CP2-7 experiment update

[MarkGritter]

So, here are the first nine iterations of my CP2-7 experiment, run with 100K hands (instead of 1K like I posted about earlier.)

(Recap: A picks a fixed arrangement for each of his 100K hands. Then B examines each of his hands and picks the arrangement that maximizes each hand's value against A's hands + strategy. Then A gets to do likewise, etc.)

Iteration/EV/number arrangements
a.1: $0.03785375 (/100000 changed)
b.1: $0.03545646 (/100000 changed)
a.2: $0.01646984 (14092/100000 changed)
b.2: $0.00252623 (16098/100000 changed)
a.3: $0.00738640 (10890/100000 changed)
b.3: $0.00140493 (9600/100000 changed)
a.4: $0.00651721 (9681/100000 changed)
b.4: $0.00069331 (8678/100000 changed)
a.5: $0.00591959 (8828/100000 changed)
b.5: $0.00013653 (8050/100000 changed)
a.6: $0.00550497 (8216/100000 changed)
b.6: $-0.00024108 (7459/100000 changed)
a.7: $0.00501711 (7555/100000 changed)
b.7: $-0.00076080 (6934/100000 changed)
a.8: $0.00471229 (7019/100000 changed)
b.8: $-0.00090690 (6437/100000 changed)
a.9: $0.00439509 (6518/100000 changed)
b.9: $-0.00123131 (6016/100000 changed)

So... we still can't tell whether a strategy for the full game include any exploitive "cycles" or not. (I.e, player A sets his hand a certain way, player B adjusts to make that choice worse, A switches back to his previous setting.) The number of cycles is trending sharply downwards, certainly, and it likely to be below 1% for the full game of 635 million hands. (Possibly 0%.) The number of cycles was about 40% at 10e4 hands, 20% at 10e5 hands, and < 6% for 10e6 hands.

What we can tell with certainty at this point that a strong CP2-7 strategy is only beatable by < 1/100th of a point, and probably much less. So as a practical point, whether the best strategy requires exploitive play (or, if you prefer, unexploitable game-theoretic play) is pretty moot.

After I run some more iterations with 100K hands I can extract what the distributions look like for each of front, middle, and back.

(Note that even a result stating that a "pure" CP2-7 strategy exists does not guarantee that there is any simple description of such a strategy--- it might be that any reasonably-sized algorithm for setting your hand is exploitable by a more complicated algorithm. But since nobody has described a CP2-7 strategy in sufficient detail for me to implement and test, I can't explore this idea.)

[quickfetus]

I wish the comp. sci stuff wasn't so over my head. Congrats on this work, it seems like you're moving the theory of the game forwards. Now, does this mean Smolens style tables are soon to follow? [img]/images/graemlins/smile.gif[/img]

[Sweet]

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After I run some more iterations with 100K hands I can extract what the distributions look like for each of front, middle, and back.


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What's the status? Love the recent threads, thx.

[MarkGritter]

The 100K-hand experiment seemed to be slowly converging so I let it run. Unfortunately this morning I discovered a couple of errors in my code, which caused it to rank a few hands incorrectly.

With some improvements in performance is now looks like I can calculate using 1 million-hand samples, which will provide better results. So I am concentrating on getting that up and running on multiple CPUs. (1 iteration of 1Mx1M hands should take about 7 CPU-days.) The recent results used the first iteration of 1M hands.

I also realized it will be possible to make my calculator available as a service through a web site, though it will take some time to get this set up correctly. (Not 100% sure I want to do this, the computation would have to be forwarded to my home machine to run.)

I haven't written the tools I would need to compile these raw hand files into summaries, but I still plan on doing so. Once I get the 1M hand computation running more smoothly I can take a look at posting the 100K hand data (with the caveat that it has some known errors.) If anyone is interested in the raw hand file, PM me and I can email it to you.