Median Best Holdem Starting Hand

[PairTheBoard]

By golly I think your on it Aisthesis. I think looking at the whole 1326 possible hands is the way to go since all are equally likely.

When I suggested finding the median best hand among 9 dealt I was thinking of sitting at a 10 player table, getting dealt my 2 cards and asking myself, what is the median best hand of the 9 remaining players? But looking at it your way, when sitting at a 10 player table, ask what hand you need for a 50% chance of being best at the table. Using your solution my calculator comes up with the hand ranked 99 out of the 1326 possible. Where do you figure that falls in the Sklansky ranking system?

btw, here's a link to a Heads UP Showdown Ranking system.

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

How does the change in Ranking Systems affect the results?

PairTheBoard

[Aisthesis]

99 sounds about right for a 10 player table. I think the difficulty is going to be selecting the ranking system, because that's very much going to depend on the context. On the Landrum system, just counting through, I get AJo as including hand #99.

I notice the ranking system you cite definitely differs from my more intuitive rankings, which gave me the ATo for 9 players. I notice 77 is put higher than AJs there, fairly large suited bonus, etc.

I actually already find it useful just to keep in the back of my mind in various situations. But I think that in order to nail it down further, one would need to enumerate precisely the situation we're talking about, then do the ranking of hands on that basis.

In light of stack-sizes in tournament play, one might also consider other percentages than just the 50% mark (and this method makes that fairly straightforward despite the fact that we're dealing with large numbers).

Do you know how well the Landrum list correlates with Sklansky-Karlsson? At the moment, I'm in a rush and don't have time to call them up and compare.

Hopefully some discussion will get started on where one can go with these things. I'm thinking there are several (particularly, late) tournament situations to which it's likely applicable, but I'm a little hazy still as to how to define them precisely.

[bugstud]

[ QUOTE ]
By golly I think your on it Aisthesis. I think looking at the whole 1326 possible hands is the way to go since all are equally likely.



[/ QUOTE ]

Not all hands are equally likely, another nice little wrench in the problem. AKs happens less frequently than AKs, etc etc. I honestly doubt this information is as practical as you had hoped, I tend to side wth Ed on this one.

[PairTheBoard]

No. That's the beauty of Aisthesis's approach. He's looking at all 52c2 = 52*51/2 = 1326 possible starting hands - each of which IS equally likely. Then when it comes time to look at a hand ranked say 110, he counts all combinations of cards that make up the top ranked hands in the Skalansky Hand Ranking system. His method is simple, sound, and I think gives a pretty accurate result.

As far as practicality I think this is like a lot of innovations. Until the knowledge is available people can't think of much use for it. But once the information is available and you have it right in front of you, people start getting ideas.

Look, there's been all sorts of computer generated results for how a hand fares going to showdown against 1,2,3,...9 random hands. How practical is that information? When does that actually happen? Yet people still LOOK at that information because it gives them a better idea of how a hand is likely to perform in actual Realistic situations. It sheds LIGHT on things. It's part of Poker Theory - which is the topic of this Forum.

Having an idea how your hand compares to the best hand it is likely to face depending on the remaining players yet to act seems like something poker players would be interested in. But like I said before, there is natural resistance to any new idea.

PairTheBoard

[Bozeman]

For a table of ten players who play showdown poker with any hand (no betting or folding), the hands are ranked according to showdown percentage against 9 random hands, and the median best is (from pzhon, etc.) best ~7%. There are 89 hands in this set, and for showdown against 9 random hands these are 99-AA,AK,XTs for 88 hands with AQo on the bubble.

For a more reallife answer, you would need to specify a complete ranking of hands. As others have pointed out, this is difficult or not too meaningful. In addition, knowing the median doesn't help much because much of the coolness of poker comes in the variations (like Ak and qq being dealt together).

Craig

[PairTheBoard]

You refernce "pzhon" Bozeman. What is that?

PairTheBoard

[Ed Miller]

You refernce "pzhon" Bozeman. What is that?

"pzhon" is a dude who posted in your thread.

[Louie Landale]

Heads up if you have hand 50% then you are even money to have the best hand. That is, the median "best" hand for one player is hand 50%.

Against 2 players your hand h% is "best" when it beats the first player AND the 2nd player. Chances it beats the first player is h. Chances it beats both is h**2. .5 = h**2. h = 2ndRoot of .5; =70.1%. So if you have hand 70.1% you are 50:50 to have the best hand against 2 random hands.

** Average best hand for n opponents is nthRoot of .5. **

- Louie

Be advised that the actual rank of hands changes somewhat as N changes: trouble hands go down in relative value as N increases (A2 ranks higher heads-up than at a full table); suited hands go up.

This is interesting if you are adopting a starting strategy that says play if you are 50:50 to have the best hand or better.

[PairTheBoard]

I'm thinking Aisthesis has the right approach below Louie. He uses your same reasoning but considers all equally likly 1326 possible starting hands. Here is a link to Hand Rankings accourding to Heads Up matchup.

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

Interesting that J5s is on the bubble heads up.

I guess I agree that in a 3 player game the Bubble would be the hand ranked in the top 70% like you say. I'm not suggesting you think this but for others reading here, that's not the same as the hand that wins 70% of the time against a random hand when taken to showdown.

Thanks,

PairTheBoard

[Ed Miller]

Interesting that J5s is on the bubble heads up.

I guess I agree that in a 3 player game the Bubble would be the hand ranked in the top 70% like you say. I'm not suggesting you think this but for others reading here, that's not the same as the hand that wins 70% of the time against a random hand when taken to showdown.

Ok, PairTheBoard, since you are going martyr on me with your, "The best ideas always ridiculed by the man," stuff...

What exactly is this "bubble" that you are talking about? For instance, if J5s is on the bubble, surely J2s is below the bubble. What conclusions about HOW TO PLAY J2s do you draw from that?