Median Best Holdem Starting Hand

[PairTheBoard]

Yes, of course you are right. But isn't a fundamental factor for whether your hand will show a profit a consideration of whether it is likely to be the best hand at the moment?

PairTheBoard

[Ed Miller]

Yes, of course you are right. But isn't a fundamental factor for whether your hand will show a profit a consideration of whether it is likely to be the best hand at the moment?

No, not really.

[PairTheBoard]

I disagree.

PairTheBoard

[bugstud]

[ QUOTE ]
By golly I think your on it Aisthesis. I think looking at the whole 1326 possible hands is the way to go since all are equally likely.



[/ QUOTE ]

Not all hands are equally likely, another nice little wrench in the problem. AKs happens less frequently than AKs, etc etc. I honestly doubt this information is as practical as you had hoped, I tend to side wth Ed on this one.

[J.A.Sucker]

You are obviously wrong. There are many hands that are "money favorites" even though they will win infrequently. This is the whole point of implied odds and reverse implied odds. I play hands that will not be the best the vast majority of the time, but that will win a lot more than a mediocre hand when it comes in. A hand that is "better than average" but a huge money dog is ATo in hold em. Pocket pairs aren't likely to be the best hand (doubly so once you take into the flop) against a field of multiple players, but you can easily release it if you miss your set while punishing them when you hit your set.

Also, which is the better hand in this situation:

As2s or KdKc, if the board is 4s5s8h? KK is in the lead, but the A2 is a favorite.

Also, your point about tournaments is also incorrect, since you neglect the blind money that's in the pot.

If you're playing headsup limit hold em, there are some players whom I will play every hand on the button against (in fact, most players that I'll play headsup will fit into this category). I will save more than enough bets when I'm not winning while extracting extra bets when I do win. Plus, there's the fact that the blind money is laying me a price. Thus, having a hand that's above or below the median is pointless.

Perhaps the best example of this comes from NL holdem. If you and your opponent are both playing deep stacks and you have a player in front of you willing to commit his entire stack on the flop with TPTK or any overpair, you could play a ton of hands, looking to outflop him and get the money in when he's in deep kimchee.

You should spend your time thinking about other things, and let Noted Poker Authority Ed Miller finish his book!

[PairTheBoard]

No. That's the beauty of Aisthesis's approach. He's looking at all 52c2 = 52*51/2 = 1326 possible starting hands - each of which IS equally likely. Then when it comes time to look at a hand ranked say 110, he counts all combinations of cards that make up the top ranked hands in the Skalansky Hand Ranking system. His method is simple, sound, and I think gives a pretty accurate result.

As far as practicality I think this is like a lot of innovations. Until the knowledge is available people can't think of much use for it. But once the information is available and you have it right in front of you, people start getting ideas.

Look, there's been all sorts of computer generated results for how a hand fares going to showdown against 1,2,3,...9 random hands. How practical is that information? When does that actually happen? Yet people still LOOK at that information because it gives them a better idea of how a hand is likely to perform in actual Realistic situations. It sheds LIGHT on things. It's part of Poker Theory - which is the topic of this Forum.

Having an idea how your hand compares to the best hand it is likely to face depending on the remaining players yet to act seems like something poker players would be interested in. But like I said before, there is natural resistance to any new idea.

PairTheBoard

[Aisthesis]

I think exactly the kind of situation you're talking about is where this consideration is most relevant. Basically, you're sufficiently shortstacked in a tournament situation that you're not going to be able to play the hand out, so you're all-in or fold.

Just to get the further consideration started, let's assume the following situation: The blinds have escalated to 100/200 with antes of 25(I like Cloutier's suggestion of viewing the ante stage as a time to move, since the antes really do noticeably increase total pot-size at this point).

So, the first question is: At what stack-size "x" (expressed as number of big blinds in your stack) is it enough for the all-in to have a 50% probability of having the best hand? With a larger stack, you'll presumably want the probability of having the best hand to be higher.

For simplicity's sake, it's probably also best to assume that it's folded to you in the given position. UTG, then, you're automatically talking about the ranking for 9-players, and it goes down from there. One will also need to assume that the "bunching factor" is irrelevant if it's folded to you in LP or in SB.

The number of callers expected is also going to be a relevant factor in choosing the hand-ranking system. But I think as first assumption, 1 caller ought to work and seems fairly typical--at least if my rough guess as to stack-size is accurate.

Then there's the further question of the probability that the all-in will fold the remainder of the field. Actually, here, the assumption made in the discussion leading to the Sklansky-Karlsson rankings seems like a good start: Just assume that only hands superior to yours will call (I think that was the way it was done in the relevant article).

I'm not sure exactly how to do this, but with the given assumptions (which seem fairly reasonable), one can assign a 50% probability to the remainder of the field folding. Then, you have to figure out what the equity is on your "median hand" vs. the superior hands. I think it should be possible to come up with an actual maximum stack-size for which it would be the best play to go all-in with the given hand (although this stack-size may vary from one position to the next).

While these assumptions restrict the scope of the question a little more than necessary (e.g., how about if you have callers before you?), I think working through the stack-size issue under these restrictive assumption would be the next step in the analysis.

[Aisthesis]

I think the whole idea is only relevant in cases where you're basically playing the hand all or nothing pre-flop. As soon as you are capable of betting the hand all the way through, everything changes completely and can't be capture in this type of model.

But I think there are plenty of tournament situations (at least I run into them more often than I'd like) where my stack just isn't going to allow me even to bet the flop adequately. Those are the ones where this idea has a great deal of relevance imo.

[PairTheBoard]

Yes. One of the things I had in mind was the recent Sklansky CardPlayer article in which he anlayzed going all in heads up. The idea was that if your stack size was small enough in relation to the BB then it could be computed to be a positive expectation play even if your opponent could see your cards and made perfect decisions when calling you. I believe Sklansky assigned a "Power Number" for each hand which determined the over-under for your Stack/Blind ratio.

I don't think such a thing has been done for when there are several players left to act behind you. While knowing the Median Best Hand for the players to act behind you may not solve the problem It may be that combining the Median Best Hand knowledge with the Sklansky Power Number concept might at least give you a good feel for the situation you're in. It may also be a jumping off point for an explicit analysis as you indicate Aisthesis.

Certainly food for thought for those interested in Poker Theory imo.

PairTheBoard

[Ed Miller]

You should spend your time thinking about other things, and let Noted Poker Authority Ed Miller finish his book!

Just sent the manuscript to Mason ten minutes ago. [img]/images/graemlins/smile.gif[/img] There will still be a few odds and ends to clean up, no doubt, but essentially we have a book. [img]/images/graemlins/smile.gif[/img]