The Mathematics of Poker

[FoxInTheHenHouse]

[ QUOTE ]
finished the book, though i haven't read this thread.

for NL cash (i play small stakes), experience is much more important than the math approach presented in this book.

after having played hundreds of thousands of hands of NL cash, i don't need math (beyond basic probability/odds) to make decisions. if i am the pfr and the caller leads small on the flop, they have a draw or marginal hand and will fold just about every time to a raise. if i raise pf, unless the opponent is shortstacked, a reraise is never AK/QQ or worse - they call with those hands. if someones minbets turn, they have a draw/marginal hand. if someone raises a three flush board on the river, they have the nuts or 2nd nuts. if i am the pfr and get check-raised on the flop or turn, my top pair (especially if it is a K high board) is no good. and so on. i don't use math for any of these because the scenarios keep repeating themselves.

so, i would definitely try to get as much experience as possible for NL rather than try to use the book's math approach of "opponent will bluff X% of the time here yet fold to a rebluff Y% of the time, so I have to win Z% of the time for it to be profitable." that appraoch is fine once in a blue moon against a tough player but for 99% of the hands, using hand reading that comes with experience is the way to go in my opinion.

[/ QUOTE ]

Thank you!! This is the first post in this thread that makes any sense!!

[WRX]

Bill and Jerrod, I hope that you're still monitoring this thread, even though it's been quiet recently.

I've had lots of thoughts and questions popping up in my mind since I started reading your book, but have waited to finish it before writing anything. It took me a LONG time to work through it all--but I think the patient approach has been rewarded a greater understanding of the game.

Taken as a whole, I believe the book is an impressive achievement, a real landmark in poker writing. You've looked at so many topics that any player who wants to be successful needs to think about--not just questions of how to mix value betting, bluffing, calling, and folding, although study of those questions form the heart of the book. Even though it offers few recipes for play, it's a book that any serious student of poker MUST tackle. And especially, all future authors who hope to write about poker at anything but a superficial level will have to understand these concepts. That's just obvious.

I do feel the need to mention one serious reservation--which is that the book suffers from way too many typos. The errata sheet you've put up only scratches the surface. I hope that for future editions, you'll bring in an editor to proofread the copy carefully. That's not an easy task for a work this technical.

While probably every chapter led to questions in my mind about practical application to playing poker, one topic seems especially important. In the final chapter, you revisit the question of the benefits of aspiring to optimal play, versus the benefits of exploitive play. This may be the easiest-reading chapter of the whole book, but it makes sense only with the background of all that has gone before. You make the vital point that while optimal strategies are elusive and difficult to ascertain (and don't even exist in any rigorous sense in multi-player games), not all suboptimal strategies give up the same value to superior opposition. A balanced strategy remains unexploitable, so that opponents' potential edge against that strategy is limited. You advance this as an argument for striving to play strategies that are at least balanced.

Furthermore, you show that in many circumstances, an optimal or near-optimal strategy gives the player an edge against non-optimal opposition. Obvious examples would be playing against opponents who put money in the pot with trash starting hands, or who call with near-hopeless hands on the end. On the other hand, there are certainly money-making opportunities for the player willing to put aside the quest for optimal play, and to exploit an opponent's unbalanced play.

These points and others raise what may be the most significant question facing a player who wants to find the best money-making opportunities. For the kinds of games commonly found today (habits and caliber of player), in public card rooms and on the Internet, where does the most money lie? Is it in playing fundamentally sound, "near-optimal" poker? Or is it in recognizing flaws in opponents' play, and altering one's own play to exploit those flaws?

Certainly the answer might differ greatly between games--for example, a game in which all players are experienced and reasonably observant, and capable of counter-exploitation, versus a game full of unskilled, casual gamblers.

Any thoughts on this topic would be welcome.

[MichaelBolton777]

[ QUOTE ]
Bill and Jerrod, I hope that you're still monitoring this thread, even though it's been quiet recently.

I've had lots of thoughts and questions popping up in my mind since I started reading your book, but have waited to finish it before writing anything. It took me a LONG time to work through it all--but I think the patient approach has been rewarded a greater understanding of the game.

Taken as a whole, I believe the book is an impressive achievement, a real landmark in poker writing. You've looked at so many topics that any player who wants to be successful needs to think about--not just questions of how to mix value betting, bluffing, calling, and folding, although study of those questions form the heart of the book. Even though it offers few recipes for play, it's a book that any serious student of poker MUST tackle. And especially, all future authors who hope to write about poker at anything but a superficial level will have to understand these concepts. That's just obvious.

I do feel the need to mention one serious reservation--which is that the book suffers from way too many typos. The errata sheet you've put up only scratches the surface. I hope that for future editions, you'll bring in an editor to proofread the copy carefully. That's not an easy task for a work this technical.

While probably every chapter led to questions in my mind about practical application to playing poker, one topic seems especially important. In the final chapter, you revisit the question of the benefits of aspiring to optimal play, versus the benefits of exploitive play. This may be the easiest-reading chapter of the whole book, but it makes sense only with the background of all that has gone before. You make the vital point that while optimal strategies are elusive and difficult to ascertain (and don't even exist in any rigorous sense in multi-player games), not all suboptimal strategies give up the same value to superior opposition. A balanced strategy remains unexploitable, so that opponents' potential edge against that strategy is limited. You advance this as an argument for striving to play strategies that are at least balanced.

Furthermore, you show that in many circumstances, an optimal or near-optimal strategy gives the player an edge against non-optimal opposition. Obvious examples would be playing against opponents who put money in the pot with trash starting hands, or who call with near-hopeless hands on the end. On the other hand, there are certainly money-making opportunities for the player willing to put aside the quest for optimal play, and to exploit an opponent's unbalanced play.

These points and others raise what may be the most significant question facing a player who wants to find the best money-making opportunities. For the kinds of games commonly found today (habits and caliber of player), in public card rooms and on the Internet, where does the most money lie? Is it in playing fundamentally sound, "near-optimal" poker? Or is it in recognizing flaws in opponents' play, and altering one's own play to exploit those flaws?

Certainly the answer might differ greatly between games--for example, a game in which all players are experienced and reasonably observant, and capable of counter-exploitation, versus a game full of unskilled, casual gamblers.

Any thoughts on this topic would be welcome.

[/ QUOTE ]


Interesting post. Ive followed this thread a bit, and have waded through the book for awhile. Obviously, the authors are very intelligent and have a solid fundaental understanding of poker.

At the beginning of the book, the intro says that ultimately the point of what they are trying to do is to teach us how to make money playing poker- extraneous math will be left out! I am no genius, but can follow the examples and toy games at least to some degree. I still have no idea, though, how any of this will help me make more money playing poker! It is difficult enough for an average joe like me to follow the numerous toy games and hypos, let alone create my own that will teach me exactly what range of hands is optimal for me to raise from the sb in limit holdem, or how often to check raise the turn w/ air on a paired board, etc, etc! Again, I respect the knowledge and effort of the authors (and am also a big fan of hosstbf!). I am just frustrated b/c i dont see how i can possibly use this info to build a coherent, solid, and closer to optimal strategy specifically for limit holdem (or NL, which i am trying to learn as well). I heard that hoss basically patterned his limit game off of this book. He must be a super genius!

Would appreciate it, Mr. Chen, if you could give your take on how a guy like me (w/ good basic math skills, but certainly nothing extraordinary), could best utilize the info in your book to specifically improve and adjust his limit (or NL) play to progress toward that elusive impossibility of 'optimal' play.


**Also, as above poster said, I am curious about the difference between optimal and exploitive. From my reading, it seems that optimal is ultimately superior (but not certain whether this is what the authors are saying- it seems obvious that in certain situations exploitive play would be far more +ev). I, too, would love to hear Bill and Jerrod discuss when and why it would be best to use an optimal approach, or to use an exploitive one. (btw, am i correct to assume that optimal play does not require any reads or attention to the play of your opponents? i.e. no stats, reads, etc...if so, this seems very strange to me, since basically every good player on 2 plus 2, every poker writer, etc, always takes an exploitive approach, distinguishing lags and tags, etc, etc, ad infinitum....)

Would love to hear some thoughts on this, guys. Teach me to play like hoss!! Thanks.

[Pirana]

Can anybody provide a numerical example of how to calculate the Malmuth-Weitzman or Malmuth-Harville equity formulas in Chapter 27? Would the Malmuth-Harville Formula give the same answers as using an Independent Chip Model calculator?

Using an ICM calculator, here are the equities for the example in the chapter:
Player 1 - $1,511.17
Player 2 - $1,416.08
Player 3 - $1,139.07
Player 4 - $933.69

[eurythmech]

Where can I find these Heads-up charts everyone's talking about? I've been looking for them in the book for quite a while now [img]/images/graemlins/frown.gif[/img]

[rakemeplz]

p136

[blues_boy_b]

p.253:
[ QUOTE ]
If he plays y weak closed draws, he will have a made hand 1/9y+1/10 of the time on the river

[/ QUOTE ]

i guess 1/10 are the flush draws and 1/9y are the weak close draws which are made hands. But i dont understand why it is exactly 1/9y, where does the 1/9 come from? :/
Can someone exlain it to me? [img]/images/graemlins/smile.gif[/img]