Mathematical Models & Turbo Texas Hold 'em

I thought I would start a new thread since there seems to be a slight misconception in our attitude towards TTH and othe simulators.


First, a mathematical model is suppose to be a simple equation that represents a complex activity fairly well. The greatest exaple of a mathematical model from history is the orbits of the planets. For thousands of years mankind could not project how the planets moved in the sky. Finally Copernicus came along and said they revolve around the sun in circles.


Notice that he was proposing a simple mathematical model. Today we know that this model isn't completely accurate since the planets actually orbiit the sun in eliptical orbits, not circles, and they are subject to other forces such as the gravitational pull from other planets. But to answer the question in the time of Copernicus, the circles did just fine.


Unfortunately, not everything has a simple mathematical model available that does a reasonably good job, and this is certainly the case with poker. I think we all agree that hot and cold simulations while a simple model will produce many inaccurate conclusions. So a very complicated model that imitates real play very well becomes needed to answer precisely some of the questions that someone like Backdoor wants to ask.


But I think that this creates a sort of a "Cache 22" situation in that to produce algorithms that play well well enough to come to precise conclusions about difficult hold 'em questions you will need computer routines that produce expert play, and the only way you can write these routines (using a decision tree approach) is to already know the answer. This is one of the reasons why I am cautious in accepting any conclusion from TTH which differs from what I already know.


For example, I believe that TTH will show that KTs under the gun is a better hand than JTs. Yet, I know the opposite is true, every competent player that I know will agree with me, and David has written a good explanation why this is the case. So when I see results from TTH like this my conclusion is that it tends to over value high cards. This may have something to do with it not accounting for extra bets that late position players can sometimes make.


So in conclusion, while I agree that TTH is a good tool for someone starting out, and that it can sometimes be used to support conclusions that expert players already know to be correct, it can also be high risk to accept it's results when it differs from what top players will tell you is correct. In time, it might eventually get there, but I don't think it is there yet.

A question about Catch 22.


If you faced a program that played almost as well as you did,

vs the same type of opps that you did,

what hands, if any, would you test?

Mason,


Interesting post. I have studied TTHE, written a bot in the style of TTHE, and I know a fair amount it.


1. In the tightest TTHE pre-built profile preflop, that of Lash/Conan, KTs and JTs are treated exactly the same under the gun. This profile sees about 22% of the flops, pretty agressively, but is a bit too loose in my opinion. But here's the deal: It can be changed in 2 seconds to treat KTs less favorably than JTs. My bot does, so does my copy of TTHE on my home computer. Other changes can be trivially made too. Which I have. My bot and my Lash+ both play about 19% or so.


One can simulate with this better version and get very useful information. Also, between these sims, and some of the posts here, (David's recent post on T9s is an example) my play has gotten WAY better.


2. After-the-flop-play can likewise be easily changed. For instance, I found that post-flop play of the strongest, most agressive player, Lash, was not agressive enough sometimes. I changed him (in my bot's version). Then I made the same change in TTHE too in 2 seconds (from a menu, so you do not need to be a computer genius to do this).


Ok, so TTHE is not that bad, and it is not a toy, and it plays pretty well. What is needed to make it way better as a tool, and some of this is in V4:


3. It needs to randomize. I did this for my bot in a very short time, and TTHE does allow random play in V4. So you can say call with 22 on the button 75% of the time but fold the other 25% (just an example). Wilson's encoding of this is really good.


4. It needs to account for how many players are left: I cannot find this in V4. It is in my bot, and made a big difference.


5. It needs to account for history of the players who it has played, and make some moves based on that. My bot does a very limited amount of this, TTHE doesn't at all that I can tell. The U of Alberta programs do a huge amount of player profiling, and they can 'guess' at levels of 70% what some players have in some situations...not too bad. This is useful, but in my opinion some of this is already encoded in the rules. So I am not pressing this in my bot too much yet.


Mason, I was surprised that you thought that it valued KTs higher than JTs; that this implies that you didn't know it was programmable (from menus) to do a lot of what a person wants, so I think you should get it and understand it better before commenting much more on it. While it is (or may be) not good enough on the 'how many players left' issue, and I believe it doesn't play well enough to beat your average 15-30 or 30-60 game, it is a much better tool than you think.


Mark

It is because precise math calculations and computer simulations are so assumption-driven, that I prefer to solicit the opinions of good players when it comes to answering some of these holdem problems and in assessing the advice in many poker books, including 2+2 books.


Let us take your example of JT suited versus KT suited when under-the-gun. Debates may rage back and forth about which is hand is better. But in a typical middle limit, ten-handed, holdem game, most experts would fold both hands from the under-the-gun position. This is because in middle limit games many pots are getting raised and there are usually no more than three players taking a flop on average. Many pots are heads-up from the start. JT suited in particular does not play well in a heads-up setting when out of position against a good player marked with a decent hand. Coming in early with these hands is a very speculative play because you have no idea how much it will cost you to take a flop or how many opponents you will have. These hands simply don't play well in early position in a typical middle limit game. That is why virtually every good player I have talked to, including many with a national reputation, muck these hands upfront.

This is completely off topic but I comment on a couple of things you say:


"This is because in middle limit games many pots are getting raised"


...and later...


"JT suited in particular does not play well in a heads-up setting when out of position against a good player marked with a decent hand."


I find these two statements somewhat incongruous. Pots are getting raised and the raiser is marked with a decent hand. The implication is that more often than not, there will be hand behind you that is better than JTs. I find that this is simply not usually the case. The conclusion I therefore draw is that often, the raiser has worse cards than my JTs and he is raising simply because of position.


Of course, the positional disadvantage you have is a fairly significant factor but still I don't consider it big enough to constantly fold JTs UTG.


Mind you, I play in a game where the postflop play of most of my opponents is no doubt way worse than your typical opponents in the LV games so maybe my thinking is skewed.


Whatever the case, I play JTs up front FWIW.

This is completely off topic but I comment on a couple of things you say:


"This is because in middle limit games many pots are getting raised"


...and later...


"JT suited in particular does not play well in a heads-up setting when out of position against a good player marked with a decent hand."


I find these two statements somewhat incongruous. Pots are getting raised and the raiser is marked with a decent hand. The implication is that more often than not, there will be hand behind you that is better than JTs. I find that this is simply not usually the case. The conclusion I therefore draw is that often, the raiser has worse cards than my JTs and he is raising simply because of position.


Of course, the positional disadvantage you have is a fairly significant factor but still I don't consider it big enough to constantly fold JTs UTG.


Mind you, I play in a game where the postflop play of most of my opponents is no doubt way worse than your typical opponents in the LV games so maybe my thinking is skewed.


In any event, FWIW, I play JTs up front FWIW....of course, that probably explains why I hardly have a household reputation let alone a national one.

of course, that probably explains why I hardly have a household reputation let alone a national one.


You're too humble.


We all loved you on Gilligan's Island.

Just circles didn't "work fine" even in Copernicus's time due to retrograde orbits. He used circles on circles to show how this could happen.

If TTH plays almost as well as you do then you are in trouble. I think that virtually all posters on these forums will tell you that if you can't crush it you have no chance to beat even a low limit casino game.


However, to answer your question there are no hands that I would test since identifying small differences between starting hand values in hold 'em is virtually worthless to improving your overall results once you have mastered a good starting strategy. Your increased earn will come from improving your play from the flop and beyond.


By the way, the above paragraph would not apply to seven-card stud.

The reason I think that it values KTs as higher than JTs is that whenever I have seen simulation results from someone who has used it to rank hands this is the conclusion that I always see.


Also as you point out TTH has gotten better with each version. That's an important point.


By the way, since I haven't looked at the current version, and don't have the time, is the advice from the advisor still lacking or has it improved as well?

"But I think that this creates a sort of a "Cache 22" situation in that to produce algorithms that play well well enough to come to precise conclusions about difficult hold 'em questions you will need computer routines that produce expert play, and the only way you can write these routines (using a decision tree approach) is to already know the answer."


This makes the assumption that poker isn't governed by a fairly small number of "laws" whose interaction is complex as physial simulations do. I believe this is incorrect. The interaction between the "laws" is the complex part, not the laws themself.


"For example, I believe that TTH will show that KTs under the gun is a better hand than JTs."


This statement isn't consistent with you comments above about decision trees. If you separate out the simulation engine as TTH and the models as user provided then TTH doesn't know anything about KTs vs JTs. Instead certain models will indicate the ranking of the two hands is one way or another depending on their assumptions.


"So in conclusion, while I agree that TTH is a good tool for someone starting out, and that it can sometimes be used to support conclusions that expert players already know to be correct, it can also be high risk to accept it's results when it differs from what top players will tell you is correct. In time, it might eventually get there, but I don't think it is there yet."


This seems completely inconsistent with the rest of what you've said. Instead your earlier paragraphs would indicate that TTH as a simulator should be eschewed by beginners because of its complex use whereas it might be useful for experts who can set it up correctly and sanity check its results.

"But in a typical middle limit, ten-handed, holdem game, most experts would fold both hands from the under-the-gun position"


This statement is absolutely rediculous. Most experts would play both hands in full ten handed games. In a very tough where the players are aggressive the KTs would probably be folded and a JTs might be folded by an expert in an extremely tough game where his opponents not only play well but are highly aggressive. There are some $80-$160 games like this. But in the games you play, $10-$20 through $20-$40 here in Las Veags, the JTs should never be folded if first in UTG as long as you are good enough to play it well.

What I meant is that TTH has value for a beginner but this value has nothing to do with producing simulations. I think the main value for a beginner, and this is something very worthwhile, is that it can help someone get a feel for what it is like to actually sit in a hold 'em game. When you are first starting out that is very important. I didn't mean to imply that beginners should even be doing simulations since identifying small differences in hand values should have virtually no meaning for them.


Thanks for pointing this out.

I think what is happening here is that Jim's mentor is simply hung up on no limit and pot limit concepts. In those games for instance having a positional disadvatage is more significant than limit. That's because the penalty for being raised is greater and the before the flop raiser, who would likely be in late position if you limp in UTG is less likely to bet automatically. Notice that if you limp in early, are raised by a player behind you who will make an auto-flop bet, then for reality you are in late position, not him. This routinely happens at limit, but not in the other forms of hold 'em.


Here's a simple example. You are playing limit and limp in UTG with JTs. Now a good player on your left raises. You don't like it but you never fold. However, if it was no limit, that raise could easily be for four or five times as much as limit, now you either fold or put a lot of money in where you could easily be making a very bad play. So the penalty for limping up front when things go wrong with JTS or a similar hand is much greater.


"of course, that probably explains why I hardly have a household reputation let alone a national one."


But I bet you have lots of friends...especially in the poker room --- Just kidding.

"That is why virtually every good player I have talked to, including many with a national reputation, muck these hands upfront."


This statement is also rediculous. That's because there are virtually no players who specialize in limit hold 'em and who would be considered experts who have national reputations. That's because almost all the players who have this type of reputation have gotten it from tournaments, and all tournaments, as I have written before, degenerate into a weak form of no limit hold 'em.


Most limit players that I know of who have national reputations are those like myself who have made reputations by writing. A good example is John Feeney. If you have read his book there can be no question that he must play hold 'em extremely well. But if he hadn't written that book most people would have never heard of him (except for those who come to Two Plus Two). The only other good limit players who I can think of who are fairly well known are this way because we have mentioned them in our writings. That's why for example some people know who Cissy Bottoms is, but how many people have heard of her husband who also plays very well or even know that she is married?

Mason writes:


So a very complicated model that imitates real play very well becomes needed to answer precisely some of the questions that someone like Backdoor wants to ask.


But I think that this creates a sort of a "Cache 22" situation in that to produce algorithms that play well well enough to come to precise conclusions about difficult hold 'em questions you will need computer routines that produce expert play, and the only way you can write these routines (using a decision tree approach) is to already know the answer. This is one of the reasons why I am cautious in accepting any conclusion from TTH which differs from what I already know.


And Sklansky wrote:


Posted By: David Sklansky

Date: Friday, 23 November 2001, at 2:56 a.m.


In Response To: Re: T9s- Is it a Call?- The Answer (NotReadyForPrimeTime)


My assumptions were for the purposes of this calculation. They were not how I thought most raisers would play. They were designed to show that T9 should call even if these adverse assumptions were true. More reasonable assumptions would make the call even better.


As Sklansky tried to say, proving that under this type of simplifying assumption a call was good with T9s, it follows that the call is good when other assumptions.


The assumptions need not be reasonable and need not simulate real play. Such calculations are very useful in poker analysis.


Naturally, since simulations are actually applied math, if you have the correct simplifying assumptions, you get correct baseline strategies.


So the statement that one needs to "already know the answer" is clearly incorrect.


For example, I believe that TTH will show that KTs under the gun is a better hand than JTs. Yet, I know the opposite is true, every competent player that I know will agree with me


Jim Brier also states that his "poll' of players indicates strategies regarding JTs differ greatly from that of Malmuth. We see why this type of analysis is getting fuzzy.


Jim Brier also reported here on the forum that a panel of experts stated they thought play in HPFAP with T9s with a board of A 6 7s was incorrect. I will not pull a Mark Glover and get the quoted text, but I believe you stated that you wanted him to show logically and mathematically why this was wrong, and the panel of experts was not presuasive.


So which is it? The panel of experts or the logic and math of Sklansky?


This is one of the reasons why I am cautious in accepting any conclusion from TTH which differs from what I already know.


I prefer a scientific approach in these cases. While its tempting to have unproven beliefs and set out to prove them, I think its better to start with trying to gather evidence in as unbiased way as possible, then make conclusions FROM the evidence. Making conclusions, then gathering the evidence has many problems. I'll let others elaborate.


Second, your statement about TTH and KTs vs JTs demonstrates your lack of knowledge in this area.

TTH does NOT show anything. What the simulator does is what it is told to do. It does not overrate pairs or high cards, the way the profiles are presently programmed might do that. This of course, can be changed.


The KTs vs JTs is trivial and not worth further comment.


In conclusion, while EV equations and equivalent simulations use various assumptions, they need not simulate expert play. They need in some cases to have an infallible baseline, and other cases just approximate how your average opponents play. This is what David Sklansky has done here in the post below, and what I did with my simulation.


There is a moral to this story, as Sklansky stated concerning the T9s thread below, if you think you can use judgement(I will add on my own, 'or merely poll experts') in cases like this, you are sadly mistaken.


Regards.

It has been pointed out to me that my statements above may be coming across in more of a negative personal fashion than I intended. If this is the case I apologize since I do not mean to belittle Jim Brier in any way. However, I do have problems with the accuracy of his statements and feel that they needed to be corrected in a very clear and concise manner.

but did you notice that there is a spell checker right next to preview message and post message.

That's won of are knew addatives and it works grate. Of corse I have to sea it two use it.

Mason,


I do not see how those sims could have been done...


About the newer advice, I don't know yet. I haven't had time to test much. I *do* know that the ability to play the same hands as the advisor to see who does better and then get critiqued by "sidewinder Sid" is pretty good. I believe that 90% of the people I have played against in Casinos would not beat the advisor.


Mark

TTH helped me as a beginner to get a feel for what marginal hands were absolute dogs and what hands had some value.


After the flop, I quickly learned to kick its $@s so badly that it soon bored the s%$&t out of me, and made me think a $125/hr. expectation in 20-40 was easily achievable.


This at a time when I played mostly 3-6, 1-4-88 and 6-12 hold em and averaged only a few dollars an hour, which I quickly lost in bigger games.


I doubt that it will ever beat me or any breathing player for more than five hours.


Therefore, results of its simulations cannot be all that valuable.

Chris,


I know EXTREMELY well where TTHE has short comings (see above), but you make it sound terrible, which it isn't. Which version did you use? What players did you sit in the game? Did you program a stronger (more random in V4) Lash or Conan to make your life more difficult? I have, and it has helped my game a lot. I cannot kick it's a#% as easily as you do, but I am kicking butt in an online 10-20 game (playing at the speed of a Casino 20-40 or 30-60 in terms of money on the table per hour), where most of the players are weaker than my Lash+ IMHO. And playing against a table of strong random Lash+'s and Conan+'s, etc, helped me greatly.


Mark

Hmm. . .


I only recently got a new version of it, and haven't played it that much or fiddled with anything. My old version (which I stomped to the point of boredom) was the first windows version. So it could have gotten much better.


I am going to play it right now . . .


C

Let us know your opinion. If it has gotten much better that's worth knowing.

Chris and Mason,


If it was the first windows version, then it is way better now (V4). But you have to customize it a bit (from menus) to get most value. Make the toughest player a bit tighter preflop and a little more agressive in some situations... and then you can play, run sims, etc, and it is useful, even to a good player.


Mark

"That's why for example some people know who Cissy Bottoms is"


people only know who she is because she has a name befitting a porn star, and a raunchy one at that. once youve heard her name in a post, or wherever, youll never forget it.


sorry that is of little use...


i, too, think jim's generalizations are untrue and of little value. for instance, his assertion that most mid limit games are 3 handed or less on the flop and beyond is just plain wrong. havent you ever played 15-30 in L.A. jim??