full ring limit handstrength list

[malicor]

just some more math i did

first number: the 'absolute' hand value, setting AA to 1.000 and comparing all others to AAs strength.

second number: percentage of win against 9 randomly distributed hands
third number: percentage of win headsup against 1 random hand
hand strength number: normed sum of both other numbers, giving the 'vs9'-number higher weight (13/2)

why 13/2 ? oh, i just experimented some, and this list looks quite a lot like about what i read how it 'should' be but it's not mathematically based on anything

AA 1.000 29.7 85.2
KK 0.870 24.6 82.4
QQ 0.766 20.5 79.9
AKs 0.705 19.9 67.0
JJ 0.687 17.5 77.5
AQs 0.670 18.5 66.2
KQs 0.648 18.0 63.4
AJs 0.643 17.5 65.4
TT 0.626 15.3 75.0
KJs 0.622 17.0 62.6
ATs 0.622 16.7 64.6
AKo 0.613 16.2 65.3
QJs 0.606 16.7 60.3
KTs 0.602 16.3 61.8
QTs 0.589 16.1 59.5
JTs 0.582 16.1 57.5
99 0.579 13.7 72.1
AQo 0.572 14.6 64.4
A9s 0.569 14.7 62.8
KQo 0.552 14.2 61.5

complete list is at http://www.malicor.com/poker.sorted....3_topdown.html

it doesn't include the fact that going against random hands might add some mistakes to the list, since you probably won't go against either one or nine random hands (though it still might be mathematical correct due to it beeing the 'middle value'). i'm thinking about a way to change this, and additionally trying to change the weight factor in a way that it uses peoples VPIP to figure out how many people will probably see the flop.

comments please

ps: this is a copy kinda from a post in the 'poker theory' section, but i think it belongs to here. maybe someone could remove the other threat, if he thinks it's no good there.

[Niediam]

What exactly is the point of this?

Anyhow I think there have be some errors here. Obviously a strength list is going to change depending on how many people see the flop. However, I'm pretty sure that AKo is a more profitable hand than ATs and KJs regardless of the numbe of opponents for example.

[malicor]

Point is to find a mathematical approach to value preflop hands.

As I wrote before, to make it dependend on the number of players in to see the flop, one could use VPIP to get a probability for how many people there'll be.

regarding AKo vs ATs:
AKo vs. 9 random hands has a win chance of: 16.1%
ATs vs. 9 random hands got: 16.7%
(pokerstove)

i do know that you will (normally) neither play against 9 opponents, nor against random hands, since those would at least partly fold, but to just say AKo is ALWAYS more profitable seems to not be correct ?

where would you put AKo in the list ? and with what reasoning besides intuition ?

[Niediam]

I could be wrong but I do believe that if you took a million trials (or whatever is statistically significant) in just about any situation that that AKo will end up winning more money than ATs.

A problem in general with hot/cold simulations is that obviously all hands are not going to the river. With AK you will often but not always see the turn when you miss the flop. But how often do you see the last card unimproved? Certainly sometimes but probably not even half the time. This is even more pronounced with a hand like 44 which is almost always going to showdown when it flops a set but will generally fold to any bet when it misses.

Anyhow, I believe that most people will decent sized Poker Tracker databases have AKo with a higher winrate than ATs. I believe it's even higher than AQs. AK performs very well online beause the games are fairly tight preflop so high card strength becomes goes up in value while being suited and connected isn't as imported. In a loose live game like 3/6 making 'big' hands becomes much more important. Because of this I do believe that AQs should have a higher winrate than AKo. I'm guessing though that ATs is giving up too much high card strength. Obviously making a flush will almost always give you a winner but too often you hit an ace or ten and end up paying a lot of bets with the second best hand. AJs is probably close.

By the way, Sklasnky has ranked the hands previously in Hold'em Poker and Hold'em Poker for Advanced Players based upon generally loose mid-level games. I'm not sure what his methodoligy was (and I disagree with thinks in these rankings too!) but he has AJs 8th, AKo 10th, and and ATs 15th.

I don't think it really matters though if ATs ends up being more profitable than AJo or not as long as you know which situations the hands should be played in.

[Bob T.]

I don't know, I've got a pretty big database currently, and my results pretty much are in line with the hand rankins from HPFAP. I would guess that most of the discrepancies are probably more likely due to sample size, and not actual differences in the hand values.

[malicor]

is the HPFAP list to view somewhere ?

so the lists you mention are not based on any mathematical information, but rather view from how it was for 'X' examples recorded by pokertracker ?

[Niediam]

[ QUOTE ]
is the HPFAP list to view somewhere ?

so the lists you mention are not based on any mathematical information, but rather view from how it was for 'X' examples recorded by pokertracker ?

[/ QUOTE ]

I wouldn't be surprised if you could find Sklansky's rankings if you tried googleing for them but I don't think Mason would appreciate it if somebody were to list them here or specifically link to someplace where they are.

I have no idea how Sklansky made his rankings but they were done before the age of online poker.

[HoneyBadger]

I recently posted a list of money won per hand, normalized at 1.0 for AA, over 250k hands. It's different from your list. It also showed how marginal some differences are, and how vastly superior AA is to any other hand.

It's this post: http://forumserver.twoplustwo.com/showth...page=0&vc=1

(I know, the sample size is way too small)

[malicor]

did you miss KQo in that list somehow ?

[HoneyBadger]

[ QUOTE ]
did you miss KQo in that list somehow ?

[/ QUOTE ]
It's probably below JTs, I stopped there. The x's mark a cut. Or maybe I missed it... don't know [img]/images/graemlins/smile.gif[/img] It only served as indication.