Poker Philosphy

ImperatorImperator Red Chipper Posts: 898 ✭✭✭
Philosophy of Strategy

I want to add an addendum and a course correction to my recent podcast appearance that Zac entitled Poker Philosophy.


The Kelly Bet, Bankrolls, and Stacks
First I want to talk about the Kelly Bet or the Kelly Criterion, which is a mathematical theory in the context of intertemporal portfolio theory.

The notion of the Kelly bet is a foundation to where I believe poker players should start constructing a top-down strategy. (I also have a bottom-up strategic philosophy of strategy which I didn't get to in the podcast, but more of that later.

I have been thinking about bankroll, and the proportion between stack protection and stack threatening ever since I started to think seriously about constructing my own strategy. The Kelly Bet has become an essential part of my top-down philosophy of strategy. I have been searching all over for the use of the Kelly Bet in poker literature. I developed my own theories about it and since I didn't find anything I thought that I might be one of the first people to talk about the Kelly Bet in relation to buy-ins in poker. Since there are a lot of finance and investment types in poker I knew there must be others who thought about there bankroll in terms of "intertemporal portfolio choice." But I didn't find anyone who talked about this openly... until now.
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Recently, I finished reading Matthew Janda's new book, No-Limit Hold'em For Advanced Players. In that book Janda references The Intelligent Poker Player by Philip Newall. When the book arrived in the mail I found that Newall's book devotes a whole chapter to the Kelly Criterion. The chapter is called Bankroll Management and Shot Selection. Since most of this chapter coincides with my own ideas of "top down" and retro-analysis strategy I would like to acknowledge that Philip Newall got there before I did. This is not surprising to me. Somebody must have thought of these things before I did. I recommend his book for this chapter alone.

On the other hand for me the Kelly Bet is a cornerstone for my top-down idea of strategy and not simply an after thought for bankroll management and shot selection.

Ideally, if we could figure out the game completely, we should cut-out our ranges, bluffs, and bet sizes through a whole session so that the proportion between threatening other people's stacks and protecting our own stack reaches an optimal strategy of exploitation and protection. This is only possible if we take into account the relation of our stack to the Kelly Bet.

This sounds very abstract, but in fact the whole debate between schools of strategy only makes sense from this point of view. The strategic landscape is skewed by the fact that we don't look at the game from this point of view.

My basic point is that neither Game Theory nor the Exploitive School nor the Old School of Playing the Player can be understood without this top-down point of view. And the top-down point of view meets reality only when we take into account some idea of portfolio theory, specifically the Kelly Criterion.

Comments

  • ImperatorImperator Red Chipper Posts: 898 ✭✭✭
    Science, Laws of Nature, and Theories;
    Compared with
    Games, Rules of the Game, and Strategy


    The second thing I want to put down here is a more precise statement of the comparison between theories in science and strategies in game. I'm putting this down, not because I wish I could include it in the podcast like the above, but only as a matter of precision.

    In science we investigate a "reality" or a system. We try to discover the rules that that govern that system. We do this by abstracting and circumscribing a portion of that reality so that we can discover the rules that govern that system. We don't study "the reality-itself" but rather the abstraction of the system.

    In other words we try to reduce and simplify reality into something from which we can derive "usable" rules. We make models to test the rules of our abstract system. We may call the rules of the system "the laws of nature" or something else it doesn't matter what we name those rules of the system. The better our models become the better we can define the rules or laws of the system. That complex of discovered rules and constructed models is what we call "a scientific theory." And the more we can create ways of testing that theory by experiment or against natural phenomena the better our confidence in the theory.

    The important point I want to make here is that we don't actually study "reality" but a simplified version of reality, a model of reality, which we then test against our notions of the world. A frictionless plane is a fictional model that we use to create a mathematical theory of reality.

    (Note: In the current state of poker theory much of GTO descriptions are less "real" than frictionless planes but that doesn't mean they aren't useful.)

    Now lets compare the scientific way of discovering the rules of a system with "the rules of the game."

    When we create a "rule-bounded game", the rules of the system come first and not last. The "reality" of the system that we call the game grows out of the rules of the game. Often we do not know what "reality" will grow out of the rules that we invent for a game. People invent rules and if the boundaries of the rules allow for enough complexity in an environment that is specific enough, then the game will allow for an evolution of strategy beyond any individuals thought.

    Think of those stud players who first started playing NLHE. When they started to play our game decades ago how could they understand the reality of our game as it stands today? They could only understand it from the bare rules. They could not could not conceive or predict the complex strategies that the game would require. They couldn't because it was the working out of tactics and strategy from within the rules that the current reality of our game was created. It is an artificial reality bounded within an artificial economy. It is important to note that by playing with in the bounds of the rules of the game and studying the game we create the ecology or cosmos of the system we call the game, and we do it collectively by competing against each other and studying together. The way we play the game creates the reality of the system.

    The thinking player creates models of the game in his head and those evolving models of the game are what we call our strategy. You can see from this statement that the concept of "theory" in science is equivalent to "strategy" in gaming.

    The more accurate the model a player can construct in her brain of the actual game she plays the better her strategy will become. Potentially at least.

    Why potentially? Think of this in terms of science. The person who develops a good theory of a system is not necessarily the kind of person who can think of the kinds of tests that will help to validate or confirm the theory. Einstein needed Eddington.

    In poker we don't have the luxury of this kind of division of labor. The person who has a good model of his game in his head also has to be the kind of person who implements the strategy at the table. Implementing a strategy is a bottom up problem; it is a day-to-day translation of the model of the game in our head into our actual praxis at the table, hand by hand. A lot interferes with this translation... quickness or slowness of thought, pattern recognition, various kinds of tilt, etc.

    To sum up; with games humans are able to turn reality upside down. In a sense the same part of our minds that invented rule-bounded games is the same part of our brains that would create the scientific revolution. But the difference is in games we start with rules and create the artificial reality that constitutes the practice of the game. We then investigate that reality to create our strategy.

    Science works the other way around. The "reality" is before it. We have to circumscribe it and try to discover the rules of that describe the abstraction of that reality. In other words there is something game-like in our definition of rules and models. But it is a game right-side up.
  • ImperatorImperator Red Chipper Posts: 898 ✭✭✭
    Top-Down Strategy and Bottom-Up Strategy: Actual and Game Theoretical

    I didn't have time in the podcast for thoughts about the difference between top-down strategy construction and bottom-up strategy construction. They are both essential.

    Also, I didn't have time to talk about what I call actual top down strategy and theoretical top down strategy.

    In short I want readers to consider the following Game Theory scenario: We are in a heads-up pot with 100 big blinds each and we have a constructed balance ranges on all streets where we potentially get to the river with a final all -in bet and each party is indifferent to a call or a fold. In this scenario we see the half-dozen frictionless planes of Game Theory as currently applied to poker.

    I came to the conclusion in my own game play that there is an actual "top-down strategy" and there is a theoretical top-down strategy. The actual and the theoretical are not mutually exclusive but they are different.

    I will give you an example from our Red Chip website: @SplitSuit and @Luke Haward separately put out product on bluffing theory and practice. Both use Heads-up pots as examples.

    The reality of all games that I play in are multi-player pots.

    The idea of a Heads-up pot is almost the equivalent of a frictionless plane for me, and yet the HU pot is a theoretical construct which is important as a simplifying model for poker study and investigation.

    I would say, even with trying to find the pain threshold, I encounter heads-up pots preflop less than 10% of the time. I encounter Heads-up pot on the turn about 65% of the time. And I encounter heads-up pots on the river about 85% of the time. If you look at these numbers your rate of bluffing. These are approximate percentages. Given this situation ones continuation range in any given pot will be a lot lower. One guarantee of spewing is to play multi-way pots in a manner that would be theoretically sound as if you were playing a HU pot.

    And the lower the stakes of the game the more likely you are going to be in multiplayer pots practically all the time. (Example: I had AA on the button in an underground game with a straddle. 5 people limped in the pot so I bet 15x the straddle hoping to go heads-up. The big blind called and so did all 5 limpers. What are you going to do? But this is the reality of many Underground New York games and it is idiocy to ignore the reality of my ecosystem when constructing a strategy.)

    So actual bottom up play is a lot different than theoretical bottom-up play. Thus when constructing actual bottom-up strategy the primacy of hand reading, range "(intelligent) guessing", player tendencies, and tells becomes very important. Knowledge of the ecosystem of our play is also important. And yet all of the ideas of balance and denial of equity still apply.

    Bottom-up strategy construction perforce involves a strategy that puts primacy on "reading" boards and people and ranges in multi-player pots with stack sizes that vary from 40 big blinds to 500 big blinds. This is how actual games play in my ecosystem.

    I talked some about top-down strategy and how differs from how I think most players think about it, but I just want to make clear that both game theory ideas and exploitive ideas are base lines but are both basically "fictional models" of our game. The actual top-down and bottom-up strategies you have to construct inside your own brain.
  • Jónas SJónas S Red Chipper Posts: 202 ✭✭✭
    Very nice podcast and quite interesting topic. I'm glad you could add the thoughts to this thread that you didn't have time to talk about on the podcast but I feel like you delivered it very well. It's up to us now how we apply your thoughts!
  • RedRed Red Chipper Posts: 2,354 ✭✭✭✭
    Great brain food. Thanks @Imperator
  • zampana1970zampana1970 Red Chipper Posts: 549 ✭✭✭
    So great - I really can't wait for your book, @Imperator

    The Kelly Bet - is this the same idea as in podcast, where our stack is essentially one bet and we are looking to realize that bet as best we can as much as we can as successfully as we can - ie: play for stacks?

    "Think of those stud players who first started playing NLHE. When they started to play our game decades ago how could they understand the reality of our game as it stands today? "

    These NLHE players today, how can they possibly understand the reality of the game 20 years hence, once the AIs get a hold of the thing?!? :-)

    Multi-player pots - I was thinking this the other night when I was playing online and EVERY SINGLE PLAYER open raises and then some significant portion of the time is either 3bet or called by the BB. Online I think we see a lot of HU flops because that tighter more aggressive style of play is conducive to the online experience (being online is a more aggressive experience all round). Plus I think you find more thinking, studied players online, which makes it a different game from the live, multi-way, I-didn't-come-to-the-casino-to-fold-poker. So I think you're right, if what you're saying is we have to have two different strategies for the two different game states. You can't just grove a strategy that relies for HU play the majority of the time if your game is only HU in the minority.

    Question becomes too - could you implement a multi-player tuned strategy in the online environment, if it's near impossible to implement a HU strat live?

    Really great stuff...
  • kenaceskenaces Red Chipper Posts: 1,503 ✭✭✭✭
    I will have a listen to your podcast soon :)

    On Kelly
    - Newell is one of my favorite poker authors - it is just too bad he a LHE guy since that game is dead/dying
    - best chapter I have read on bankroll is in MAP
    - problem with applying Kelly to poker is that stakes(especially live) doesn't scale smoothly so choosing to bet a certain % of BR for given situation and accurately estimating the EV is almost impossible. That said it is a useful framework to use to think about bankrolls.
  • ImperatorImperator Red Chipper Posts: 898 ✭✭✭
    edited November 2017
    kenaces wrote: »
    - problem with applying Kelly to poker is that stakes(especially live) doesn't scale smoothly so choosing to bet a certain % of BR for given situation and accurately estimating the EV is almost impossible. That said it is a useful framework to use to think about bankrolls.

    I agree and disagree. If you are talking about any single bet you make at the table then of course I agree. But if you are talking about your willingness to buy-in as a single Kelly Bet then I think the calculation is not only possible but the ground of strategic thinking. (Well it is the ground of my top-down strategic thinking, at least.)

    So here are the reasons why I disagree:

    First and most importantly is this; each buy in is a single bet or investment and if we look at the investment properly within an historical context (our own win-rate is one historical context) then we should be able to understand the percentage of our bankroll we can risk on this particular session. Newall doesn't cover this but I believe we can also calculate the proper ratio between protecting our stack and attacking the stack of others by properly considering the Kelly Criterion. In other words the proportional risk to our whole stack (our investment per session) is embedded into the idea of the Kelly Bet.

    One possible reason why Newall did not extend the idea of the Kelly bet to strategy is because he is a Limit Hold-em player. It is my contention that No-Limit games of all kinds are uniquely tuned to Kelly bet considerations because they require you to acknowledge the risk to your whole investment: i.e. to factor into your strategy that your "first bet" is your buy-in and that your risk to your whole stack is calculated by your willingness to attack the stacks of other balanced against your need for stack protection. In other words from my point of view the Kelly Criterion is a way to ground our strategy.

    At least, I have put this idea at the foundation of my own way of thinking about strategy. As a rule of thumb I would advise many poker players to do the same thing. (Of course some don't need to do this because they have no bank roll concerns or no bank roll; or because their skill-set is so far beyond those they play with that they don't need to think too much about variance.)
    kenaces wrote: »
    - best chapter I have read on bankroll is in MAP

    I'm very bad on abbreviations. What are you referring to when you say "MAP"?

    Is it Chen & Ankenman's Mathematics of Poker? I agree that their bankroll chapter is very good. But shouldn't the abbreviation for this book be "MOP" and not "MAP"?

  • kageykagey Red Chipper, KINGOFTAGS Posts: 2,241 ✭✭✭✭✭
    @Imperator
    not sure that qualifying your buy-in as a bet in proportion to your BR is a valuable gauge. As I'm sure you've heard Berk say - when our BR is so small, the risk of ruin is negligible because it's a small percentage of our net worth.
    if I were to lose my BR... if I remain committed to playing full time, I'd find the means to get more (beg, borrow or beg!)

    So for me - if I'm in a good game - and it makes sense to cover the drunk donkey who's playing with a sum that's ½ or more of my BR... I'm not backing down. (as long as I feel comfortable making the right plays regardless of bet sizes)

    A lot of the BR management stuff has really come from the online players - where they would want to reduce their exposure when playing multiple tables. But in the live realm... I may be wrong... but I don't think it applies, or should apply so strictly.
  • kenaceskenaces Red Chipper Posts: 1,503 ✭✭✭✭
    Imperator wrote: »
    Is it Chen & Ankenman's Mathematics of Poker? I agree that their bankroll chapter is very good. But shouldn't the abbreviation for this book be "MOP" and not "MAP"?

    Yes I was talking about the Chen book
  • kenaceskenaces Red Chipper Posts: 1,503 ✭✭✭✭
    I had listen to the Pod, and I feel like you might be missing a few things on Kelly Criterion.

    on Kelly
    - It is NOT just risk only ~5% of BR like you said
    - The entire point of Kelly is to scale bet sizing with your estimate of the edge/odds you are given. If you have a very large edge with favorable odds the formula will tell you to wager WAY more than 5% of BR
    - So the challenge with applying this to poker is that you have to 1)know your edge/odds 2) scale up/down our bet sizing each time our BR changes and our edge/odds change. Doing this with any kind of precision is impossible.
    - I think Kelly and the dissucusion of cut-off brankrolls from MoP are great lenses to use to examine how we think about BRs but they are only part of a larger picture that needs to be considered.

  • kenaceskenaces Red Chipper Posts: 1,503 ✭✭✭✭
    Imperator wrote: »
    kenaces wrote: »
    - problem with applying Kelly to poker is that stakes(especially live) doesn't scale smoothly so choosing to bet a certain % of BR for given situation and accurately estimating the EV is almost impossible. That said it is a useful framework to use to think about bankrolls.

    I agree and disagree. If you are talking about any single bet you make at the table then of course I agree. But if you are talking about your willingness to buy-in as a single Kelly Bet then I think the calculation is not only possible but the ground of strategic thinking. (Well it is the ground of my top-down strategic thinking, at least.)

    In above post I am using Kelly in the context of BR or buyins, not for each individual bet. So in order to use this as your "BR system" or primary strategic lense you have to know your expected edge in all games/line ups. Yes you can rely on past expericence/data for some of that but this is a very very rough estimate. I can tell you with high confidence what my WR is at 2/5NL but my estimate of WR at 1/2NL would just be a guess as I have very little data on it. I can also tell you my WR at 5/10NL but this would also not be as clear as the lineup of the game can vary so much that there are games where I have nice WR and other games where I might have a very small WR. So while I feel like I am decent at estimating my edge as I have many years experience I would still be just guessing.

    If we are talking online it is even harder as bb/100 WRs are much smaller and also way harder to accurately predict.

    Another problem is the "scalability" issue. If I am live player my choices are 1/2, 2/5, 5/10, and the occasional bigger games. So even if you can estimate your WR better than me you are left with a formula that might be telling you to play .50/1 or 6/12.....

    I think it is important to consider ROR, utility of money, cut-off BR, depelting or non-depleting, and psychologial factor in addition to Kelly.

  • chip_hoggchip_hogg Red Chipper Posts: 82 ✭✭
    Still catching up on podcasts, and I have to say -- you really missed an opportunity for a dad joke. Focusing exclusively on one game at a time makes you "mono-maniacal"? No -- it makes you monogameous!
  • NYCRyNYCRy Red Chipper Posts: 336 ✭✭✭
    edited November 2017
    "I think it is important to consider ROR, utility of money, cut-off BR, depelting or non-depleting, and psychologial factor."


    Would you mind doing a quick explanation of the above terms?

  • kageykagey Red Chipper, KINGOFTAGS Posts: 2,241 ✭✭✭✭✭
    Ryan A wrote: »
    "I think it is important to consider ROR, utility of money, cut-off BR, depelting or non-depleting, and psychologial factor."


    Would you mind doing a quick explanation of the above terms?

    I think ROR is "risk of ruin" and BR is "bank roll"
    I also think he meant to write "depleting and non-depleting"
    you can wikipedia some of these terms to get an in-depth explanation

    he's basically saying that there are more factors that should go into your decision of what portion of your bankroll you should play with depending on if you've got other sources of income, and if losing will affect how your play...

    but I'll let @kenaces tell you in his own words...
  • kenaceskenaces Red Chipper Posts: 1,503 ✭✭✭✭
    kagey wrote: »
    Ryan A wrote: »
    "I think it is important to consider ROR, utility of money, cut-off BR, depelting or non-depleting, and psychologial factor."


    Would you mind doing a quick explanation of the above terms?

    I think ROR is "risk of ruin" and BR is "bank roll"
    I also think he meant to write "depleting and non-depleting"
    you can wikipedia some of these terms to get an in-depth explanation

    he's basically saying that there are more factors that should go into your decision of what portion of your bankroll you should play with depending on if you've got other sources of income, and if losing will affect how your play...

    but I'll let @kenaces tell you in his own words...

    +1

    Utility of money means that we have to recognize that managing a 1K BR is different than managing 100K BR

    cut-off BR formula is covered in MoP and is a way to examine move-up decisions (i.e. would we play 5/10NL on BR X, if the 5/10 WR is $60/hr and the 2/5 WR is $50/hr)

    depleting BR is one where you are taking money out to live every month, and it has a HUGE impact on ROR calculations
  • NYCRyNYCRy Red Chipper Posts: 336 ✭✭✭
    Ok I'm actually reading MOP now so that should clear things up, thx
  • silverrosesilverrose Red Chipper Posts: 11 ✭✭
    Hey @Imperator --

    I just finished listening to last week's Poker Philosophy podcast, and found it very enlightening. I'm a college professor at a small liberal arts college, and although my formal academic training is not in philosophy as such, I am fortunate (because of the nature of the program in which I teach) to spend a great deal of time studying philosophy (ancient, medieval, enlightenment, and modern) with my undergraduate students. In addition, my philosophic studies, like yours, frequently have a great deal to offer to my life as a poker player. So a podcast entitled "Poker Philosophy" naturally pushed all of my buttons.

    So of course, I'm a long time poker player. I multitabled online limit holdem until it got hard in about 2006, and I also played live low limit holdem in southern California cardrooms until it got scarce in about 2009. Then I shifted almost exclusively to live NL holdem, which I continue to play today. Sometimes I dabble in live PLO or PLO8 if the games are good (and they almost always are) and if my bankroll can manage the massive swings.

    I'm not a professional poker player because I have a full time teaching job and a demanding family life. But I play as much poker as my time allows, which means sometimes means I take extended breaks away from the game. I've been profitable at poker for many years because live poker players at the small to mid stakes were, and continue to be, on the whole, terrible. Ironically, I absolutely adore playing live poker because of these same people; they are fascinating and wonderful folks who just so happen to have a penchant for giving away little bits of their money over long stretches of time. I have played at the same small poker room in southern California for about 15 years, and it's a bizarre but wonderful little community.

    Because I'm not a pro, I have the luxury of drawing a distinction between my poker bankroll and my life bankroll. I found @Imperator 's comments about the distinction between these quite poignant. For me, I can play or not play, and there is no stress, because I live my financial life as if I were not a poker player. I have a small but steady income away from poker, and I have normal family expenses (mortgage, cars, kids education, braces, etc.), When I have time to play cards, that's just a bonus.

    I have, over the course of my poker playing life, given a great deal of intellectual thought to some of the things that @Imperator covered in the podcast: strategy, tactics, bankroll, politics, ethics, etc. Thanks to him for taking the time to contribute in the forums (something I almost never am inclined or have the time to do), and thanks
    also for making the effort to do this podcast.

    I am fond of this Red Chip community, even though it's not easy for me to contribute to it regularly. I'd love to find a place here where I could share some of my gifts and experiences, but time is so scarce. I'm immensely impressed with James @SplitSuit and the other coaches, who work tirelessly to provide invaluable content to us all. Keep up the good work, lads.

    Bob "Silverrose" Drago

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