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.

[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?

[pzhon]

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

[/ QUOTE ]

Suppose the hands are represented by independent numbers drawn uniformly from [0,1]. The probability that n hands will all be between 0 and x is x^n. You want the median best, x so that x^n = 1/2; x = 1/nthroot(2). For n=10, that is 0.933, so look at the hands that are in the 93rd percentile of your ranking system.

The problem with this simplification is that the hands are not independent, e.g., hands in the top 0.4% tend to repel each other. Nevertheless, I would guess this approximation is reasonably accurate.

[cnfuzzd]

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

peace

john nickle

[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

[PairTheBoard]

I refer everyone to Ed Miller's post and my reply.

Typical of a Novel idea. The first responses are usually, "it's already been done" when it hasn't, "it wouldn't be useful" when it would, and "it can't be done" when it can. Don't worry guys, when it finally gets accomplished I'll let you say it was your idea all along.

PairTheBoard

[uuDevil]

[ QUOTE ]
Typical of a Novel idea. The first responses are usually, "it's already been done" when it hasn't, "it wouldn't be useful" when it would, and "it can't be done" when it can. Don't worry guys, when it finally gets accomplished I'll let you say it was your idea all along.


[/ QUOTE ]
PairTheBoard,

I suggest patience.

You have almost 400 views on this thread. You got a couple of confused responses and a couple of clarifying ones. You got one helpful suggestion on how to approach the problem. Most people reading this are going to skeptical about your idea, but that's not (quite) the same as dismissing it.

The following are still possible:

The right person hasn't seen it yet.
Someone is thinking about it or actually working it out.
Someone has an idea/suggestion but is too busy to respond at the moment.
People are too bashful to post a possibly helpful but incomplete response.
People think the idea has merit but don't want to invest time in a speculative project.

--uuDevil