behind the glory: hand rankings

[emp1346]

so i understand that certain starting hands are better than others, but how is this determined (and supported) mathematically?

forget that it just is, but why is AA better than other hands?

also, i'm not interested in a hand vs. hand comparison (i.e. AA is better than KK because...) but instead a generic AA is better than ?? because...

i can see how doing a heads up comparison of all starting hands can produce these results, but is there something easier?

[Subfallen]

Huh? AA is best because it rates to be the best hand pre-flop like 100% of the time. Am I missing something?

[Siegmund]

All you have to do is define a measure of goodness, then see how each of the hands score on it. There is no one unique measurement - and no one unique ranking of starting hands, either! AA is best on all the lists, performing better against just about any lineup of hands you throw at it than any other does.

One possibility is to calculate your chance of winning a heads-up all-in vs one random hand. If so, 32o is the worst hand, not 72o. Another possibility is to calculate your chance vs. 9 random hands if they all see the showdown; this overvalues suited connectors and undervalues things like TT. You could observe a large number of hands, and keep track of how often each one won a showdown - but this will undervalue the hands which are so good they often win before a showdown. Abdul did a famous study several years ago with Turbo Texas Holdem and calculated the EV of each initial action on each UTG starting hand vs. a certain set of AI opponents (who don't bet exactly the way real humans do.)
All those, of course, require a lot of calculating.

A few days ago someone proposed a definition for "hits the flop hard" and wanted to calculate the chance for each starting hand. Tedious, but tractable, and I think the result would have made a pretty good ranking list.

One thing you can calculate more easily than doing all possible hand pairs is calculate the chance that both hole cards will play for each starting hand. I made a list of that last summer; it wasn't bad but overvalued small pocket pairs badly (rating 22 about as good as KQs or AKo if memory serves).

So. Pick your definition of goodness, and crunch some numbers.

[emp1346]

subfallen, yes you missed the entire question...

siegmund, i kind of see what you're saying, but at the same time, i don't understand what you mean when you say that certain methods over- or under- value a hand... wouldn't that value also be subjective to the definition of goodness, as you already say is subjective as well...

i'm curious as to not necessarily what will get played either, seeing as i'm interested more in which hands, straight up without any consideration of playing ability or playing style, are better...

and again, how would this overvalue suited connectors if they actually do win more often than TT as you imply? if the numbers indicated that this was in fact the case, why would you not be inclined to accept that as truth?

[querulous]

There's too many variables to just state which hand is 'best'. Heads up, TT is about a million times better (note: rough estimate) than T9s. Against 8 other players, T9s is a monster favorite compared to TT. Facing a reraise in a deep stack NL situation, most players would rather have 67s than JJ. Shorthanded in a high blind/short stack situation? JJ is much better than 67s. You suspect your opponent has AA? You'd rather have 66-99 than KK. You have no idea what your opponent has? You'll take KK.

[Siegmund]

[ QUOTE ]

i'm interested more in which hands, straight up without any consideration of playing ability or playing style, are better...


[/ QUOTE ]

You can't take the playing style out of it. The list of hands that are best vs tight agressive opponents is different than the list vs loose passive ones. The list of hands also changes with the number of players at the table.

There are hands that are near the top of everyone's list (AA, KK, QQ, AKs) and near the bottom of everyone's list (83, 82, 72, 32 and their friends). All the hands in between WILL be in radically different places depending what criteria you use. There ISN'T any one "right list."

[ QUOTE ]

and again, how would this overvalue suited connectors if they actually do win more often than TT as you imply? if the numbers indicated that this was in fact the case, why would you not be inclined to accept that as truth?


[/ QUOTE ]

If you're in a game packed to the gills with limpers and calling stations, it's the truth that suited connectors are very valuable. If you're in a game where every hand is raised preflop and two or three people are taking the flop, 87s is just two random pieces of cardboard. The list based on 9 random hands all going to the river will (very, very) badly mislead you about the value of suited connectors and cost you a whooole lot of money if you follow it in a real game that's not loose-passive.

[SycoFrogg]

Don't forget position

[Mark1808]

Which hands are best really depends on the range of hands your opponents play. If someone could come up with 5 or so player profiles and then you could estimate which of these profiles fit the players in your game you could come up with a pretty good starting hand ranking based on who has entered the pot and who is likely to enter. As a simple example if all your opponents only played AA and someone opened the pot, KK would not be a good starting hand.

[wdeadwyler]

I think hands should not be ranked by statistics. I think at some point in your playing career, you arrive at your own ranking of hands, based on their intrinsic value in each different situation you find yourself in while playing (position, reads, stack sizes, plus many more variables) . Obviously, we have to start somewhere, and hence group 1, group 2 etc., but as a player progresses more and more, he mind find that his value for a hand is different from an opponents value. All that really matters is the EV that you get from each hand you play.

["spaceman"Bryce]

IM SO CONFUSED /images/graemlins/confused.gif /images/graemlins/confused.gif /images/graemlins/confused.gifI hope i get AA then we can ask ourselves "why is it better?"

[gergery]

[ QUOTE ]
There's too many variables to just state which hand is 'best'. Heads up, TT is about a million times better (note: rough estimate) than T9s. Against 8 other players, T9s is a monster favorite compared to TT. Facing a reraise in a deep stack NL situation, most players would rather have 67s than JJ.

[/ QUOTE ]

All of the above is incorrect.