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Poker AI
I'm curious what people here might know about the current state of the art in Poker Artificial Intelligence programs. It seems to me that this is the biggest long term threat to online poker. Automating the interphase with the online poker site's software might require some specialized work on the installed code. But that aside, I can't help but think current state of the art poker AI programs could easily beat nearly all the games played online by humans. I doubt the sites themselves would want to be running such BOTs, but what's stopping ambitious gamers from plugging them into their Online play?
Anyone know the word going around on this? |
Re: Poker AI
Hi PairTheBoard,
I play NLH tournaments, and perhaps I'm underestimating expert systems (which is what you mean, not AI), but I just don't think a computer opponent would be much of a worry in the games I play. Perhaps it's because NLH offers a wider range of possibilities and rewards intuition and creativity more than limit hold'em or stud, but I just don't think it likely that even a state of the art expert system could be in the same league with a good NLH player. Cris |
Re: Poker AI
I disagree, I think a well written computer program would be a disater to online poker.
A program that could customize its play based on opponents past play history, could use game theory optimally, and could play without any tilt-issues would destroy online poker, even NL. Sure some players might be able to beat it, but I would guess that even a moderate computer program would be capable of beating 90%+ of the players online. Think of it like chess, most chess players even ones who are pretty good probably can't even beat a storebought chess program set to max difficulty. If the poker equivalent of Deep Blue (or whatever the top chess program) were to be developed, I would be quite worried. |
Re: Poker AI
Beating 90% of the players online might make you a breakeven player but hardly a winner.
You have little understanding of how difficult it would be to write a poker bot that could beat even 50% of the online players. The incomplete information is overwhelming. An exception would be if your bot played against the same 9 oponnents in a 10 handed ring game for 50,000 hands or so. Then it might become one of the best players in this particular game but would go back to being mediocre if several new players were introduced. This would only be true of an extremely advanced AI program far more advanced than even POKI. |
Re: Poker AI
[ QUOTE ]
Beating 90% of the players online might make you a breakeven player but hardly a winner. [/ QUOTE ] I think this is a huge exageration. [ QUOTE ] You have little understanding of how difficult it would be to write a poker bot that could beat even 50% of the online players. The incomplete information is overwhelming. An exception would be if your bot played against the same 9 oponnents in a 10 handed ring game for 50,000 hands or so. Then it might become one of the best players in this particular game but would go back to being mediocre if several new players were introduced. This would only be true of an extremely advanced AI program far more advanced than even POKI. [/ QUOTE ] I never said it would be easy, but I think you are vastly overestimating the ability of an average player. Someone could probably write a bot that just plays ABC by the book poker and it would probably be a winner. If the bot could be tied into a database similar to pokertracker and played max-tables 24/7 it would have a huge database of player information to work with. As for POKI, I think it would probably do pretty well in an online game. |
Re: Poker AI - Prisoner\'s Dilema - Genetic Algorithm
I really don't know. I'm just throwing out ideas. There IS a difference between Poker and Chess. The Forte of chess programs like Deep Blue is their Vast memory of previously played "Book" openings, and their ability to compute all possible move combinations for many moves ahead. In poker it's maybe not so clear how important "Book" moves might be nor is it so clear how to compute all game theoretic future repercusions of Poker "moves". Still, I can't help but recall the widespread Human bluster and bravado years ago, about how computer programs would NEVER be able to beat the best human chess players. Although Kasparov can still make it a match with the best computer programs, the writing is pretty well on the wall for the human vs. computer chess question.
Yes, an "Expert System" trained by a world class player would seem the natural way to produce a Poker program that might imitate AI. But that may not be the only solution. In many ways I think Poker is similiar to the Prisoner's Dilema. Two accomplises in a crime are interrogated. If neither rats on the other they both go to jail for say 1 year. If one rats on the other but the other remains mute, the rat gets say 0 time and the chump gets say 4 years. If they both rat they both get say 2 years. You can change the numbers to make it a better game if you want. A challange was issued by Scientific American years ago for people to submit algorithms to play essentially this game against a population of other algorithms. Two algorithms from the population randomly meet. If they co-operate they both gain a little. If one co-operates and the other betrays, the deceiver wins more while the fooled loses. The alogirthms retain memory of at least the transactions they are involved in. One way of playing this game, rather than just tallying points for each algorithm, is to let the population evolve by rewarding successful algorithms by reproducing them. I believe such a "game" has many of the same dynamics as Poker. For example, there are Non-Transitive aspects to it. A does well against B and B does well against C. But C may badly beat up on A. It was somewhat suprising that out of all the complicated algorithms submitted for the contest, the ones that did the best were the simple "Tit for Tat" programs. You co-operate, I co-operate. You betray, I betray. Algorithms that tried to improve on this had a lot of trouble working well against the while population. A very suprising later finding was that the Genetic Algorithm could be applied to this problem with considerable success. Strategic variations on the Tit for Tat were encoded into 16 bit strings. A population of such 16-bit Sring algorithms were run using Genetic crossover and mutation to search for imporved versions. The champ was then run against the human alogrithms and did considerably better than the best Tit for Tat human champs. I suspect something like this could be done for Poker to produce a viable Poker AI program. |
Re: Poker AI: An Essay on the Topic
I think many of you are missing several key differences (and potential advantages) of an automated online poker player, or ‘bot’. At the root of this misunderstanding is not realizing that a bot essentially represents a paradigm shift in what constitutes an effective player.
One: The ability to calculate the odds of every situation with perfect accuracy and make other strategic adjustments as ring size and table texture change. Given the huge player turnover in online games, the speed of the games (40-100 games an hour) human tracking of these changes is near impossible for the vast majority of players. Two: The ability to play 24/7/365 with no fatigue, steaming etc. i.e., without emotion. Three: Since your win rate requirement can be much lower than when you are playing in person, the bot can play much more patiently than any human player ever could. Since all current poker theory is based on squeezing the maximum out of every situation (i.e., to be as efficient as possible), an approach not driven by this consideration, in effect, allows for the creation of a hitherto unknown style of expert player. Four: The ‘soft’ skills the expert has built up over many years are irrelevant, since no-one ever sees your face, tics, expressions etc. (I, for one, have played tens of thousands of hands without ever once sitting down at a real table). Five: Anyone who can develop the technology to create a bot of this type could also design an automated opponent tracker. The tracker would sit in on tables gathering information on all the players. Over a period of a few days substantial statistical dossiers on the playing habits of the regulars would be available. This information ,would be updated in real-time during the games and coordinated with table texture stats. Five, the bot would roam the online HE tables looking for soft games. (Visualize the snoop-and-attack drones in the Matrix!). Six: Simple random behavior would be built in to vary response times and other electronic tells making the bot virtually indistinguishable from its human competitors. Given the tens of thousands of highly inexpert human online players, a few bots of this type would be able to survive indefinitely. Now two challenges: One: Tell me what you think of the preceding argument. Two: How would YOU design the bot to take maximize its superhuman capabilities? |
Re: Poker AI: An Essay on the Topic
"human tracking of these changes is near impossible for the vast majority of players." And for a bot as well, at least in real time.
" The ability to play 24/7/365 with no fatigue, steaming etc. i.e., without emotion." A losing bot will simply lose more money and quicker. "Since all current poker theory is based on squeezing the maximum out of every situation (i.e., to be as efficient as possible), an approach not driven by this consideration, in effect, allows for the creation of a hitherto unknown style of expert player. " The reason this is so is to win in the first place, not to win more. Without the ability to "squeeze" those extra bets you go from a winner to a loser. "The ‘soft’ skills the expert has built up over many years are irrelevant..." So is this statement, think about it. "Anyone who can develop the technology to create a bot of this type could also design an automated opponent tracker. " Not to mention they would also be able to design a device that spins straw into gold which by the way would be more profitable. "Over a period of a few days substantial statistical dossiers on the playing habits of the regulars would be available. This information ,would be updated in real-time during the games and coordinated with table texture stats. " Incomplete information, enough said. "Now two challenges: One: Tell me what you think of the preceding argument." I did. " Two: How would YOU design the bot to take maximize its superhuman capabilities?" I have no time for this, I am still working on that straw to gold problem. Do you know where I might find a little fella named Rumpelstilzchen? That being said I believe a winning bot is possible, just not with today's technology. |
Re: Poker AI
Some previous threads to check out:
http://www.twoplustwo.com/forums/showthreaded.php?Cat=&Board=genpok&Number= 186902 http://www.twoplustwo.com/forums/showflat.php?Cat=&Board=inet&Number=159004 http://www.twoplustwo.com/forums/showthreaded.php?Cat=&Board=books&Number=1 90061 http://www.twoplustwo.com/forums/showthreaded.php?Cat=&Board=genpok&Number= 197446 Through these links, check out some posts by "Botman" who claimed, plausibly, to have made a successful bot for lowlimit online play. Also, there was a fascinating article produced by the University of Alberta people that won a prize at an AI conference. The paper was about software they wrote to play "pseudo-optimal" headsup limit holdem. Theoretically using game theory you could play "optimal" headsup holdem (i.e. a mixed strategy against which no other strategy would have positive EV). However, the computing power to obtain the optimal strategy is much too large, so the University of Alberta team reduced it by several orders of magnitude by making some simplifying assumptions. Most of the paper was about why they thought their assumptions would not cause very much deviation from the true optimal strategy. |
Re: Poker AI
Great list of links M.B.E. Thanks. It looks like they're working on it but have quite a ways to go yet. The Acespade software looks interesting. I wonder how it would do at a Party Poker 2-4 game.
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Re: Poker AI
[ QUOTE ]
Think of it like chess, most chess players even ones who are pretty good probably can't even beat a storebought chess program set to max difficulty. If the poker equivalent of Deep Blue (or whatever the top chess program) were to be developed, I would be quite worried. [/ QUOTE ] But it is really quite different from chess, since most of the advantage that computers derives in chess comes from: 1) Their ability to store in memory tens of thousands of previously played or analyzed opening moves. 2) Their awesome processing power, which allows them to analyze a tremendous number of ply to the nth degree, which allows them to see with perfect accuracy potential positions which might occur. The above two advantages are even more pronounced with programs that utilize a "brute force" over a selective search paradigm, with the latter being more analogous to human thought processing. The one advantage good human players in poker would have against a computer is that there is not an insurmountable degree of memory or computation required. Whereas a computer could probably make a fair amount of money playing limit poker against loose computation by just by maximizing value betting, I don't see how a computer would necessarily beat the Monday night 2+2 table. |
Re: Poker AI: An Essay on the Topic
OH: Thanks for your comments. You are probably correct with most of your comments.
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Re: Poker AI
Thanks. I was familiar with most, but there were some interesting new ones.
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Re: Poker AI: An Essay on the Topic
Brianmarc -- put me in the camp of believing that it's possible (given the present state of computer science) to design a bot that would beat most ring games, even at high limits. In other words I think a well-programmed computer would play poker as well as the best ring-game players in the world (although it would play differently). The only way to beat it would be through cheating (i.e. collusion).
You just have to consider the PsOpti program designed by Darse Billings et al., which beat The Count at headsup limit holdem. The Count is the winningest shorthanded limit holdem player online. And PsOpti did not use opponent modeling. Think of how good a program would be if it did. As for no-limit and pot-limit, I tend to think that a computer could play these well too, although it might require more power. The one part of your post I didn't understand was this: [ QUOTE ] Three: Since your win rate requirement can be much lower than when you are playing in person, the bot can play much more patiently than any human player ever could. Since all current poker theory is based on squeezing the maximum out of every situation (i.e., to be as efficient as possible), an approach not driven by this consideration, in effect, allows for the creation of a hitherto unknown style of expert player. [/ QUOTE ] Why would you not want to have the highest possible win rate? I can think of a few reasons, e.g. create deception, reduce variance, not-get-caught, but in general it seems to me they wouldn't be worth it. |
Re: Poker AI: An Essay on the Topic
That's funny, I was thinking exactly the opposite. Where the topic of discussion is "where are we going with this in the future", I don't see that a reply of "we aren't there now and other people will be somewhere else" adds anything of value to the conversation.
The statement that those who could make a winning bot could make more money designing other kinds of program (which is how I interpret the spinning straw into gold comments) in my view overlooks the essence of the spirit of invention. Society has advanced because of people responding to their own muse, not that of other people or what other people think would be more profitable. Few Nobel laureates started down their path to the prize by saying, "Yeah, this is it. This is what's going to make me rich." Broadway is full of some of the greatest actors in the world, who could have made more money in film. Medical progress has been the result of scientists who chose not to make more money by developing a better diet pill, or a pill that helps people quit smoking. While a poker bot certainly isn't something that will make the world a better place, it is a fascinating problem of the highest order. If we're focusing on a bot that uses artificial intelligence (as opposed to just a really well written program) then in my view poker is the perfect platform -- it strikes a very nice balance between game theory and the inherent flaws in human behaviour. My view is that given the problem posed -- a bot that can beat the crap out of the online games that currently exist -- the current processor speeds, storage capacities, and memory size are more than sufficient that such a thing is possible, particularly given how much time the sites give each player to make a decision before timing him out. 'hoof |
Re: Poker AI: An Essay on the Topic
Translated in into strategy, the bot could afford to pass up opportunities that the regular player could not. one simple example: require a premium on pot odds to go for a draw.
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Re: Poker AI: An Essay on the Topic
Brian,
Here is a Yahoo discussion group you might like to join which will be better able to answer your questions. PokiPoker Group |
Re: Poker AI: An Essay on the Topic
[ QUOTE ]
Translated in into strategy, the bot could afford to pass up opportunities that the regular player could not. one simple example: require a premium on pot odds to go for a draw. [/ QUOTE ] But why? Just to reduce variance? |
Re: Poker AI: An Essay on the Topic
to simplify programming or avoid possible counterstrategies (assuming not headsup)
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Re: Poker AI: An Essay on the Topic
I am surprised at many of your responses which relate to application of computer technology, particularly as you are in the field yourself.
Considering the computing power and algorithms recently put to use against the world chess master, and drawing, the only thing stopping the same happening in poker is focus and access to the leading edge technologies that IBM have employed. And then again, who would know if someone is not already doing it. They certainly wouldn't publicise it, and they wouldn't be be showing players winning millions. It would be a gaggle of golden geese hatching several small golden eggs, a few hundred $'s at a time. |
Re: Poker AI: An Essay on the Topic
It is precisely because I am in the industry and it's applications to gaming that I hold my opinion. Programming Big Blue to bring chess Grand Masters to a draw was certaily quite an achievement.
If you spend enough money most anything can be accomplished, most anything other than a successful poker bot that is. [img]/images/graemlins/smile.gif[/img] I did state that it will occur someday, just not today. To adequately argue this point a pure definition of winner needs to be accepted. I simply am using the one quoted by Mason Malmuth (1 BB per hour winner in mid limits and higher). If you wish to offer me your definition as being more liberal my response would likely change. EDITED BELOW: Actually now I seem to recall that Mason's definition might have been for an expert. If so I must reconsider my position. |
Re: Poker AI: An Essay on the Topic
If that's what MM says, and it's OK for you, then I suggest you both need to get out more. That's old B&M thinking. All that expertise; all that practice and the best you can do is $40 or $60/hr. There are so many online games that are much easier than that where a more reasonable goal is more like 3-5 BB/hr.
Actually, BB/hr is not a good way to measure success. $/hr is the only thing that matters. |
Re: Poker AI: An Essay on the Topic
I've been working on such a project on/off for about a month.
Designing an AI pre/flop and flop strategy based on EV calculations and heuristics is pretty trivial. Turn and river actions are even more straightforward. I find the most difficult portion to design is the "tracker". The toughest part (and it's a major problem) is the difficulty in finding "maniacs", "calling stations", etc. and finding a precise adjustment to the bot's default play in these scenarios. |
Re: Poker AI: An Essay on the Topic
The thing is, if you could program a bot that could win even a fraction of a bet/hr, say 1/3 BB/hr you could make a fortune because you could run multiple bots playing multiple tables, and they could play 24 hrs a day, every day. Because of the greater volume of hands the bots could play, you might not mind sacrificing the small edge plays that would increase the difficulty in making the program (but would probably also increase the variance) because even if their hourly take is small compared to a typical winner they would be capable of playing so many more hands than a human that they would still make more. Of course this could be used to detect them, but you could get around that by running your computer players in shifts (even adding in random starting times and session lengths with in a reasonable range) and always having a number of them going at the same time.
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Re: Poker AI
I'm a Computer Science student at Carnegie Mellon. I am 100% positive an AI poker player could be written to consistenly beat a LLHE game, and what's more, could be written relatively easily. Here is why:
We all seem to be forgetting the FTOP (which I'll reinterpret for the sake of this thread) At any point in a hand, there is a play that is absolutley the correct play Only knowing the other players' cards prevent us from making this play every time. In other words, a lack of information. If a bot were able to catalog the play of a large number of players in a meaningful way (which it easily could) it would be better suited than any human player to determine the correct play. Remember, most opponents in LLHE do not vary their play enough not to be easily read, if you are willing to pay enough attention. Everything else is just programming heurisitic rules, and this is the simplest form of AI. Anyone who thinks that the processing power doesn't exist for this is out of their mind. I'm sure a program such as the one described above could easily run on a 500mhz pentium with 64m RAM. In fact, I had a highschool programming project to create an AI hearts player, and it was easy to make it able to beat most human opponents. Those were run on a system simmilar to the one described above. Just reading/replying to this thread has almost given me the incentive to write one. Let me reiterate, it's not only possible, it's easy. |
Re: Poker AI
I have to agree with jknupp. I'm still a poker newbie, just started the 1/2 tables at Party.
But, I still I believe it would be possible for a program to consistently beat the low limit games on the net. I would not be surprised if there are 'bots' that play and win. A chess program and a poker program are very different. After playing the standard opening moves (the same ones human chess players play), chess playing programs use Min/Max algorithm find the "correct" move. This involves a brute force method of searching through a tree of possible moves to some depth. While the nodes grow exponentially, it does not take much computational power to defeat a mediocore player. My Palm Pilot would beat me at chess pretty regularly if I set the depth high enough. That being said, a poker bot doesn't need super computer. I don't think it would be that difficult, certainly not impossible to create a Bayesian Network to make correct plays to beat mediocore players. Gren |
Re: Poker AI
"I'm a Computer Science student at Carnegie Mellon. "
After your first sentence above I lost interest. |
Re: Poker AI
Now what sentence in what post might that be?
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I built a poker bot... Read This for more info.
I've come to believe that many people do not understand how easy it is to build a poker bot. I have built a poker bot and well to be quite honest, its been losing money. I tried letting it play the 3/6 and 2/4 tables with just good hands but that won't cut it... what limit will? .50/1.
For the last few days, its been playing .50/1 and the variance as been quite huge. My bot plays on PartyPoker and it has the current abilities: -Can tell how many people are seated at a table -Can Autojoin tables if (numplayers <= 6) -Plays only good cards (this REALLY needs to be worked out) My next version will support the following: -Has the ability to do players tracking (I can track a users play [fold,call/check,bet] on the preflop,flop,turn,and river - then analyze that play and determine the best strategy) -Neural Network Analysis - Based on http://spaz.ca/aaron/poker/nnpoker.pdf - Neural Networks have really good prediction capabilities and this paper describes that Honestly, I'm trying to build a winning poker bot... but so far I've come up short... I haven't played .50/1 long enough to see if it can win but only time will tell. -jdarwin. |
Re: Poker AI
There were a couple of interesting threads at the Zoo speculating about bots in the 1/2 games at Pokerroom:
http://forumserver.twoplustwo.com/sh...202#Post401202 http://forumserver.twoplustwo.com/sh...;Number=413073 |
Re: Poker AI
Let's say this whole Poker Bot thing starts happening for real. Can sites such as UB and Party stop bots or will they even know if Bots are being used?
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Re: Poker AI
One possible way in stopping bots is by popping up messages that confuse or mess up a bot's current status. This would be annoying but it is still a preventable measure against bots.
However, I could certainly program part of my code that allows me to search the screen and detect anomolies. If found, it would autoclick the region to get rid of the box, to continue playing -- thus it's not foolproof. Other methods including measuring how much a person plays online - for example I've run my bot on Party for atleast 2 days straight... but no one has complained or emailed me about it. Unusual ... yes... But it's not that wierd - If the operators of such sites see that players are playing for weeks on end without disconnecting one could say that a bot could be employed... However, I could still get around this by allowing my bot to play on certain times of the day (b/c the night is juicier than the day) and I could disconnnect my bot for several hours of the day and then reconnect. overall there isn't really a way to stop a bot... b/c if there's a will there's a way = the hacker mentality. -jdarwin |
That would be a waste of time
It would be foolish for the cardroom to devote energy to reduce it's own revenue. Bot's are effectively players, bad bots = bad players, ok bots = ok players, good bots = good players:) except they play much more often and help fill the tables.
A cardroom can still maintain its integrity and say that they don't use bots to enhance the efficiency of their cardroom, but that doesn't mean they can't benefit if there are artificial players induced by a third party. Besides, it's difficult enough to become a winning human player, much much more difficult to become a winning bot player. Don't reply to me, I won't post again. |
Sure you can play poker poker, but can you win?
Take away the ability of the human to use intuition, psychology judgements, and feel to play. Worst than the unimaginative rock.
Then this task becomes much much more difficult than to be a winning player yourself. Don't reply to me, I'm outta here. |
Re: Sure you can play poker poker, but can you win?
of course i'll reply [img]/images/graemlins/smile.gif[/img]
Poker is not an intuitive as people make it out to be. If a neural network can stimulate and figure out that a player will Fold, Call/Check, or Raise -- 85% of the time what does that say? That says that bots can win in the long run... coupled with the fact that it can't go on tilt, it doesn't give a [censored] about losing to good cards, it can play "forever", and it practically can't be detected. Instituting random play isn't hard, opponent modelling has already been done, and now the programming and bots are coming. The papers have been written folks. All that's left to do is to take them and turn them into working poker bots -- which I guarantee there are out there. I'm practically 75% done with mine... all that needs to be done is add opponent modelling and bluffing and bam... money in my pocket. go figure. -jdarwin |
Re: Sure you can play poker poker, but can you win?
I call BS.
The fact that the NN has 85% accuracy does not mean that it's going to be a winning player. I'm guessing here, but I wouldn't be surprised if you could get something like 70-80% by just folding when you have nothing, raising with a big hand, and calling with the rest (i.e. most decisions are easy). And this is almost certainly not enough to beat most games. Post some results of your bot, maybe even some hands that it played. That will be interesting to see. I'm sure your bot can beat the really soft games. I think Poki will probably beat the really soft games (I don't know if those kinds of results have been published). But I have yet to see something that can beat a game where the players use their brains more than occasionally. |
Don\'t reply to me!
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Re: Poker AI vs player adjustments on the fly
I do agree that a program could be made to play agaisnt and beat low limit hold'em BUT i don't beleive that it could ever beat any skilled player or group of skilled players, especially short handed. The reason is this.
I jump on to an 10 player empty table and someone else and a player joins me, i quickly notice the player will check call anything and only bet if he/she has somthing, I lose 10 BB learning this info and then start to exploit it praying that the table stays heads up. I win my 10BB quickly but then 2 other players join the table. watch a couple of hands and started playing. 1 played all hands preflop, rarly raised but would fold post flop with nothing and raise with top pair. the other was tight passive and could be bluffed. Now the trick is not to look if you put a bot in my place but see if you could predict my play as any of these players before i adjust. for 7 hands i played like a calling station heads up just to see what my opponent was betting with. and even reraisd with nothing to see his reaction. afterwards i am pushed out by any bet of my opponent and bet anytime i have anything and my oponent checks or calls. when two other players join i bet no matter what vs 1 of them and call and raise alot of preflop situations that will put me heads up with the guy who can't play preflop. NO AI COULD FIGURE OUT WTF I WAS DOING WUSING THE NUMBERS. i might play a hand with 72o from UTG one time and show it just to scew evryone up. so there is AI will have one of these two problems vs any specific human player that dosn't play like a bot. If it collects data long term and uses it vs a skill player it will not notice any short term varience in the players game and usually that will be enogh of an edge for any skilled player. IF I NOTICE THAT THIS BOT OR PERSON ALWAYS CALLS MY bluffs i will bluff less and make it pay, and soon and if it has recorded 20 000 hands that i have bluffed less often and it won't stop calling my good hands until the statistical numbers tell it too wich could take forever. 2. if it uses only sessional data it won't have enough info to make any good assumptions on my play And the one problem AI will always have is it is a BOT if it always folds Top pair top kicker to 3 bets you better belive a skilled player will figure it out quickly. the bot may eventually, after a number of losses, figure out that it needs to start calling it down but the first time it does the player may adjust and make it call him down when it really is facing a set or better. you could make a machine that makes these human dicisions quickly but it is not trivial and the machine would have two little info to make them correctly by the numbers |
Re: Poker AI vs player adjustments on the fly
Why would anyone go to the trouble of building a bot and then play it in unfavorable situations (SH and against experts)? There are many more weak than strong players, esp. in low-mid limit games. No reason to go anywhere elsa. BTW: Same applies to humans; why not look for the easier games and feast there?
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