The ace killers

[tardigrade]

I've been running some stats from a new program I've written to calculate preflop odds heads-up. Essentially I have a matrix of all possible starting hands and for each valid combination, the number of all possible community card combos that the row wins, the column wins or they tie.

First, I'm wondering if there are some independent stats that I can verify my results against. The results seem reasonable, but I'd like to get some confirmation from an independent source before I put them to use to make sure I don't have some subtle errors in there.

Secondarily, here are some interesting preliminary results:

Heads-up, all-in versus A[img]/images/graemlins/spade.gif[/img]A[img]/images/graemlins/diamond.gif[/img], the best hand to have, of course, is the remaining AA. Interestingly, the second best hand seems to be either 6[img]/images/graemlins/heart.gif[/img]5[img]/images/graemlins/heart.gif[/img] or 6[img]/images/graemlins/club.gif[/img]5[img]/images/graemlins/club.gif[/img]. I'm guessing this is because of a) the maximum winning flush and straight combos, b) none of the straights contribute any cards to a higher straight for the AA, c) half of AA's straights (A2345) are stolen by the 6.

The worst possible hand seems to be either K[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/diamond.gif[/img] or K[img]/images/graemlins/diamond.gif[/img]2[img]/images/graemlins/spade.gif[/img]. I'm guessing this is because a) neither hand can win with a flush, b) any straight the K participates in at best splits with the ace and often loses, c) when the K2 gets two pair, any pair on the board (except for kings or twos) counterfeits the hand and the aces win, d) if either the K or 2 pairs up, the aces are one card closer to a straight that would only make a 4-straight for the K2.

Has anyone seen any similar stats?

[Nottom]

56s thing is pretty well known.

I always thought the worst hand vs AA was A9o with the 9 suited with the A.

http://twodimes.net/h/?z=147098
pokenum -h ac ad - kc 2d
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Ad 1538197 89.83 165043 9.64 9064 0.53 0.901
Kc 2d 165043 9.64 1538197 89.83 9064 0.53 0.099


http://twodimes.net/h/?z=424554
pokenum -h ac ad - ah 9d
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Ad 1598785 93.37 89199 5.21 24320 1.42 0.941
9d Ah 89199 5.21 1598785 93.37 24320 1.42 0.059

[tardigrade]

Thanks for the great links! I should be able to use that utility to run through and check the generated tables so I can correct any problems with them.

[hummusx]

[ QUOTE ]
b) any straight the K participates in at best splits with the ace and often loses,

[/ QUOTE ]

This isn't exactly true, right? QJT9x or 6543x would both make straights for K2 while doing nothing for AA. Or did I miss something?

[tardigrade]

[ QUOTE ]
This isn't exactly true, right? QJT9x or 6543x would both make straights for K2 while doing nothing for AA.

[/ QUOTE ]

You're right. Although the K doesn't participate in the 6543x one, you're right about the QJT9x one. I really must give up this crack habit.

The K2 seems to be incorrect anyways. I think I have a problem in my EV scanner, since the A9 Nottom mentioned is quite a lot worse.

[tardigrade]

After a fix to my EV scanner, I can now match the result of A9 with the 9 of the same suit as one of the aces in AA as being the absolute dog-worst hand to have against a pair of aces.

The K2 with matching suits does still seem to have the dubious distinction of being the worst hand not containing an ace.

I think you can see part of what was wrong with the program loop.... [img]/images/graemlins/tongue.gif[/img]

[Nottom]

Happy to help.