Yet More CP2-7 Hands
 

How would you set the following in 2 point/4 point Chinese Poker with 2-7 in the middle?

a) 2444789JJJQKK no flushes
b) 223335667TJJK
c) 45A[img]/images/graemlins/club.gif[/img] 8A[img]/images/graemlins/diamond.gif[/img] 2345A[img]/images/graemlins/heart.gif[/img] 25Q[img]/images/graemlins/spade.gif[/img]
d) 22467778TTQQA
e) 7TA[img]/images/graemlins/club.gif[/img] 46[img]/images/graemlins/diamond.gif[/img] 578[img]/images/graemlins/heart.gif[/img] 4678T[img]/images/graemlins/spade.gif[/img]

(Today's hands have a dual theme. All of them contain trips, obviously. They are also hands which a simple heuristic I'm exploring gets wrong.)

Re: Yet More CP2-7 Hands
 

a) I'd favor JJJKK Q9872 444 over JJJ44 98742 KKQ. First analysis leaves them about on par in my book, but then my lack of As makes the jump from KKQ to 444 bigger than usual (more likely for opponent to have AA up top), while my glut of Js makes the jump from Q9872 to 98742 smaller than usual (less likely my opponent has J hi in the middle).

b) I'd favor JJT72 76532 33K slightly over JJ332 76532 KT6 over 333JJ T7652 K62. Again, I'd call it very close upon first analysis, but the fact that we're missing As makes A hi up top seem a little more likely than usual, which is why I'd split JJ33 (very sketchy on that one), and the fact that we're missing 5 ranks higher than 3 leads me to believe that there is a high chance we'll run into a full house bigger than 333JJ, so I devalued that.

c) I'd favor straight flush Q8542 AA5 over AAA44 Q8322 555, because I think that AAA44 and the baby straight flush are essentially identical, and only 333 fits between AA5 and 555 given my holding, while tons of hands fit between Q8542 and Q8322.

d) 777TT with either (QQA 86422) or (QQ2 A8642). What's more likely, running into the other two queens on top or running into a worse A hi in the middle? It sure looks like a toss up to me.

e) 77788 A6544 TT6


Those are just my guesses. I look forward to seeing what your program suggests.

Re: Yet More CP2-7 Hands
 

I'm used to the CP17 w/ badugi but i'll give this a shot.

a) JJJKK 2789Q 444
b) 33362 2567T JJK
c) A2345h 2458Q AA5
d) TT772 24678 QQA
e) 77788 4456A TT6

Re: Yet More CP2-7 Hands
 

(a) JJJKK 2789Q 444 is correct. This hand is kinda fun because there are exactly four undominated alternatives:

0.557949 JcJdJsKcKs 2c4d7c8d9h 4h4sQh
1.26697 4d4h4sKcKs 2c7c8d9hQh JcJdJs
1.38895 4d4hJcJdJs 2c4s7c8d9h QhKcKs
1.74266 JcJdJsKcKs 2c7c8d9hQh 4d4h4s

I agree with your analysis. Having three of the fours also reduces the number of strong middles we'll see. I hadn't thought about the jacks but you're right there too.

(b) 333JJ 2567T 26K is best here, JJ/23567/33 is somewhat worse.

-1.55387 2c3c3hJhJs 2d3s5d6h7c 6sTdKc
-1.43147 2c3c3h3s6h 2d5d6s7cTd JhJsKc
-1.39131 3c3h3s6h6s 2c5d7cTdKc 2dJhJs
-1.38871 2c2d3c3h3s 5d6h7cTdKc 6sJhJs
-1.36294 2c6hTdJhJs 2d3c5d6s7c 3h3sKc
-1.35682 2c6hJhJsKc 2d3c5d6s7c 3h3sTd
-1.35505 2cTdJhJsKc 2d3c5d6h7c 3h3s6s
-1.35465 6hTdJhJsKc 2c3c5d6s7c 2d3h3s
-1.143 3c3h3sJhJs 2c5d6h7cTd 2d6sKc

It's not a good hand. The absence of the aces which you point out actually reduces chances of winning with 33 or JJ in front--- he's quite likely to have two aces, and they are quite likely to find their way up front. The trip threes in our hand improve the strength of the T7 in the middle considerably; I think this is what lead your analysis astray (and it's what fouled up the heuristic I was experimenting with as well.)

(c) The straight flush in back is a clear winner.

1.3298 4c4hAcAdAh 2h2s3h8dQs 5c5h5s
1.35538 2h3h4h5hAh 2s4c5c5s8d QsAcAd
1.37529 5c5hAcAdAh 2h3h4c5s8d 2s4hQs
2.0446 2h3h4h5hAh 2s4c5c8dQs 5sAcAd

Simple heuristics generally prefer 4c4hAcAdAh 2h2s3h8dQs 5c5h5s, but the opponent having 444, 222, or AA in front are impossible. So going with AA5 in front instead of 555 only loses to 333 (and we even hold one of the threes.) So it's not enough of an advantage to pair up the middle, though the Q is still going to mostly lose.

I would think the 8 is extra-strong here, though--- even though we don't see any 7s, it will be harder to make a seven in the middle with 22344555 gone.

(d) The surprising 277TT 24678 QQA is best.

-0.804978 7c7d7hTcTd 2c2d4h6s8s QhQsAc
-0.765026 7c7d7hTcTd 2c4h6s8sAc 2dQhQs
-0.747804 7c7d7hQhQs 2c4h6s8sTc 2dTdAc
-0.745591 2c2d7c7d7h 4h6s8sTcAc TdQhQs
-0.73437 7c7dTcTdAc 2c4h6s7h8s 2dQhQs
-0.608787 2c7c7dTcTd 2d4h6s7h8s QhQsAc

87642's strength is somewhat improved by holding two extra 7's and another one of the deuces. It looks like that's enough to favor putting strength in the middle rather than in back. (Though note it is still a losing hand.)

(e) The weak flush is best:

-1.90312 7c7h7sTcTs 4d4s5h6dAc 6s8h8s 127286
-1.79204 7c7h7s8h8s 4d4s5h6d6s TcTsAc 127286
-1.74248 7c7h7s8h8s 4d4s5h6dAc 6sTcTs 127286
-1.74164 6d6s7c7h7s 4d4s5h8hAc 8sTcTs 127286
-1.57014 4s6s7s8sTs 4d5h6d8hTc 7c7hAc 127286

4456677788 is a lot of low cards to kill--- our opponent isn't going to be able to make many 87's. T8654 would normally be a 43rd percentile hand, but it is about 50th against hands missing these cards. Either way it's much better than putting a pair in the middle, even though the boats are 64th percentile while the flush is 33rd percentile.

Re: Yet More CP2-7 Hands
 

3 out of 5 and 1 hand was very close. I'll take it ! Keep it coming Mark, I'm enjoying it.

Re: Yet More CP2-7 Hands
 

Mark, any chance you can give us the median 2-7 and 3 card high hand in your program ? If you have it, thanks in advance.

Re: Yet More CP2-7 Hands
 

[ QUOTE ]
Mark, any chance you can give us the median 2-7 and 3 card high hand in your program ? If you have it, thanks in advance.

[/ QUOTE ]

Median hands:
Back: A6542-flush
Middle: 98754 low
Front: QQJ

There is more information in this thread:

http://forumserver.twoplustwo.com/showfl...35#Post10849035

Re: Yet More CP2-7 Hands
 

[ QUOTE ]

(d) The surprising 277TT 24678 QQA is best.


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Wow! I didn't even notice that possibility. Nice hand.

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(e) The weak flush is best:

-1.90312 7c7h7sTcTs 4d4s5h6dAc 6s8h8s 127286
-1.79204 7c7h7s8h8s 4d4s5h6d6s TcTsAc 127286
-1.74248 7c7h7s8h8s 4d4s5h6dAc 6sTcTs 127286
-1.74164 6d6s7c7h7s 4d4s5h8hAc 8sTcTs 127286
-1.57014 4s6s7s8sTs 4d5h6d8hTc 7c7hAc 127286

4456677788 is a lot of low cards to kill--- our opponent isn't going to be able to make many 87's. T8654 would normally be a 43rd percentile hand, but it is about 50th against hands missing these cards. Either way it's much better than putting a pair in the middle, even though the boats are 64th percentile while the flush is 33rd percentile.


[/ QUOTE ]

Do you mean 74th percentile?

Great stuff.

Re: Yet More CP2-7 Hands
 

[ QUOTE ]

[ QUOTE ]

(e) The weak flush is best:

-1.90312 7c7h7sTcTs 4d4s5h6dAc 6s8h8s 127286
-1.79204 7c7h7s8h8s 4d4s5h6d6s TcTsAc 127286
-1.74248 7c7h7s8h8s 4d4s5h6dAc 6sTcTs 127286
-1.74164 6d6s7c7h7s 4d4s5h8hAc 8sTcTs 127286
-1.57014 4s6s7s8sTs 4d5h6d8hTc 7c7hAc 127286

4456677788 is a lot of low cards to kill--- our opponent isn't going to be able to make many 87's. T8654 would normally be a 43rd percentile hand, but it is about 50th against hands missing these cards. Either way it's much better than putting a pair in the middle, even though the boats are 64th percentile while the flush is 33rd percentile.


[/ QUOTE ]

Do you mean 74th percentile?


[/ QUOTE ]

Nope, I mean the T-high flush is stronger than only about 33% of opponent backs, after taking out the cards we hold.

Re: Yet More CP2-7 Hands
 

[ QUOTE ]
[ QUOTE ]

[ QUOTE ]

(e) The weak flush is best:

-1.90312 7c7h7sTcTs 4d4s5h6dAc 6s8h8s 127286
-1.79204 7c7h7s8h8s 4d4s5h6d6s TcTsAc 127286
-1.74248 7c7h7s8h8s 4d4s5h6dAc 6sTcTs 127286
-1.74164 6d6s7c7h7s 4d4s5h8hAc 8sTcTs 127286
-1.57014 4s6s7s8sTs 4d5h6d8hTc 7c7hAc 127286

4456677788 is a lot of low cards to kill--- our opponent isn't going to be able to make many 87's. T8654 would normally be a 43rd percentile hand, but it is about 50th against hands missing these cards. Either way it's much better than putting a pair in the middle, even though the boats are 64th percentile while the flush is 33rd percentile.


[/ QUOTE ]

Do you mean 74th percentile?


[/ QUOTE ]

Nope, I mean the T-high flush is stronger than only about 33% of opponent backs, after taking out the cards we hold.

[/ QUOTE ]

I was surprised to see the *boats* at 64% instead of 74%, is that right?