Streib article

[droidboy]

There appears to be a bug in the basic (cash game) solution. It doesn't agree with my solution, or the sample case which eastbay posted a few weeks ago.

You are correct that the solutions are not exactly correct, but they are very close. The reason is that the method I was using to solve these problems can't deal with mixed strategies. Unfortunately I'm not a programmer, so I don't have as powerful resources as I would like. So I did the best I could and came up with the closest approximation, which isn't too far off. For most people reading the article, it won't matter if a few hands are off a tiny bit.


It's pretty important, if you're going to present solutions to problems, that you properly state what problem you are solving. You didn't present a game theory optimal solution, so presenting it as such is a bit confusing. As far as how close the solutions are to the game theory optimal one, they look like they are off by quite a bit, especially for small stacks.

- Andrew

[trojanrabbit]

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You didn't present a game theory optimal solution, so presenting it as such is a bit confusing.

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I'm sorry if you felt decieved. Unfortunately, working with a 1000-word limit per article has it's limitations. I describe the method I used (as well as its shortcomings) with more detail in next month's (Dec) article, where I expand this to a 3-player solution. I didn't describe it in detail here since:

1) People interested in the exact solutions probably have figured it out themselves
2) Most people probably don't care enough about the differences to hear it all spelled out

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I'd like to mention that I think it is a very good illustration of that.

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And I thank you for that... [img]/images/graemlins/grin.gif[/img]

[droidboy]

I wrote:

There appears to be a bug in the basic (cash game) solution. It doesn't agree with my solution, or the sample case which eastbay posted a few weeks ago.

I went back and took a closer look at Streib's solution for non-mixed strategies, and the game theory optimal jam/fold solution, and part of the discrpency has to do with the fact that some key hands (63s, 53s, 43s) fall into and out of playability. Streib chose the higher stack sizes to define playability. His solution is correct for small stack sizes, but slowly diverges from the game theory optimal solution, At 10xBB the solution is only different by a half dozen hands or so.

- Andrew

Andrew Prock:

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It's pretty important, if you're going to present solutions to problems, that you properly state what problem you are solving. You didn't present a game theory optimal solution, so presenting it as such is a bit confusing. As far as how close the solutions are to the game theory optimal one, they look like they are off by quite a bit, especially for small stacks.

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I agree that honesty is the best policy, although I think we can cut Streib some slack given that he was publishing in a magazine, not a scholarly journal.

In the same vein, I would similarly suggest that anyone comparing their solution to his should fully explain how they arrived at their solution and why they believe it to be correct.

I've seen a number of solutions that claim to be optimal, but they don't all agree. It seems to be time for a public discussion of methods of solution so that the peer-review process can take place.

I'm more than happy to talk about how I arrived at my (very good) approximate solution.

For those worried about losing EV, don't. The willfully ignorant will remain blissfully so.

[droidboy]

[ QUOTE ]

I've seen a number of solutions that claim to be optimal, but they don't all agree. It seems to be time for a public discussion of methods of solution so that the peer-review process can take place.

I'm more than happy to talk about how I arrived at my (very good) approximate solution.

For those worried about losing EV, don't. The willfully ignorant will remain blissfully so.

[/ QUOTE ]

I got my solution by using ficticious play (as did Streib). I checked my solution against one that was constructed independently using the same method and they agreed. My solution agrees with the sample solution posted by eastbay, who used the simplex method to solve the problem directly. If I remember correctly, both methods produce the same optimal solution. The simplex method produces it directly, whereas ficticious play slowly converges to the solution.

Streib used ficticious play, but didn't allow for mixed strategies, which meant that his final solutions probably oscillated around the optimal solution, but never converged. My guess is that he just picked one of the solutions when it started to oscillate.

I certainly didn't mean to impune Streib's honesty. I was just looking for clarity in my heavy handed manner. And to be fair, the main point of the article isn't the solution per se, but how deviating from the solution affects your EV.

In truth, because it's the solution to a toy game, it's not vital that it be 100% correct, because it doesn't map directly to true play.

- Andrew

www.pokerstove.com