Hi card wins x% of time?

[RJT]

I find helpful the following odds from Herrington On Hold ‘em. It is for 2 players pre-flop.

Higher pair vs. lower pair : 4.5:1
Pair vs. 2 lower cards: 55:45 %
Pair vs. 2 lower cards: 5:1
Pair vs. higher and lower card: 5:2
2 higher cards vs. 2 lower cards: 5:3

Another statistic that I think might be useful, especially in a tournament, is: What are the chances ( % of times) that high card from either player’s pocket wins. That is, neither pairs his own cards or better? (The board can do what is wants, pair, trips, etc., so long as the outcome is determined by the high card in pocket.)

(The easiest way to find this, I would think would be from one of the simulated 1,000,000, or so, hands generators. I am sure it could be figured mathematically. But an answer from a simulator is sufficient for me. I tried on my own to find it and could not)

We can also include as a separate statistic if the board ends up playing and pot splits.


Thanks.

p.s These stats would only be relevant if the %(the answer) becomes of any worth. If answer is too low to matter, than of course, who cares?

[RJT]

The odds Harrington gives btw are for the hands to win if played to the end.

I think I made the previous post more limiting than necessary. What I am actually looking for is an expansion of the odds of winning with 2 high vs 2 lower (no pairs in either pocket - forgot to write that in first post, but I think it was understood).

What are the odds of winning if one has any of the combinations of having one and/or 2 higher cards; i.e, 2 higher, one higher one lowest, one highest with other pocket card the 3rd highest of the 4?

[captZEEbo1]

[ QUOTE ]
The odds Harrington gives btw are for the hands to win if played to the end.

I think I made the previous post more limiting than necessary. What I am actually looking for is an expansion of the odds of winning with 2 high vs 2 lower (no pairs in either pocket - forgot to write that in first post, but I think it was understood).

What are the odds of winning if one has any of the combinations of having one and/or 2 higher cards; i.e, 2 higher, one higher one lowest, one highest with other pocket card the 3rd highest of the 4?

[/ QUOTE ]

It depends on if it's suited or not, of course (adjust about 3%) and connectedness.

I highly suggest you go to http://www.twodimes.net and figure some of this stuff out.

Some interesting ones that many people probably don't realize:
A2o vs 98s (51.5%:48.5%) or even A2o vs 43s (54%.5: 45.5%) which is why I find people calling allins with A2o just baffling...

In terms of the rank, in general I think if it's:

12 vs 34 it's 60:40.
13 vs 24 it's about 62:38
14 vs 23 it's about 58:42
but if the 23 are connectors, then it's about 54:46
if the 23 are 1 gappers, it's about 55:45
if the 23 are 2 gappers, it's about 56:44

I hope that made sense.... let's use this example:

14 vs 23 with a 1 gapper, it's about 55:45
I mean, if I have K4s vs 97s (different suit), then odds of K4s winning is about 55%.

So just make roughly appropriate changes for connectedness and suitedness, and experiment a lot using twodimes.net. Also pokerstove is a good program I've heard that let's you calculate hands vs a RANGE of possible hands they could have. Let's say you think they'll call with AK, AQ or any pocket pair, you can figure out how good 88 is vs that range of calling hands on average.