CP2-7 experiment update
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.)
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