Median Best Holdem Starting Hand

[PairTheBoard]

I believe this is an open question as far as Poker Literature is concerned, yet it should be basic knowledge for every profesional Holdem Player.

Pick a Hand Ranking System. Or better yet, do this for several of the best recognized hand ranking systems.

What is the Median BEST 2 card starting hand dealt to 9,8,7,6,5,4,3,2,1 players?

It has been solved and published for one player but not 2-9 as far as I know. I challenge the 2+2 analysts, including David and Mason, to answer this.

PairTheBoard

[cnfuzzd]

I know i am misunderstanding the question. Please help me.

wouldnt it be aces? what about the rankings of hands listed here hot naked chicks

peace

john nickle

[manpower]

I believe the question is: of the ten starting hands dealt, what will be, on average, the best of those ten hands?

No idea how to work it out without generating a dataset, but I'd guess it's going to be pretty similiar to the recommened hands for an UTG raise at a full table.

[cnfuzzd]

Good, i hate it when my simplistic responses turn out to be correct. Makes me feel dirty inside.

peace

john nickle

[Louie Landale]

Your chart shows how each hand fares against N random hands played hot-and-cold. Curious that 63s wins "fair share" 10% against 9 opponents. Its a fair judge as to which hands are better than others.

The original question is "what's the chances I have the best hand right now?"; or more specifically "What's the median best hand I have to beat" which is the same as "What hand can I have that's 50:50 to be the current best".

Now "best" means you ranked the hands from best to worst, say AA, KK, QQ, AKs, yaddy yaddy and do some analysis. Your chart would work; just sort it on the "9 opponents" column then weigh each hand based on how many of each there is (6 for each pair, 4 for each suited hand, 16 for each unsuited hand). Keep a running total; may look like this:
Hand # Total %(divided by 1326)
AA 6 6 .45%
KK 6 12 .9%
QQ 6 18 1.35%
AKs 4 24 1.8%
...
72o 12 1326 100%.

Thus if you have QQ your hand is no better than 1.35% of all hands.

There will be righteous debate on the rankings, such as whether JJ is better than AKs. But that doesn't matter.

- Louie

[uuDevil]

You seem like a pretty sophisticated poster, so maybe I'm not understanding your question, but WTH:

The rankings against 1-9 random hands are well known:

http://www.gocee.com/poker/HE_Value.htm

The median hand for any number of players is easy to pick out from the list. E.G. against 9 opponents, the median hand is J4s, since half the 169 possible hands have more equity and half have less (assuming I picked the right row).

Of course "random" is not much of a system, so I guess you mean a ranking of hands within a preselected group of hands? I think this is pretty easy to generate assuming all hands go to showdown. I haven't seen it done, but offhand I don't see how the relative rankings would end up different from the random case.

FWIW, eastbay did some interesting things in this thread. But he started with random hands and only considered the HU case.

Edit: I see now cnfuzzed posted the gocee link too. The naked chicks thing threw me off. [img]/images/graemlins/grin.gif[/img]

[Ed Miller]

He's asking about the median "best" hand. For instance, say ten random hands are dealt, and out of those hands, the "best" one is KJs. Then ten more random hands are dealt, and the "best" one is KK. It you did this like 100,000 times, what would the median "best" hand be?

That's what he's asking about. 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. There is no relaible or meaningful way to identify the "best" hand out of 10 random hands.

Even if you could reliably identify the best hand, how would knowing the median best hand help you?

[PairTheBoard]

Yes, that's the idea Ed. However you miss the point of the Hand Ranking System when you say,

Ed: "There is no relaible or meaningful way to identify the "best" hand out of 10 random hands."

Once you pick a hand ranking system THAT is how you judge whether one hand ranks higher than the other. You also point out that some hands play differently according to the situation. That's why I suggest doing this for several different Hand Ranking Systems.

For example, you are in a tournament and thinking about going All In with 5 players left to act including the blinds. The most applicable Hand Ranking System here is probably just the one that determines which hands are favorites in a heads up show down matchup. In that situation do you or does anyone here know the Median Best hand you are up against with the 5 players left to act?

I think such knowledge would be very useful.

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.

[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.