CP2-7 decisions

[MarkGritter]

[ QUOTE ]
(With 2h9hQhKhAh 2s3s4s6c8c 6sKcAc--- no diamonds--- the flush is about +0.55 and AA/KK is +0.40. With 2h9hQhKhAh 2s3d4s6c8d 6dKcAd, a more even distribution of suits, the flush is +0.54 and the AA/KK split is closer, about +0.44. If we make the 3 and the 8 hearts, the AA/KK is about +0.33.)

So Mark, do you mean if no diamonds there is more chance they will play a lower flush on the back and our flush becomes stronger?

[/ QUOTE ]

Well... I wondered if that had a noticeable effect. It looks like it doesn't change the value of the flush much, it is always about +0.55 points and always the best option (in the variations I tried.) Perhaps if it were a weaker flush there might be some impact.

But the value of splitting AA in front and KK in back does vary, probably because your opponent is more likely to make a flush if one suit is especially live.

[MarkGritter]

Well, Badugi (as usual) guessed what I was up to. (Next time I'll have to post a bunch of utterly straightforward hands to third-level him.)

The examples I gave all have at least two options within 1/10th of a point. (Each was evaluated against a bit more than 4000 relevant hands, so the numbers probably aren't accurate to 3 places but most likely are to two.) I have generally left out options which merely switched kickers around in inferior ways.

#1: 2233555668JQA (vs 4380 sample hands):

-1.86986 2d3c5d5h6c 2s3s5s6h8c JdQcAd
-1.88813 5d5h5s6c6h 2d3c8cJdQc 2s3sAd

55533 28JQA 662 comes in a bit worse, at -1.97, but still close. I found the choice of A23 in front interesting, but it does strengthen the Q-high middle slightly. The similar alternatives are actually very close, well within the margin of error:

-1.89566 2d2s5d5h5s 3c6c8cJdQc 3s6hAd
-1.89361 3c3s5d5h5s 2d6c8cJdQc 2s6hAd

This hand had a surprisingly large number of undominated alternatives.

#2: 4568JK[img]/images/graemlins/heart.gif[/img] 23899JA (4434 samples)

karpov got the best option correct, but playing the flush is quite close, with either 99A or 9JA in front.

-1.14118 6h9c9sJdJh 2d3d4h5h8h 8sKhAc
-1.17163 5h6h8hJhKh 2d3d4h8s9c 9sJdAc
-1.18606 5h6h8hJhKh 2d3d4h8sJd 9c9sAc

#3: 344579TTJJQKA (4331 samples)

The best option here is actually the surprising JJ/TT split. Playing the straight doesn't look quite as good but is still within 1/10th of a point.

-1.5366 4hJcJdQcKc 3s4s5c7h9d TdThAs
-1.55553 4hTdThJcJd 3s4s5c7h9d QcKcAs
-1.60125 TdJcQcKcAs 3s5c7h9dTh 4h4sJd

The straight + 9-low seems significantly worse.

-1.81413 TdJcQcKcAs 3s4h5c7h9d 4sThJd

#4: 22445678TTJQK (4444 samples)

Another surprise, playing an 8 in the middle may be the best play, though both 2461Badugi and karpov identified the best alternative:

-1.85329 2dTdTsJsKh 2h5c6c7s8c 4h4sQc
-1.88726 2d4h8cTdTs 2h4s5c6c7s JsQcKh

Playing the straight is awful:

-2.52048 4h5c6c7s8c 2d4sJsQcKh 2hTdTs

#5: 3569J[img]/images/graemlins/diamond.gif[/img] 35789TJQ (4522 hands)

Another nonobvious split two pair is a strong play here, though the flush/9 low is competitive:

-1.86577 3d5dTcJdJh 3h5s6d7h8s 9d9sQh
-1.90801 3d5d6d9dJd 3h5s7h8s9s TcJhQh

Playing the straight in back is a bit worse as the best play involves abandoning the front with J-high:

-2.02875 8s9dTcJdQh 3d5d6d7h9s 3h5sJh

Going for the 9-high straight instead is pretty bad:

-2.22247 5d6d7h8s9d 3d5s9sTcQh 3hJdJh

[2461Badugi]

I'm obviously overvaluing pairs in the front, though jacks up being better than splitting the two pairs in #2 is still surprising.

[MarkGritter]

[ QUOTE ]
I'm obviously overvaluing pairs in the front, though jacks up being better than splitting the two pairs in #2 is still surprising.

[/ QUOTE ]

I should have included that as an alternative, it's actually pretty close to the other options.

Here's the complete list of non-dominated options for that one:

-2.60442 6h8h8s9c9s 2d3d4h5hJd JhKhAc
-2.47903 8h8s9c9sAc 2d3d4h5hKh 6hJdJh
-2.424 6h8h8s9c9s 2d3d4h5hKh JdJhAc
-1.80469 4h5h6h8hKh 2d3d8s9c9s JdJhAc
-1.80356 9cJdJhKhAc 2d3d4h5h9s 6h8h8s
-1.70862 6h8h8sJdJh 2d3d4h5h9c 9sKhAc
-1.64885 4h5h6h8hKh 2d3d8s9cAc 9sJdJh
-1.45377 9c9sJdJhKh 2d3d4h5h8h 6h8sAc
-1.23207 8hJdJhKhAc 2d3d4h5h8s 6h9c9s
-1.22801 6hJdJhKhAc 2d3d4h5h8h 8s9c9s
-1.21065 6h8hJdJhAc 2d3d4h5h8s 9c9sKh
-1.19689 6h8hJdJhKh 2d3d4h5h8s 9c9sAc
-1.18606 5h6h8hJhKh 2d3d4h8sJd 9c9sAc
-1.17163 5h6h8hJhKh 2d3d4h8s9c 9sJdAc
-1.15562 8h9c9sJdJh 2d3d4h5h8s 6hKhAc
-1.14118 6h9c9sJdJh 2d3d4h5h8h 8sKhAc

[karpov]

Hi Mark, what a fantastic job you are doing. I play chinese like 5 days a week, $100 the point or higher. So your posts have great value for me.

[karpov]

[img]/images/graemlins/wink.gif[/img]