Quick question on Malmuth's article

[Malcom Reynolds]

Hey, in Malmuth's article this month, he writes,
[ QUOTE ]
I would still have the best hand on the flop, even though he holds an ace and there is an ace on board, 17 out of 35 times.

[/ QUOTE ]

But I counted 32 times:

AK = 2x4 = 8
AQ = 2x4 = 8
AA = 2c2 = 1
KK = 3c2 = 3
QQ = 4c2 = 6
JJ = 4c2 = 6

32 possible hands, 17 times ahead.

Where did I screw up?

Thanks.

[Mason Malmuth]

Hi Malcolm:

Aren't there six possible ways you can have kings: 4C2 not 3C2.

But there is an error in this section of the article. can anyone find it? (However, it doesn't affect my conclusion.)

Best wishes,
Mason

[jdl22]

[ QUOTE ]
But in addition, also notice that those times I do have the ace he is drawing very close to dead -- running deuces will win it for him and the last ace or a six will tie it. But if I have a pair less than aces they'll improve to the winning hand roughly 5 percent of the time.

[/ QUOTE ]

If you had a pair you would catch up about 8% of the time and not 5. Also, I think you are oversimplifying your case for him drawing completely dead. You are correct if you have AK but if you have AQ-A3 (not including A6 of course) he is drawing to any cards above your kicker as well as the 6 to chop. Unless you really mix it up in NL I can't see you playing your hand this way with anything less than perhaps AQs.

[andyfox]

Won't your pocket pair improve to a winner more like 8% of the time (rather than just 5%)?

[Mason Malmuth]

Hi Andy:

That's the answer. The 5 percent number is for the next card but I'm in there for two more cards. By the way, I think it's more like 11 percent than 8 percent.

best wishes,
Mason

[jdl22]

It's 8:

http://twodimes.net/h/?z=799427
pokenum -h ad 2h - 3d 3h -- ac 6s 6h
Holdem Hi: 990 enumerated boards containing 6s Ac 6h
cards win %win lose %lose tie %tie EV
Ad 2h 910 91.92 79 7.98 1 0.10 0.920
3d 3h 79 7.98 910 91.92 1 0.10 0.080

http://twodimes.net/h/?z=799437
pokenum -h ad 2h - kd kh -- ac 6s 6h
Holdem Hi: 990 enumerated boards containing 6s Ac 6h
cards win %win lose %lose tie %tie EV
Ad 2h 906 91.52 83 8.38 1 0.10 0.916
Kd Kh 83 8.38 906 91.52 1 0.10 0.084

[The Dude]

I think it's only 8% because there will be times when the AK hand fills up as well.