Median Best Holdem Starting Hand

[PairTheBoard]

Louie: "The median best hand information is a fairly useful number but is by no means a mechanism for deciding what to play."

That's what I was thinking Louie. Interesting that with your adjustment for value of position this approach produced starting hand requirments similiar to well recognized ones. One of my thoughts was that even if this approach produced nothing fundamentally new, sometimes looking at things from a different perspective can add new insight.

PairTheBoard

[PairTheBoard]

As far as starting hand requirments I think it's usefull just to get an idea about where you're at in relation to the likely better hands out there against you. You could tweek things by using a hand ranking system taylored for each situation, eg limping in a multiway ring game. You could just move your 44 up the list and rank it higher than AQ if you want to. Still, like Louie said, I don't see this producing any mechanical solutions in this area, just shedding some light on where you're at.

PairTheBoard

[Aisthesis]

True, but I think there are some dangers of misleading yourself if you go very far with it on starting hand selection in most situations. For one thing, once the betting has started, you're no longer dealing with random hands. For another, it's hard to factor in the classic distinction between hands that will "win lots of small pots" and those which will win the occasional big pot with only minimal losses when you hit.

Due to the continued information deficit UTG, I'm definitely still not interested even in playing AJo (and I'm pretty much on the fence as to AJs) at a full table.

However, another context to which it might well imo become more applicable is shorthanded, where it could give you a much better idea of where you're likely at on hands where you might consider trying a blind-steal and where huge hands after the flop are likely to have less leverage for winning huge pots.

[PairTheBoard]

I think you're looking at the Median Hand Filip - which is not without merit itself. But what I'm looking for is the Median BEST Hand. In other words, deal out say 10 hands. Pick out the BEST of the 10 hands. The Median Best Hand is that hand such that there is a 50% chance the Actual Best Hand ranks higher and 50% chance the Actual Best Hand ranks lower.

If you're interested in calculating this for 1-9 hands, look at Aisthesis's first post. I think his method is sound and just requires some moderate calculations to do for the rest of the hands numbers. Aisthesis came up with a Median Best Hand being that ranked 110 out of 1326. Using the Sklansky-Malmuth hand rankings he then went through all card combinations making up the top ranked hands and determined the 110 ranked hand in that system is ATo. I believe this is the Median Best Hand dealt to 8 players - Aisthesis viewing it as an observer sitting at a 9 player game thinking about the Median Best Hand of his opponents.

I guess if no one else wants to carry forward Aisthesis method for all the cases 1-9 I will get around to doing it eventually, But it would be great if you'd give it a shot Filip. Thanks for the interest.

PairTheBoard

[PairTheBoard]

Yes. I agree. As soon as there's action then everything changes. You might check out my posts in the "Proababilty" section on how Bayes' Theorum applies to poker. As I see it it's basically in this area. You start out with estimated probabilities of what your opponents hold. Then when betting action occurs you adjust your estimation of their holdings according to your estimate of the probabilites that they would act as they have with the hands in your initial estimate. This is a seat of the pants application of Bayes' Theorum that we are doing all the time. But the jumping off point is the estimate of holdings before seeing action and the Median Best Hand calculationo ought to be one more tool in making those intitial estimates.

I also agree with your observation that the MBH idea should tend to have greater application in short handed situations. I've recently begun playing more 6 handed games and I think this has motivated my interest in this along with all the SNG's I've been playing. At the higher limits, even in a Full Ring game it's often the case that everyone will fold around to you when you are in late position and a raise by you will force the hand into heads up action. It's often the case that you will be playing heads up against someone with the Best Hand of the players yet to act. Of course an adjustment is needed if your opponent ends up being the Big Blind but knowing what the Median Best Hand is of the remaining players in that situation ought to be useful in giving you a feel for what you might be up against.

PairTheBoard

[George Rice]

[ QUOTE ]
Unfortunately, I am highly skeptical that this process could possibly identify any new and useful information. One major issue is the value of hands varies significantly with how many players enter the pot.

[/ QUOTE ]

I haven't read the responses to your post, but it would be relevant under the gun, or when everyone up to you has passed (assuming you're not near the button, where other factors increase in relevance). It might become downright useful for an UTG player in less than a full game, because many players have less experience playing short handed and might learn something.

[PairTheBoard]

Yea, I thought the Sklansky "Power Number" article was of more theoretical than practical value in that it was not necessarily the way to maximize +EV. However, it contained some interesting concepts that were worth thinking about. And I think it did have some practical value in more borderline situations where you might not feel your hand was strong enough for the big move. Especially if your opponent was one you would be reluctant to get involved with normally. No need to be afraid of him if even his perfect playback cannot beat you. We all know that as the blinds get bigger and our stack/blind ratio gets smaller we have to make moves in tournies. Sklansky was able to Quantify the Stack/Blind ratio aspect of the problem which I thought was pretty cool.

PairTheBoard

[Aisthesis]

I agree fully. I think a lot of the skepticism expressed in this thread may be due to over-ambitious ideas concerning its applications.

There are way too many factors that go into general starting hand rankings for this model to have any potential at all for trying to revise the lists currently in existence.

It wouldn't be very hard at all at this point to make a spreadsheet with which hand is "median best" against a field of x number of opponents--IF one can settle on a ranking of the starting hands.

But I think before settling on such a ranking system (or systems--since the context of application is going to have a lot of bearing on which list one should choose).

I think it's mainly applicable in situations where you're basically playing the hand hot and cold--although it might also yield some surprizing results regarding things like what hands might be worth a limp on the button if it's folded to you.

But I think the way to go from here is first to specify the narrowly-defined situations where "median best hand" is clearly relevant for actual betting decisions. I'm thinking shortstacks in a tournament as well as some shorthanded situations (of which the "folded to you on the button" is really one, even if it's at a full table) are the best candidates for figuring out some specific applications. But only with a clear definition of context is it going to be possible to decide which hand-ranking scheme to use.

[PairTheBoard]

For the short stack tourny situation Aisthesis, wouldn't the natural hand ranking system just be according to heads up showdown performance? Here's a link to the GoCee site that gives that ranking system.

http://www.gocee.com/poker/he_ev_pe.html

As for a ranking system where there is more play after the flop, I'm not sure. Has anyone actually done that for say Heads Up Play? Or Three way play? Not that you're playing heads up but you may be likely to go heads up after your bet.

PairTheBoard

btw, I too agree with George Rice's sentiments.

[Aisthesis]

I agree. And I don't see why with your idea one can't do the same from other positions really. Also, the shorthanded situations several people have talked about have some interest. I just hesitate for the moment to run through the whole thing without figuring out the parameters beforehand (it shouldn't be that hard, but will involve a little time counting through all the hands and finding the n-th root of the appropriate number).

My main interest at the moment would still be: How short does your stack need to be to want to go all in with the median best hand? I'm thinking slightly larger stack-sizes might then require more like 60% chance of being the best hand, and so forth... basically, until the stack-size gets to the point where you can afford to limp and play the hand.

Just on the basis of experience, I'm also thinking it starts to become interesting at a stack size of 10 BB or less, but I feel like there should be a way to at least bring additional mathematical aspects into play here.