmetric equilibrium strategies forms a fractal.


Two players have equal infinitely divisible stacks and secretly divide them into 3 corresponding piles. The winner is the player with two larger piles.

In Russian poker, you have to make 3 poker hands from 13 cards, and you have to beat 2 of your opponents hands. I guess this is a similar game to what you are referring to.


The strategy for this game I am sure is well documented in a gambling book on the topic somewhere. I have seen the strategy but I can't remember where right now.

Well, Russian poker (or Chinese poker, or 13-card poker) isn't quite the same problem, because


- you don't always have the same size "stack"

- the values of your hands aren't "fungible" -- you can sometimes sort of move power around among the hands, but it often comes at some cost.


So, although a clever reference, 13-card poker isn't really a model for the three stack problem, or vice versa.