Serious question: What does this statement mean in terms of specific hands?

Is this 99+, Ajs+, KQs, AKo like on this website??
--> http://www.pokerhandrange.com/
or TT+, AQo, AQs+, KQs like on Flopzilla (definately not right imo)???
or perhaps the several other versions ive observed over the years (Sklansky-Chubukov, Slanskly-Malmuth etc etc)...

With respect to the range in the first link: I Noticed how the values change when you change the number of opponentsin the side box... why would this be?? It seems like the publisher is factoring in that the hand value are dynamic whether HU or MW... but to me this is actually an advanced betting notion that recognizes that some hands are going to realize different amounts of action when they hit and not a pure statement of mathematical equity or rank. Put differently, from an argument of continuity if A is any hero hand and B is any villain hand and A > B Heads up, there cannot be a hand C such that B > A (ignoring the case of blockers etc.) if we simply make it multiway by adding it in.

To me when someone says "Player X 3 bets the top 5% of hands" that means that if I went back home to my pokerstove or flopzilla or whatever and ran equity calculation of all hands HU and ranked them and then wrote out the top 5% hands we should be talking about the same thing. Despite this there seems to be such variance in what is top 5%? What am I missing?

If I am right and top 5% should in all logic be a mathematical statement where can I find a list of hand rankings or calculator that will show me ranges based on their true equity strength and not post flop/MW/playability/metaphysical(lol) value??? I have never seen one...

Thanks,

PS if we just used pure equity I would have a pretty pair heavy top 5% range(55 crushes AJ haha) which I doubt correlates to howvillians would empirically behave.

Hand rankings that are available on poker sites or on the internet typically do not take betting (e.g., how much is won/lost per hand) into account. That is very difficult to model systematically with any precision or consensus.

These hand rankings are typically equity rankings among N all-in hands preflop. I would hazard to guess that anyone who has played any significant amount of poker realizes that the hand rankings (in general or specifically all-in preflop) depend upon N.

Depending upon how many players are at the table (in the hand), high cards vary in strength, suited connectors vary in strength, small pairs vary in strength, suited cards vary in strength, etc. I don't know how to convince you but heads-up hand rankings are significantly different than 9-player hand rankings.

As whosnext said those hand rankings are based on empirical data collected by authors based on preflop all-in equity vs a particular number of random hands (some systems may not be random hands but defined ranges I'm not sure).

The basic idea is that as the number of opponents in the hand becomes larger, generally the stronger your hand needs to be at showdown to win. So a hand like AJ becomes better than a hand like 55 because it makes bigger pairs, it makes top straights, and it makes nut flushes which are really hard to beat at showdown. Conversely, heads-up 55 can stand to be the best hand at showdown quite frequently without improvement.

Yea actually Charlie Swayne has really good insight into this in "Advanced Degree in holdem" whereby he shows graphs of relative strengths on hands and then goes on to index "Win Factors" to hands based on Table conditions (Loose tight) and # of opponents. In theory you could order them by WF and incorporate this into your model (perhaps add aggression).

Have to run off to work now... going follow up with a question later tonight. Thanks so far.

One thing that I forgot to mention and might be interesting is that stack size plays a similar role due to the potential loss of future betting. Some hands that might belong in certain ranges at certain stack depths while not at other stack depths.

Agree, this point is the one that most people fail to consider when it comes to hand value.

As was already pointed out, each hand changes value with the number of players, stack size, and styles of play to your left and right.

Also position, and Hero's image play key roles.

In general:
As the number of players go up, than the value of premium pairs go down and the value of small pairs or suited connectors go up due to pot odds/implied odds and making sets/straights/flushes will hold up against a crowd better than an over pair. This is important for games like Limit where you will see more players get to the flop.

With position, hands like suited connectors gain a little value, out of position pairs gain a little value. The reason being, in position, you have more control when you have some kind of draw for getting cheap or free cards or for two barrel semi-bluffs depending on the situation.

Out of position, you miss the flop too often so a pair can allow you to donk bet, or call many flops where your pair still rates to be good.

As stacks get shorter, than you get closer to pre-flop equity. Big aces pick up a lot of value since a shove get's to see 5 cards but if we look at each thing that we've already talked about so far:

You have AKo and raise in EP, get several callers and stacks are 200bb avg. You will get taken off of a lot of flops and AK doesn't look so good anymore.

Stack size along with styles can be a very potent mix in deeper stack play.
Similar to the number of players, as stacks get deeper, premium hands get weaker while gambling hands get stronger, however, it will be even more exaggerated if you have a good image relative to your opponents and position.

The reason being that implied odds are more effective for paying off your monsters than with pot odds.

You can think of it as the deeper the effective stacks, the later the streets where the action will tend to be.

The turn and river also happens to be where suited connectors gain a lot of value and big pairs lose a lot of value.

This is due to the fact that c-betting on the flop is far less effective because there's lot's more room to call with thinner draws. Backdoor draws are now a significant factor because of the value you can pick up for FE with semi-bluffs on the turn or value betting when you hit the river due to their disguised nature.

On the other hand, if your only looking at a pot sized stack behind, there's really no implied odds to speak of when it get's in on the turn.

Big one pair hands such as TPTK or OP are not all-in hands anymore so pot control is a big factor and bet sizing with balance will be smaller relative to the pot in general.

As you get deeper still, there are special hands that stand out such as 97o or 64o where you can get excelent matchups that will take the best advantage of your improved implied odds.

For example, when very deep at ~300bb effective, I'd say that

97o>>98s

Among other reasons these hands play so well, the 97o will hit a donkey end straight vs the more commonly played hands hitting two pair, TP+big draw, etc. Notice your not really that worried about having the bottom end since you have 2nd nuts vs a very unlikely Q9 that's almost never betting this board.

Finally with one gappers, your DBBSD's are extremely easy to be overlooked by your opponent.

Example:
350bb effecive from the HJ and you have:
JT
Your std raise gets a call from a LAG in the CO which is no surprise.

J85 flop

You make a std bet on the flop and get a call.

T hits the turn, if you missed the DBB on the flop which many would, You can't very well put him on a set. JT looks like the effective nuts against a player that improved a ton of hands you still crush but most are still very live vs your hand.

Lets say betting was 5bb pref, 8 flop making the pot ~27, you bet, 30 and get re-popped to 100...

Sure it's a fairly rare cooler but given the implied odds, it's worth it. To do as well you'd usually need to see FH over FH. Also it's hard to see a better situation with 98s.

One you get below the top 1.4% of hands (AA, KK and QQ) hand strength has little relevance to full table poker. In heads up strength matters farther down.

The reason is top pairs make money unless you actively try to misplay them. For example, if you go all in with AA every time at a full table, you will make some money on average. But with weaker hands, the stronger the hand, the more often it wins, but the more you lose when it loses. The hands on which people lose the most money, on average, are Ax. These are reasonably strong in terms of win probability, but they are also often dominated, and when they're not dominated but win, the pot is usually small.

Another problem with strong hands is they tend to involve high cards. If other players also have high cards, that hurts your chance of improving, and increases the chance that cards that improve your hands also improve someone else's. If other players don't have high cards, you usually win a small pot. Hands with low cards can do well when no high cards show up on the board, and their wins are always more surprising, hence more profitable.

I'm not saying 2's are better cards than J's, only that hand rankings are not that relevant to full table poker. The type of hand, middle pair, suited connector, and so on; is more important than it's strength.

What you are missing is that there is no such thing as an absolute ranking of starting hands for Hold'em. Unlike final poker hands, starting hand rankings are a measure of potential. And all the various ranking systems have different criteria to measure that potential according to their purpose.

Poker Stove ranks hands according to their preflop equity against 3 random hands.

Another common ranking is preflop equity against 1 random hand (Heads-Up Rank).

Pokerroom.com rankings are based on actual performance in full ring cash tables.

Sklansky-Chubukov rankings are based on a specific jam/fold scenario.

There are many other systems, and here is a list of some of them:

http://www.bigbetsoftware.com/holdemviewer/rankings/

So when you speak of top 5% of hands, that needs to have a context for defining it. Things like stack size, number of opponents, limit or no-limit, etc.

Hand strengths are dynamic, and absolute strength and relative strength (post-flop) changes as the board changes.

Quick example.
Flop is Jc 7d 6d.

On that board, a set of sevens is strong in an absolute sense. It's the second nuts, after all. But what if your opponent has pocket jacks? You'd be drawing to one out. If villain turned his hand face up, you'd be much better off with 98dd than 77. In that (contrived) spot, 9-high has more equity than middle set.
Similarly, in multiway pots, a draw to the nuts is arguably more valuable (and more likely to win the pot) than one pair with no backdoors or blockers.

The Sklansky-Chubakov rankings are great for pre-flop all ins heads up, but for playing post-flop, you need to alter the rankings according to playability, number of players, blockers, likelihood of going to showdown etc.

thanks guys for all the responses.... this concept is actually one of the bigger leaks in my game and my next step in becoming a better player. I tend to observe my opponents, count the number of hands they play (in that position) and assign their range according to that % and what hands I thought were in that % of hands based on the one (no seriously) ranking I knew. Obviously this is way too simplistic.

My follow-up question is this then: If a complete ranking set depends on a finite number of factors, then how many ranges do you think would be sufficient to describe hand strengths adequately in every (yes every) situation. Obviously the more the better, but would it be realistic to say you could know 20 rankings variants and be pretty accurate in all situations or would need to develop many more like this --> # of opponents (9 choices) * table looseness (4 choices e.g. very loose/loose tight/ very tight) * Stack size (2 e.g. deep, shallow) = 72 discrete sets of rankings (or even more as factors increase)

The real challenge would be constructing each ranking but I feel my knowledge of the game would be sufficient to at least roughly write out some and refine them over years of play and/or literature. I just am trying to appreciate how many variants one would need to know before you would have extremely diminished returns in doing so :P.

What is your goal with formulating a dynamic preflop hand ranking formula?

I simple want to be able to take % values (pfr/vpip/whatnot) and convert to hand ranges with more accuracy than I currently have using a static model. (With those hand ranges I can easily evaluate how each flop interacts with each range using algorithms and empirical data mined from flopzilla and pokerstove and help make better decisions on the flop.

For example: You are playing a nitty UTG who pfr @ 5%.

He raises you cold call and the flop comes A96 rainbow

You know from your (incredibly advanced :P) static model that 5% is 99+, Ajs+, KQs,AKo and as such he has top pair or better 46.2% of the time. You also calclulate the % for 8 outs or better as you don't think he would float a bet with less. You bet accordingly.

Problem is in his spot 5% was actually TT+, AQo, AQs+, KQs and he instead hit 43.6%. That difference (although small I admit) is likely what will separate a soso grinder from a world class player in the years to come

and that difference is just at 5%. The variance in a 30% range is larger and on select flops have punishing differences in flop connection (% hit of opponents range)

One problem I see with your plan is that you're assuming that your opponents x% is going to be equivalent to your model's x%. How would you guarantee this is the case? How do you know players will choose their ranges based on your rules?

Hi Everyone:

While this is certainly a good question, I don't think it matters much as long as the top 5 percent of hands listed is a good list that clearly represents top notch hands as do both lists in the original post.

The reason for this is that when you look at statistical distributions, they tend to be shaped like bell curves and do not come to sharp points at their maximums (or minimums). Stated another way, statistical distributions tend to be broad.

Translating this to poker, when you look at two distributions of hands that each do a reasonable job of representing the same thing, such as the two 5 percent distributions in the original posts, or two 10 percent distributions, or two 20 percent distributions, and so on; when analyzing how to play in a particular situation, it should almost never matter which one you use; and in those cases where the suggested play is different, they should each have approximately the same expectation.

Best wishes,
Mason

The perfect way of building a range is by building a ranking of all hands from +EV to -EV in the specific situation you are in.
. That is, there is a different ranking for each specific situation, although many are similar, and as Mason said, in most cases they are so similar that you can use common rankings from some other very specific situations (Sklansky chubukov is one, even though it is very different from other rankings.)

I disagree with Mason in that in some specific cases, the ranking you choose makes a lot of difference. Most notably cases where blocking cards make some obscure hands much better than more classical hands.
For example, if 100BB heads up you are 3bet by an opponent who only 3bets with AA, KK and low suited connectors, but folds the weaker hands. The ranking you should put yourself in would be (AA,A2s,A3s etc...). Thus, if your opponent sees that you are 4betting top 15% in this situation, he would be incorrect to assume you are 4betting with pokerstove's 15% (77+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,QJo), and would be more on point by assuming you are 4betting with the actual 15% of this situation's ideal ranking(AA,A2o+,A2s+)

Using an approximation like PokerStove's ranking is fine mostly. But it won't provide a perfectly correct answer.

EDIT: To clarify, range and distribution of hands refer to the same thing. But ranking would refer to the order of the hands from best to worst in the given situation, independently of which or how often they are played.

Could also be 88+,AQs+,KQs,AKo or JJ+,AJs+,KQs,QJs,AQo+.

There's no way to figure that out without using a HUD that shows you a range that this specific player open raised from a specific position.

As soon as ranges are not 100% static anymore, you need to see how often he raises a specific hand from that position and build a range from there. Maybe from UTG+2 he raises 77 60% of the time and T9s 50%? Now it's getting pretty difficult calculating that without some software assistance.

In the next step, you'll need to figure out if the range is dependent from other players at the table. Maybe he raises A4s from MP if both SB and BB have VPIP >20% AND BU has VPIP <20%?

Good luck doing that without huge sample sizes and some smart software.

You bring up a good point.

Back when I was playing tournaments, I looked into optimizing push bot ranges because the optimum push range was dependent on a players calling range.

I thought about approaching it as finding optimum vs optimum and try a recursive method to see if it would converge. (Still not sure if it does)

However, once you take ICM into account it became too big a problem for anything but sit-n-go's and I didn't have much interest in those at the time so I never followed through.

Trying to solve the entire problem for all situations for NLH becomes too gargantuan to solve.

Just looking at the permutations of various table layouts considering all variables turns it into a lot of problems to solve for. Something like a 10 wheel combination lock with each wheel ranging from binary(such as facing all-ins) to infinity(deep stacks). Have you ever had to fear the reverse implied odds of second set? i.e. deep enough to make it a factor.

That's only looking at it from a pre-flop point of view. Then you need to approach it with looking at all streets adding even more wheels.

Backwards or forwards, it's just too big to solve for in NLH. That's assuming it's solvable which I don't think it is as far as finding convergence which I think was Mason's point.

BTW, Bill Chen did create an algorithm for Limit which is a much easier problem to solve. Even so, I think he took more of a subjective approach rather than an objective one but, I think it's the right approach.

Heat maps were generated with Poker Solver.

Here I broke down 6 range rankings. Note that each started by using different units. For example, Pokerstove uses Eq (I believe, I still have the disabled copy) Chens formulas gave power rankings, PokerRom showed EV.

Most of these ranges came from a tool called Insta-Range which came from one of these forums. I'll need to dig for the sources and will follow up, but I know that Skalansky/ChubaKov came from this forum some time ago.

I converted them all into percentiles in order to be consistent. Basically just rank each combo then take the percentile as the sum of combos at or above each ranking divided by the total number of combos.

Notice that Skalansky/Chubakov is very similar to the HU vs Random ranking. The reason for this is that it was a blind vs blind scenario from memory.

Notice that Poki-Bots ranking seems to be influenced pretty heavily on Poker Stove's ranking of vs 3 random.

It appears to be equity vs N Random hands. Based on the results, I highly doubt that post-flop action was taken into account.

Next we can see Bill Chens ranking for limit holdem which is what you get after plugging all combos into his formulas. Notice that this is the first ranking system that attempts to solve for equity beyond pre-flop equity. Unfortunately I seem to have lost the link but I believe it can be found in Wikipedia, from my notes:

Found a link:
http://www.simplyholdem.com/chen.html


Finally, we get "Real World Equity" which was from a database provided by Poker Room. Unfortunately I don't know how they collected these numbers, i.e. Limit? NL? 6-max? FR? stakes? all of the above?

They only provided a sample size.

Link to the stats:
http://www.pokerroom.com/poker/poker...alue&x=43&y=11

Chen is for Limit. And I've heard the pokerroom.com is mostly limit history too (it was years ago before NLHE dominated). That's why they both value suited connectors so much higher than the others, because drawing hands have more power in Limit. So if you take out those two, the others look remarkably similar, and those two on their own also look very similar. This makes Mason's point, that it doesn't matter enough to significantly affect your results. Just pick the model you like (from the NLHE ones) and go with it. Creating a super-model that combines them all situationally might be useful for computer play, but not for humans.

Link to Insta-Range Thread by HyperMegachi in the software forum:

http://archives1.twoplustwo.com/show...fpart=all&vc=1

However, in the thread, I saw the ranges came from Curious123

Skalanski-Chubakov link was broken but just Google it and you'll find plenty of references.

The Poki-Bot range turned out to be my own reference because Billings, Davidson, Schaeffer & Szafron didn't fit into my application. Sorry about that.

Here's a tip: Long titles don't work well with drop down lists lol.

If you don't know, Poki-Bot was the first, it think? AI bot for Limit Holde'm that they developed. Therefore Poki-Bot was an assumption on my part since I didn't have a direct source at the time.

Link provided by Curious123:

http://www.propokertools.com/orderings/heordering.txt

actually linked to ProPokerTools which refered to another link:

http://pokercoder.blogspot.com/2006/...-of-hands.html

Which wasn't the source but did refer to the source finally:


This is where the links dead ended because the next ling was broken.

I'm not sure, but I think Poke-Bot was a HU limit bot but this research refers to 9 handed play so Poki-Bot may have been an inappropriate name.

So apologies to Mr. Billings, Mr. Davidson, Mr. Schaeffer and Mr. Szafron but I didn't have anything released yet anyway. I hope none of you is a woman but... poker and AI... I'll take my chances.

Now how the heck do I fit that name into my drop down list...Maybe I'll just use "*PokerAI Guys" with a footnote.

It seems to be something like an AI approach to solving for pre-flop equity vs 8 random ranges established as the initial condition.

Why didn't they just run a Monte-Carlo sim? IDK, I'm sure Monte-Carlo was around back then but the Poker Stove tool, as I recall, didn't have Monte-Carlo when it was first introduced.

Running a complete solution for 8 random ranges would take a long time, especially back then.

Also they did account for ranges folding pre-flop so it's not actually the same thing but the results are very similar.

Notice that, as I predicted, Post flop action was not actually taken into account

Thanks for the info. and I'd agree on all points.

Wow, this explains soo much, I kept looking at them as mostly FR NLH 100BB and there were things that I was having trouble with vs what I would have expected.

Also, I thought Chen was overvaluing those AXo, KXo hands, lol.

It looks like he did a reasonably good job on the rest though.

Almost everything written about hold'em starting hands before 2003 was about Limit Hold'em. This gets confused all the time when beginners go looking for starting hand guides. In NL big cards increase in value and drawing hands decrease in value.