*Originally posted by CarrollJeff*

I find it very well done but the comments on how to apply for 3-handed poker are not detailed enough. I would like to have more discussions on the solutions of iterated differential equations especially when it settles down.

I'm just going through the motions there. I think that there's very little to be learned about playing real poker from this paper.

I find page 23 the most interesting with the time diagram showing the frequencies for different actions. Do you have an explanation for the two different frequencies that occur for (a2,b3 ~ every 16 hands) and (b2,d1 ~ every 6 hands)? I would like to see more diagrams like this one for others solutions.

Because I set all the constants ki to one, the timescale on the x-axis is the timescale over which players adjust their betting frequencies. It doesn't correspond to hands directly. That's precisely what you lose when you take a continuous limit like this.

Did you think about exploiting these frequencies for a player, anticipating and shifting his curve left, could he do better than just exploiting current frequencies of other players?

I didn't think about any sort of higher order strategy like this. I think you're overestimating how closely the current strategy corresponds to a real poker game.

Also is it possible to check how the payouts change if two players collude when the other one just follows his Nash equilibrium solution (Lemonade stand type of collusion)?

I did have a look at this, but it didn't seem to provide much insight beyond the obvious 'if two players collude, they can win more against the other player's equilibrium strategy'.

I think some figures are missing for Figure 12: "Periodic behaviour when P = 3.75 for three different initial conditions. The

red circles indicate the location of Solution 5." but I can see only one initial condition?

Each of the three closed curves is a solution from a different initial condition.

Thanks for the great work and awaiting the follow-up for even nearer to poker solution including some raises...

You're welcome! I'm currently working on full three player Kuhn poker. I have an idea for a new numerical solution method, but it's proving a bit troublesome to implement at the moment.