Classical Chinese 2-7 Choice

[karpov]

One kind of hand that comes very often in Chinese Poker 2-7 is this type of hand:

JJJTTAAK22689
and you have to decide between:

A: JJJTT K9862 AA2
B: JJJTT 22986 AAK

Which one do you think is stronger? What about if we replace 22 for 33 or 44 or 55?

[MarkGritter]

How about JJJ22 689TK AAT? That provides the same strength in back, a pair-free middle, and a front nearly as strong as AAK (especially since you hold two T's and three J's.)

[MarkGritter]

I ran the calculator; the following three options are pretty close.

Sample error might switch things, these numbers are _not_ accurate to six figures! I would only trust about two digits (+/- 0.03 I think is a reasonable estimate), each hand has about 12K-13K samples.

JJJTT 22689 AAK: +1.01977
JJJTT 2689K AA2: +1.02526
JJJ22 689TK AAT: +1.08465

Here are a couple similar hands:

QQQTT 33689 AAK: +1.23931
QQQTT 3689K AA3: +1.26218
QQQ33 689TK AAT: +1.33393

TTT99 44678 AAK: +0.720626
TTT99 4678K AA4: +0.851657
TTT44 6789K AA9: +0.888801

[karpov]

Since I created this hand I overlooked that possibility, let me correct it:

JJJ3322689AAK: This one is more interesting. The main thing is to find out what is more important, the kicker or no pair in the middle.

[MarkGritter]

It's very close (possibly within the range of error of this experiment), but I think on balance you should prefer to play an upaired hand in the middle.

22JJJ 3689K 3AA: +1.06765
33JJJ 2689K 2AA: +1.06593
33JJJ 22689 KAA: +1.02294

[karpov]

No wonder is such a difficult decision for everybody. I asked many good players about this play and nobody was sure how to play it. I wonder if you have to use psychology to set this hand.