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Old 06-26-2007, 01:28 AM
Sweet Sweet is offline
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Default Re: Distribution of CP2-7 Hand Values

[ QUOTE ]
I put up some new data, from a 10M-hand sample. (These files are pretty large, 236KB for the backs, 356KB for the middles, and 28KB for the fronts.)

http://www.lowballgurus.com/cp27/10M-backs-2.txt
http://www.lowballgurus.com/cp27/10M-middles-2.txt
http://www.lowballgurus.com/cp27/10M-fronts-2.txt

http://www.lowballgurus.com/cp27/10M-backs-3.txt
http://www.lowballgurus.com/cp27/10M-middles-3.txt
http://www.lowballgurus.com/cp27/10M-fronts-3.txt

I put up the distributions from two different iterations over the same set of hands, to illustrate how the maximally exploitive strategy switches strength between the front and the back/middle. There are about 2% fewer pairs in front in "3" than in "2".

[/ QUOTE ]

So, is this just oscillation, or is the "3" set better than the "2" set?

At this point, do you think that this data is an accurate reflection of the percentiles of hands we would see in the front/middle/back in people that play well (or, among well-played hands in some sense)?

I guess there's an overall question of, "what should we conclude from this awesome data"? I love your algorithm... it would be interesting to see if this method applied to traditional CP would yield the same results as Smolen. Someone posted the 10th, 20th, ... percentiles for the front hands in CP (from Smolen?). Would this algorithm produce the same results? Would it be easy to run a 100k trial as all high?

In any case, thanks for the excellent work.
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  #22  
Old 06-26-2007, 02:15 AM
MarkGritter MarkGritter is offline
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Join Date: Jan 2005
Location: Eagan, MN
Posts: 1,376
Default Re: Distribution of CP2-7 Hand Values

[ QUOTE ]

So, is this just oscillation, or is the "3" set better than the "2" set?


[/ QUOTE ]

It is oscillation. Another couple iterations would provide another set "4" that looked pretty much like "2". (Iteration "1" looks a lot like "3".)

[ QUOTE ]

At this point, do you think that this data is an accurate reflection of the percentiles of hands we would see in the front/middle/back in people that play well (or, among well-played hands in some sense)?


[/ QUOTE ]

I think it is an accurate representation of a strong strategy; if there were a way to do significantly better, my algorithm would find it. And I'm using enough hands that sample error is fairly small.

I did a post in my LJ--- locked so I can't just link to it--- where I tried to calculate the standard error. It's about +/- 0.012 of a point per hand. There are plenty of hands where the best two arrangements are within this error, but most oscillating hands are not.

I don't know how well humans are actually playing the game. [img]/images/graemlins/smile.gif[/img]

The number of hands that fall into an oscillating pattern has fallen for each larger size of experiment I ran, but not by an order of magnitude, so I think the "oscillating" (exploitive) behavior will always be present. The value of the exploitive play did drop significantly, though.

[ QUOTE ]

I guess there's an overall question of, "what should we conclude from this awesome data"? I love your algorithm... it would be interesting to see if this method applied to traditional CP would yield the same results as Smolen. Someone posted the 10th, 20th, ... percentiles for the front hands in CP (from Smolen?). Would this algorithm produce the same results? Would it be easy to run a 100k trial as all high?


[/ QUOTE ]

I actually started to run such an experiment with 1M-hand samples. I haven't talked much about it in public yet because I'm having such a hard time believing the results that I think it's more likely I made an error in the code.

Briefly, what I saw is that, where CP2-7 will have perhaps 4% of hands oscillating for that size sample, nearly 50% of the CP high hands changed their best setting to maximally exploit the opponents' strategy! Not only that, but the effect of this exploitive play was orders of magnitude larger, as much as 20% of a point.

The changes were generally shifts of strength between the front and the other two hands, like in CP2-7. Strategy "A" would put a lot of unpaired hands in front, then strategy "B" would adjust to that by making weaker fronts and middles in order to put a pair in front.

One thing I hadn't anticipated but which I find easier to believe is that there are generally more possible undominated arrangements of a hand in CP high than in CP-27. The reason for this is kickers--- in CP high you can switch a kicker from front to middle or back to middle and create a slightly different version of the hand which is stronger in some parts and weaker in others. In CP2-7 you can only swap kickers between front and back this way; moving them into the middle will usually make a hand that is either strictly better or strictly worse.
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