Exact HU probabilities

[KJ o]

Is there somewhere an exhaustive table for all the probabilities for all pairs of possible starting hands?

If I want to find out Ks 4h vs 9d 8c I can always use twodimes.net/poker, but if I want to know K4o vs 98o, I have to list all the possible combinations (7, right?), run them indivually and add the pieces up, taking into consideration that not all of the seven combinations are as likely to occur.

What I look for is the exhaustive table featunring all the 169*168/2 + 169 = 14365 possible combinations of starting hands, and for each I want P(win) and P(tie), not just EV. This is obviously a fairly large table, but hey, that's what computers are for, right?

[Cooker]

Actually, if you want to know K4o vs. 98o you can just pick any combo you like to do one run and take that as the answer. For instance, you should get the same answer for Kc4d vs. 9h8s as you do for Ks4d vs. 9h8c. There will be some small differences between these and some combinations like Kc4d vs. 9c8s (because now the second hand cannot win with 2 different types of flushes), but I think these differences can be largely discounted. However, you can see for yourself exactly how much a difference of this type makes and do a weighted average for the 3 different situations, so you only need 3 runs vs. several runs if you try all the combinations of K4o vs. 98o.

[ChromePony]

There was a post about this a while ago and someone came up with a 169x169 spreadsheet of them which I have. If you PM me your email i can send it.

[KJ o]

Well, I wanted the exact values, so I do care about the difference between Ks4h vs 9s8d and Ks4h vs 9c8h, small as it may be.

Also, are there not 7 cases, and not 3 as you state?

[Popinjay]

PokerStove is what you seek.

[KJ o]

[ QUOTE ]
PokerStove is what you seek.

[/ QUOTE ]

No, not unless you talk about somehting else than the pokerstove.exe.

What I want is a complete table giving me the win% and tie% for pairs of starting hands where the starting hands are one of the 169 (e.g. K4o), not one of the 52*51/2 (e.g. Ks4h).

An earlier poster said he had a fiel, and I have PM'ed him, but can't check my mail right now. Hopefully this is moot by now.

[KJ o]

Ok, now I bothered to look at the program just a tiny bit more. Sorry for being as dense as the average poster...

Anyway, while it lets me calculate hands such as K4o vs 98o, what I really want is the API to it, so that I can write some code that uses the evaluation engine to compute the 15000 pairs of hands. I'm not going to do that by hand, for obvious reasons...

[astroglide]

i believe it has a command line interface, just generate a script. all of the hand vs hand for every number of players is already done for you though and the heads up stuff is intuitive to know who's ahead.

[Cooker]

Actually, I wrote that quickly, but I believe that there are only 4 (not sure why I said 3) relevant cases (i.e. four cases that will have slightly different outcomes). However, I guess that is moot now that you have found that the softwware will do what you want anyway.

Just for interest, I see the only cases as follows: all 4 cards have a different suit, the K from one hand is the same suit as either the 8 or 9 with the 4 different from all 3, the 4 from one hand is the same as the 8 or 9 and the K is different from all three, and finally, the K is the same as the 8 or 9 and the 4 is the same as the card that is not the same as the K. I believe that it is obvious that Kh4c vs. 9h8d will give the same result as Kh4c vs. 9d8h. If you think my reasoning is incorrect on the number of cases needed, I would appreciate you pointing out my error since I am fairly new to this and would like to straighten out my thinking. Thanks.

[KJ o]

[ QUOTE ]
Actually, I wrote that quickly, but I believe that there are only 4 (not sure why I said 3) relevant cases (i.e. four cases that will have slightly different outcomes).

[/ QUOTE ]

There are seven: Kh4c vs 9h8c, 9h8d, 9c8h, 9c8d, 9d8h, 9d8c, 9d8s. (Yes, some of these are very, very close)

[ QUOTE ]
I believe that it is obvious that Kh4c vs. 9h8d will give the same result as Kh4c vs. 9d8h.

[/ QUOTE ]

From PokerStove:
Hand 1: 54.9353 % [ 00.55 00.00 ] { Kh4c }
Hand 2: 45.0647 % [ 00.45 00.00 ] { 9d8h }
---
Hand 1: 54.9351 % [ 00.55 00.00 ] { Kh4c }
Hand 2: 45.0649 % [ 00.45 00.00 ] { 9h8d }

The difference is, I believe, 5 diamonds all larger than 8/9 and excluding hands that require the 8/9 for the straight flush. Also some straight flushes in hearts differ.

[Cooker]

[ QUOTE ]
From PokerStove:
Hand 1: 54.9353 % [ 00.55 00.00 ] { Kh4c }
Hand 2: 45.0647 % [ 00.45 00.00 ] { 9d8h }
---
Hand 1: 54.9351 % [ 00.55 00.00 ] { Kh4c }
Hand 2: 45.0649 % [ 00.45 00.00 ] { 9h8d }

The difference is, I believe, 5 diamonds all larger than 8/9 and excluding hands that require the 8/9 for the straight flush. Also some straight flushes in hearts differ.

[/ QUOTE ]

If I ever end up in a situation where I will fold if I am a 1.21903 to 1 dog but call if I am a 1.21902 to 1 dog, I will stop calling these two situations identical. Until then, I stand by my statement that there are really only 4 outcomes that need to be simulated for this match up. However, I concede that the difference between Kh4c vs. Qh5s and Kh4c vs. Qs5h might be significant enough to consider all 7 possibilities when simulating (but I doubt it will be that interesting).

[KJ o]

[ QUOTE ]
If I ever end up in a situation where I will fold if I am a 1.21903 to 1 dog but call if I am a 1.21902 to 1 dog, I will stop calling these two situations identical.

[/ QUOTE ]

Well, duh. The reason I want the exact values is that I look into simulations and algebraic solutions to specific situations where any errors are compounded. (Plus, as you noted, even though it doesn't matter in this case, it does matter in other cases and it's not reasonable to go throught them by hand and guess if each case is one that matters or not.)

Anyway, I did receive the full spreadsheet, som I'm very happy now.