Median Best Holdem Starting Hand

[PairTheBoard]

Of course if you use the information to draw all the wrong conclusions then your are right in that you will obviously be wrong.

PairTheBoard

[Ed Miller]

Ok, dude. You've presented the problem to 2+2. You got a lukewarm response. You think that this lukewarm response is simply resistance to a new idea, and that really you are on to something important.

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.

Well, under those conditions, you cannot ask 2+2 analysts, including David and Mason, to do the work for you. If you think you are on to something important, YOU do the calculations, YOU present them in a cogent and convicing fashion, and YOU will get the credit, I assure you.

Furthermore, if you do cobble something together that is both new and insightful, I will gladly eat my words.

[PairTheBoard]

I refer you to the posts by Aisthesis and my responses to him where progress is being made.

PairTheBoard

[J.A.Sucker]

This isn't really true either, since the caller usually requires a significantly better than average hand to call, especially in tournaments where chips are so valuable. If your lone remaining opponent had a huge stack (or an infinite bankroll) and would call with nearly all hands, then you have a good point. However, this is hardly ever the case. If you are playing in tournaments this way, it means that you are stealing the blinds too little and calling steal raises too much, and this could explain why you're always short on chips.

[J.A.Sucker]

Congrats.

[Louie Landale]

My solution agrees with Aisthesis'; although mine has a continuem where hand 100% is best and his is quantified and hand 1 is best.

The median best hand information is a fairly useful number but is by no means a mechanism for deciding what to play. Position matters a lot. Also, the median best hand by no means relates directly to you chances of winning the pot. AT is going to lose more often when its currently not best than it is going to win when it is currently best (e.g. J9 and 65s are going to outdraw AT more often than AT is going to outdraw AJ or 88). It also ignores the effects of increased blinds and antes.

Thus, even though ATo may be 50:50 to be the best hand against the field does NOT mean you should open raise with it UTG.

Several years ago I used this notion to calculate starting hand requirments. I "weighted" those who had position on hero by 1.25 and "weighted" the blinds at .75 (hero has position on them). Thus, with 9 players left to act 7 of them weight 1.25 and two weigh .75 resulting in an exponent not of 9 but rather 7*1.25+2*.75 = 8.75+1.5=10.25. Plug that into the equations and (IIRC) results in AJ being on the bubble UTG. That means play LESS than your fair share Early and more late. SURPRISE; that pretty much agrees with Jalib. I personally feel position is even more important than some others, especially when the competition is competant: fold AJ early in a table of Jalib's and Malmuth's and Sklansky's.

I suppose you could assign each opponent a separate weight based on their over-all competancies; somewhere between Jalib +35% and my idiot half brother Bozo at -35%. Good luck doing those calculations.

- Louie

[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

[Filip]

[ QUOTE ]
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

[/ QUOTE ]

I was bored so here is my solution:
<font class="small">Code:</font><hr /><pre>
Players MedianHand
1 T8o
2 J7o
3 K4o
4 Q7o
5 22
6 K6o
7 A2o
8 42s (????)
9 87o
</pre><hr />

I find the 42s very strange but.......

[Aisthesis]

Yes, I thought that whole analysis was very interesting, although mainly applicable if you get shortstacked. Basically, the calculations showed precise conditions under which all-in was a +EV play. But that doesn't mean it's the best EV you can get. According to the analysis, regardless of stack-size, going all-in on AA is +EV. Well, that's certainly true, but you're probably not going to want to play AA that way unless you have an extremely small stack or else other conditions have created a situation where you think you might actually get a caller.

Anyhow, I definitely need to look at the article again to see if one might apply the calculation method to the other situations you were originally envisioning. In practice, this kind of purely mathematical approach to the situation does tend to ignore certain other important aspects of the overall circumstances. But I think it provides a very good "point of departure" for considering the less quantifiable aspects of the situation.

[Aisthesis]

I agree pretty much with all of this. And another dimension that adds to the problem of using this for starting hand selection in a ring game is the type of flop required to get a truly big hand. I'd much prefer to limp UTG with 44 than with AQo, although AQo is ranked pretty high. With 44 I have huge implied odds if I hit my set, although I'm going to lay the hand down immediately on most flops. Suited connectors raise other, similar issues.

For that reason, I think it would be going too far to try to use this kind of thing to provide criteria for starting hands in a cash-game situation. I think there will be too many complications to make it really doable.

I'm really thinking the place it has the most use is in short-stacked tournament contexts.