Median Best Holdem Starting Hand

[Aisthesis]

Yeah, that was the one I used originally. Do you know the methodology behind it? At least in the heading, it seems to suggest that it might be based on 2 billion actual hands and what they won. If we're talking more about hot-cold betting situations, I'm actually inclined to go more with a computer simulation or with the Karlsson-Sklansky scale, which is looking for a different numerical value but as I see it HAS to give an accurate relative ranking of how hands hold up heads-up with no further betting after the pre-flop all-in.

The messy part in doing the further work on this is going to be to run equity values on how the given hand holds up against the (superior) calling hands. It won't be too bad for 8 or more players, but once you start having lots of possible superior hands, it will require running a fairly large number of matchups through something like pokerstove (particularly taking into account the variations in suits).

[PairTheBoard]

Hey you know what. There was a poster here a while back who did some really interesting stuff regarding that question of how the hands actually hold up against each other. When I get a chance I'll look through the threads and try to find it - about ready to crash pretty soon. I think the title mentioned "Recursion". Anyway I believe he took something like the GoCee rankings and picked the top half of the ranked hands and reran the GoCee program to see how hands faired against the restricted list instead of against random hands. He then got a new ranking and repeated the process. The Recursive process reached equilibrium after a few runs. I wasn't sure what to make of it at the time but it just might apply here. As he mentioned, the same process could be done by picking the top third and so on. I'll have to think about this some more.

btw, here's a situation brought up in a thread at UPF where I thought the Median Best Hand was a natural thing to apply to the analysis. Something I might have never thought of.

http://www.unitedpokerforum.com/forum.asp?m=82234

PairTheBoard

[Louie Landale]

This MBH stuff DOES show light to the disciplined-challenged folk who play KT UTG. Its easy to confince them that they are a 2:1 (or whatever) dog to have the "best hand" right now AND wield a trouble hand out of position. General situations don't get much worse than that.

Anybody who still likes THAT shouldn't be playing for keeps.

- Louie

[uuDevil]

[ QUOTE ]
There was a poster here a while back who did some really interesting stuff regarding that question of how the hands actually hold up against each other.

[/ QUOTE ]

PairTheBoard,

That poster was eastbay, in this thread:

Self-balanced hand rankings

[PairTheBoard]

Great! Thanks uudevil. I thought that was a remarkably clever and interesting idea by eastbay. I didn't see much application for it at the time but low and behold it might be just what we need for what we're looking at here.

PairTheBoard

[PairTheBoard]

I'm still thinking about some of the points you made in your last post Aisthesis. Also, see uudevil's link below to eastbay's "Self Balancing" method for possibly improving on the GoCee Heads up vs Random Hand Showdown rankings.

I'd like to describe the situation in that UBF thread I linked to above so people can see what I'm talking about. Your at the last table of a tourny, in 9th place with top 5 making the money. You have 4000 in chips, the blinds are 2000-4000 and you are UTG+1 with Q7o. UTG has a large stack and moves All-In. Should you call or hope for a better hand to play in the next two hands. Notice you will be forced all in by the blind when it gets to you.

Isn't one of the first things you're going to consider is how your Q7o compares with what you are likely to be dealt in your next two hands? In other words, how does Q7o compare to the Median Best hand out of the 2 hands you would wait for if you fold? That would be good to know wouldn't it? In fact, wouldn't you be asking yourself this same question all the way around the table as you see the Bustout Blind coming up on you inexorably for hand after hand 7,6,5,4,3,2,1 positions away from your next blind.

This is an application for the MBH that I would not think of until the situation actually came up. Now that I think about it, I've been in that situation more than once.

PairTheBoard

[Aisthesis]

I like this list a lot. I think you do need the iteration because the way they hold up against the superior hands is going to strongly influence just "how good" the hand is.

I don't mean to keep harping on Karlsson-Sklanksy (which was of course developed for a different purpose and a different methodology), but I think that list is at least VERY similar. I just finished drawing up a spreadsheet with those rankings (K-S) and then in a final column the number of superior hands. So, if the list is valid for the purpose at hand, all one would have to do is the math on the equation for 2-10 players to come up with an actual hand. Calculating win percentage for all of the superior hands is still going to be a little messy, though.

[Aisthesis]

Hmmm... just did a comparison. The iteration makes the medium-high pairs much less dominant, but they still get higher marks than in K-S. On K-S you have ... AKs, QQ, AKo, JJ, AQs, TT, ...

Here, you still get all the way down to TT before putting in AKs as the top non-pair hand (just below TT).

I actually think I like K-S better for the purposes envisioned. I'm guessing the math behind it must put more weight on how well the hand fares against other very good hands. I don't know... Intuitively, I'd probably rather have QQ than AKs in that situation, but the reason that AK gets such high marks in K-S has got to be that KK dominates QQ much more heavily than it does AKs.

[Aisthesis]

Yes, I've been in that situation several times as well, although I usually try to start thinking about its possible arrival early enough to be able to catch a true (relatively) good hand. But sometimes that situation is unavoidable (or at least wasn't successfully avoided!).

Anyhow, yes, I think the median best starting hand list will provide a very close approximation of "best hand you're likely to get" in the next n hands--say n=5, where you figure you're going to have to double up or die in the next five hands. The exact calculation would be a little different, though, because you don't have any cards already out to compare it to. Actually, given a hand ranking list, isn't it more accurate (in addition to the virtue of simplicity) to just say: "This hand is in the top 20%, hence likely to be the best hand I'll get between now and the next four hands."

So, if you truly have to go all-in over the next five hands, you just see if it's in the top 20% for the first hand, then the top 25% on the next hand, top 33.3% for the next, etc.

[PairTheBoard]

What is Karllson-Sklansky?

PairTheBoard