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Position Precision

By: chiralarihc @ 12:06 (EST) / 329 / Comment ( 0 )

As this is my first post,  I'd like to point out that I have not been playing all that long, and have not been the model student, mastering all the theory, as many do, before even playing a real money game.   All my understanding of the game (or lack of understanding!) has come from time playing and mostly losing (but steadily improving), along with courses made available by Poker School Online, as well as reading blogs and forum posts here.  


Perhaps most helpful to me has been reading carefully, and then re-reading, the excellent series of blog posts by ArtySmokesPS:   Smokin' Poker - The ABC of 2NL.. This and a few skim-read chapters from David Sklansky's Theory of Poker are the sum of it and for this reason, some of my comments may appear naive to someone who has grown up with the game  If this is the case, feel free to ridicule me in the comments, and I'll take it in good humour.  Most importantly though, if I have written garbage, by which I mean mathematically incorrect statements or illogical reasoning, please, please, please take a few minutes to put me right.


Now to poker...

...and the topic of this post, which is my first attempt to add a little quantitative reasoning to my previously rather hand-wavey understanding of the importance of position in poker, and how it influences the way a hand is played.

For some time when I started playing, I struggled to see quite why position at the table was such a crucial factor.  As far as I could see, what ultimately determined the outcome of a game of poker was simply the cards that you held, whatever position you happened to be in when you were holding them.  I recognised that if you had the opportunity to act last, you had more information than if you were first but I didn't really appreciate why that extra information made such a difference to who ultimately has the strongest hand at showdown which seemed to me to be a predetermined matter to a large extent.  

I'm the sort of person who has to make mistakes in order to learn.  It's no use telling me which hands are playable UTG and which I'm allowed to play from the CO;  I'll just go ahead and see what happens anyway.  As I played more and more, I found I was beginning to get a sense of danger dependent upon my position at the table and this was beginning to inform an instinctive position dependent range.  Unlike rules which are there to be contemptuously disregarded, fear irresistibly enforces our compliance with the only real laws, which are just the truths that describe our limitations.  In poker our limitations are those pertaining to information;  that which is unknown because it is hidden from us but nevertheless knowable, and that which is unknowable because it has not yet happened. 

I found I was developing a rudimentary understanding of position which was nothing but an awareness of danger that prevented me from playing donkey hole cards from earlier positions. This was similar, lets say, to the fear that instinctively stops us from overtaking on the brow of a hill or the bend of a road.  Provided of course that we're not a suicidal maniac, or the poker equivalent, which we just call a maniac, or perhaps an aggrodonk....

This is all very well but it doesn't give us a quantifiable method of arriving at the starting hand catagories appropriate for playing from positions according to the betting action that has taken place at the table.  Some may be happy to take the wisdom usefully written down by great players and find amongst the playing styles, one that suits them and develop their own game from there.  I prefer to make things hard for myself and demand at least a feasible mathematical framework that I can understand and use to set my game on firmer ground.

A breakthrough came for me when I read ArtySmokesPS's explanation of the importance of position.  He writes that although you will often hear reasonable sounding suggestions offered such as the ability to be able to see before you the actions of each player and observe the whole table before playing or folding your hand, the crucial point that is often ommitted is that the later you act, the more control you have over the size of the pot..  I would describe it slightly differently by saying that the later you act, the more precise you can be in estimating the size the pot will reach by the end of the betting round.   I realise this may be obvious to many and has probably been formalised countless times but for me it all came together as follows:

The unknowable information (i.e. the community cards yet to show on the board) can be made manageable through probability theory.  We can talk about the mathematical odds of making a draw.  This is as precise as it gets.  Assuming we are confident that we know it will win if we make the draw, we know the long term odds of winning, that's just statistics.  In poker we will always make money in the long run if the price we pay to play the hand is less than the amount we expct to win on average everytime we play the hand.  Another way of saying this is that we must ensure the pot odds are less than the mathematical odds of winning the hand.  This is equivalent to the condition that we have positive Expected Value (+ve Ev).  It's no different in essence from refusing to pay more than 50p to toss a coin where you receive £1 for heads and 0 for tails.  In the case of a coin toss however, there is only the probability, known to all, that the chance of winning is 50%; there is no hidden information.

In the case of poker, we have the unknown that is our opponents hand.  If the game was played with cards upturned and visible to all, we would know the correct action to take and although we would still be getting our pocket aces busted by the aggrodonk's 93o sometimes, if we played enough hands we know we'd steadily make money in the long run (as long as others weren't playing as carefully as we were).  In a poker game, especially an online poker game, there is only one metric we can use to get to that hidden information which would turn the game into a simple arbitrage.  All of the information that tells us how to act should of course be contained in the bets made and reflected in the pot odds.  If we can calculate the pot odds we are getting exactly then theoretically we know precisely how to act.  If we are getting pot odds of  10:1 and we're going to be heads up we will play any two cards allways.  If we are getting pot odds of 1:1 then we need to ensure that we only play our hand if it has a greater than 50% chance of winning against our opponent's entire range which if we're being shoved on we have to assume is not garbage.  

The road to Damascus moment for me was when I realised that the most important factor affecting our ability to calculate the precise pot odds is our position at the table.  If we are first to act then we have very little way of predicting the pot odds we are actually going to be offered by the end of the betting round.  Since we have no clear idea of the price we're getting, we have no way of knowing what mathematical odds of winning are required to ensure +ve Ev play and therefore we must assume the most adverse pot odds to be safe and consequently only the best starting hands can be played.  The dependence of pot odds uncertainy with position must be a simple linear one with the last to act knowing precisely the pot odds he is being offered and therefore, if there have been no raises at this point sitting on the button he can make a very reasonable decision to play a speculative/marginal hand with some confidence that he is still in +ve Ev territory.

So to summarise: my understanding now is that as we go from earliest to latest position, information is steadily revealed that enables us to narrow down the range of probable pot odds being offered to stay in the hand.  In turn we are able to make an increasingly better informed decision about the likely equity we really have, if any, and thus we can be more confident if we play a marginal hand that the margin we expect to receive is positive and realisable over the long term.  

This way of thinking helps me to rationalize the game and still make sensible choices when bad luck hits and I need the faith of scientific reasoning to do battle with the tilting demon threatening to sabotage my game.


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