Sterno’s playkit #1. Inflection points : The “M” theory (full)

[SternSwiss]

Hiya Friends.

In the interesting thread started by street66 some time back (general poker Question), I exposed bits and pieces of what is known as the “M” theory, as was applicable to the concrete problem proposed in the OP.

Here I will propose and exhaustive overview, for those interested in the more complete picture.

More largely, I will try to post such theory blurbs here every now and then... as some of you know: I love to study and to discuss theory, as the knowledge nerd that I am.



A) The general concept of inflection points


Harrington, on which this presentation is largely based, offers an analogy with football games (American, for him), from the coach’s perspective:

In the beginning of a game, the coach has a general strategy and a very wide array of options to develop. As times passes, and as the result evolve (here negatively), the number of options shrink until some “desesperate” moves might be the only choice left.

Applied to no-limit tournaments, it means that the slow building-up of subtle bets and moves that characterize the early game starts to gradually change into a wild battle of bluffs, desperate all-in moves and climaxxxx-tic showdowns.

But this latter phase if far form being a bingo random process: it is quite strategic, actually and this is precisely what the theory address.

What the Inflection theory proposes are guidelines to tackle different possible configurations, depending on one’s stack, other’s, blinds and antes structures, etc.

The model which I find the most convenient is widely known as the “M” model (or “M-ratio”) invented by Paul Magriel, a great poker & backgammon player (like Gus Hansen).

Harrington has his own model, which he calls “Q”, and which is a bit more difficult to calculate, since one needs the average amount of chips per player left in a tournament (a figure not always easily accessible, especially in RL play). Himslef says that if the two models product conflicting results, one should go with M as it is more powerful, except in the case of qualifying tournaments, where a number of players all get the same prize (a qualification for something) and the others get nothing. I won’t develop Q here, but you can find it explained in Harrington’s book (referred to at the end of this text), in case you often play qualifiers.



B) Ok, Sterno but what is M concretely?

M is a measure of the health of one’s chip stack as a function of the cost to play each round.

In simple terms, a player can sit passively in the game, making only compulsory bets, for M laps of the dealer button before running out of chips.

A high M means the player can afford to wait a number of rounds before making a move and be very selective about them.

A low M means that it’s time for the coach in you to make daring moves, which wouldn’t make sense earlier in the game

A very-low M means desperate moves, such as in the example discussed in street66’s thread I referred to above.


In very concrete terms, M is the ratio of your stack to the current blinds (sb & bb) + the antes (hereafter “the opening pot”)

With less words:

M = one’s stack / [(small blind + big blind + the sum of antes), aka “the opening pot”]


A concrete example:

Blinds are 1000/2000 with antes of 200 and 6 players at the table.

Your stack is 15’000 Chips.

Your M =

15’000 / [3000 + (6x200)] = 15’000 / 4200 = 3.6
(3.571 actually but these decimals do not matter)


It basically indicates how much rounds of the table you can survive passively before being eaten-away by the blinds... in the current situation (blinds raise, tables reconfigure).


I know the figure of 3.6, which is a red zone (see below), and it's strategical implications might seem steep for some of you unfamiliar with the theory (as it was for me at first, before I started to apply it in some RL biggies).

Remember that this theory concerns big league play.

Here, were play is, nolens volens, much more random and loose the theory cannot be considered in the strict sense.... It can only give inspiration.




C) Sure, I understand the general principle but how is that going to help me get shiny medals?


Ok, now that the principle is concretely laid-down, here is the general strategy that the model recommends.

It divides one’s tournament’s situation into FIVE ZONES:


1) The Green Zone (you have 20 or more times the opening pot)

This where you ideally would like to be as much as possible: all options and styles are open to use and switch from: conservative, aggressive, super-aggressive.

In other words: it is where you can be the most functional and versatile and it is worth to take some risks to stay there, according to Harrington.


2) The Yellow Zone (you have 10-20 times the opening pot)

As you slide down, the blinds are starting to affect you and you start to loose the ability to play conservatively.

You have to start, at chosen times, to make moves with weaker hands than a conservative tight style would elect to play with.


3) The Orange Zone (you have 6-10 times the opening pot)

In the yellow zone, you need to play even more aggressive and loose the ability to make moves that require a reasonable stack to succeed.


4) The Red Zone (you have 1-5 times the opening pot)

In the red zone, your only option is to go all-in and to choose when (though you have little time margin) before being eaten-up. Any other bet would consume so much of your stack (on a proper table) that you would be pot-commited anyway and going all in gives you a chance to reload a bit by taking the pot here and then with your first bet.


5) The Dead Zone (you have less than the opening pot... lame-o)

It looks like you are still alive, but the odds don’t see it that way. You are a “gnat to be swatted” (Harrington).

You have one move left: all-in, and when you make it others will most likely call just to get rid of you.

Unless you get the messiah hand, the crucial thing is to make your move in a yet unopened table before the big blind arrives next. By moving first some might not call because of the potential dangers of someone raising after them.

According to Harrington: “The need to move first is so great that your cards really don’t matter anymore”. At all.



D) More on the Green Zone

Well: nothing more to add. You cruise and can play your best game(s) with all options open.

As much as it is possible, avoid sliding down the zones or heat-up the colour spectrum (mel’s panties or the idea of sa11y opening her blouse should take care of that).



E) More on the Yellow Zone

As you slide to yellow-ness, three shifts in strategy occur:


1) As obvious, you start to become more aggressive, both in betting at pots and calling bets. The general pre-flop requirements lower down a bit and you will raise or call with a few more hands than when all is green.

About calling: this is so because others will be adjusting their plays as well and more will be in the same kind of situation.

Make sure to look at other’s M first and then ask yourself if they are indeed modifying their play or not (here chances are they may not). Don’t miss any showdowns so as to understand whether people understand inflection points or not.

Beware of 2 things:
- A good player will never play inflections points mechanically and be predictable.
- a showdown with “normal” strength of hands (as in green zone) do not give you any information (of the kind discussed just above)


2) Much less obvious (even counter-intuitive for me at first) is the fact that you must be much more conservative while playing small pairs, a point true for both yellow and orange zones.

The reasoning lies on implied odds. It is a bit long and complex and, but adamant. I won’t unfold it here, but you can refer to Harrington’s book (pp 133-137).

Same holds true with suited connectors which are also heavily dependent on implied odds.


3) In the yellow zone, you loose the ability to make any “big moves” (much too dangerous for your stack and tournament life) and have to content with “small moves”... that is when you are making moves, which shouldn’t be too often.

A “move” is not necessarily a bluff, but it implies either that (no hand and pure representation) or not much of a hand (bottom pair on flop, for example).


“Small moves”: blending probe and continuation bets, or calls followed by small raises, or bets based on position. The idea with those is too put down pots cheaply without much of a hand, or not at all. Evaluating other players’ manifestation of strength is crucial here and you should ask yourself how they are playing and how they perceive you from the recent table history as well. Since not all of small moves will work you shouldn’t invest a lot in any: just swing your way trying to keep a positive balance (Gus Hansen is an absolute master in that) and wait for the great hands / hits that will allow you to gather a fat load of chippies.

“Big moves”: here you construct big, outrageous (that hopefully won’t be seen) moves, representing strength from the beginning and you keep hammering consequently until everyone lays down. They have a higher rate of success than small moves, but when you loose one, you are in bad shape, unless your stack is huge. That is precisely why being very aggressive with a huge stack is good strategy and nothing like “bingo-player”, as I remember someone calling me once while I was exactly doing that some months back. My chat response was rather dismissive. We have become friends since, in case you wonder.

AS WITH ANY MOVES THOSE SHOULDN’T BE OVERDONE OR YOU WILL BECOME PREDICTABLE.

Overdoing starts at 10 % of played hands for a conservative player and perhaps 25% for an aggressive one, I ‘d say... in serious games. These figures are highly debatable and do not hesitate to do so if you estimate things very differently.



F) More on the Orange Zone

The orange zone is a continuation of the yellow zone, where the previous constraints are intensified.

In this zone you mostly need to conserve your chips, saving them for big decisions that could double your stack. Semi-speculative moves based on good pot odds (implied or regular) become lethal and inappropriate in the orange zone, while they are fine in the green zone, and to a lesser extent in the upper yellow. For such moves, independently of those pot odds that look oh so good, you will be spending a larger and larger proportion of your stack as your M shrinks (which you contribute to if you choose to play this way).

Pot odds are just that: pot odds. You need some stack to play them purposefully, as you do not have anything like the nuts in hand and base your choices on statistics of hitting solely / mostly. That is fine when you can develop a series and absorb a bad-streak (and if you calculate properly). Not if your own nuts are held with a knife by the rest of the table.

Small pairs and suited connectors become even more undesirable as starting hands. Note that this point doesn’t apply to all-in moves, though, but to bets and raises.

A notion that is always important takes a crucial role here: Opening table momentum.

This especially true for all-in moves, where small pairs and good suited connectors regain value... as hopefully should be easily graspable by now (or one of us didn’t do his/her job well, lol).



G) More on the Red Zone

So, in the red zone you have lost the abilty to make anything else but all-in bets and have only little margin as to choose when.

Note that if your M is below 3, you all-in bet will usually fail to drive anyone away since your weakness, the prospect of booting you out for others and interesting odds will result in at least one call.


Corollary questions for decision making (about whether to push all-in or not):

1) Has anyone already entered the pot before you. If yes, you need to be careful and only go all-in with the sort of hands that you would raise up with early in the tournament

2) How good is my preflop hand? The answer to this is much less important than the answer to question 1. In Harrington’s words "I am only folding the very worst hands here. 10-6 off-suit is plenty good enough.


A paradigmatic red zone example is discussed in street66's thread linked to at the top of this page.



H) More on the Dead Zone

You shouldn’t be there, unless you like to flirt with the reaper, but that hasn’t anything to do with poker, but rather your personal kinks.

If you are in the dead zone, as it happens to everyone, it means either you let yourself being blinded away (bad play) or because you made a good move while being-short stacked and got unlucky.

You are basically food for the fishes... Make your prayers.

Of course, sometimes miracles happen and they feel great, but counting on them is naive and silly.

The basic advice here is the same in spirit than the one I would give concerning being bitten by poisonous snakes: avoid getting bitten in the first place.

Or in Harrington’s words: “[Good] players arrive here only by accident”.



I) Additional remarks

According to Harrington, the more your M goes down, the more your M becomes an important factor, every bit as, and finally more, important than the actual cards you are holding.

The danger of playing too tight in the low middle-zones is thus. You wait and wait to get a strong premium, gently getting your stack eaten up by blinds and antes. First there is the risk of never getting anything that good and simply being blinded away. But there is also the risk of getting the desired hand too late.

Ok you waited, waited and waited until you slide in the red zone. Here finally come the desired cowboys (KK): not the messiah, quite likely. You double-up but might very well still be in the red zone. The chance to get another of the best premiums again soon, is very, very low (even with OP66’s “random” generator, lol).



Knowing your own M and pondering your options is the first step, but it is as important to follow other’s M, so as to contribute to your reading of their moves.

An example I gave in the other: slowplaying good hands (more often than not risky if not lousy play) against low M's (that will have to make moves which will be looser than earlier in the tournament) can be actually a fruitful strategy.


Like any theory, you off course have to keep varying your game so as not to be predictable.


To cool-down possible enthusiasm immediately, here is a little example that happened to me recently:

Tournament with approx 80 entrants, late stage (perhaps 13 players left total, our table is 7). The player under the gun goes all-in with a red M of around 4. Nobody calls.

I am in mid-position, with a yellow M. My hand is A 10 off-suit and I think it is more than good enough to call him. I raise to try to ensure no one else calls in the few players yet left to speak and we had up face to face for a showdown.

The git had bullets (AA).... and he doubles up, deservedly so.

The morality is the usual one: nothing is ever guaranteed in our favorite game (not even his bullets which were an 87-13 % favorite against my A 10)

This example is reconstructed by memory. The spirit is here, but a few actual details, not relevant for the theory, might be slightly different (I hadn’t planned on writing this, then, and didn’t take notes).


Finally, inflection points theory has implications in other forms of play than big multi-table tournaments, but it would bring us much too far to tackle them.



Voilà.



I hope some of you found reading this blurb interesting. Please let me know here or via pm if so, because it takes quite some time to sum-up and redact such things, so if no-one gives an excrement... it is a bit useless!



J) Sources

Mostly summed-up from Dan Harrington’s “Harrington on Hold’em. Expert Strategy for No-Limit Tournaments, volume II”, chapter 9

M-ratio - Wikipedia, the free encyclopedia

Dan Harrington - Wikipedia, the free encyclopedia

Paul Magriel - Wikipedia, the free encyclopedia

Some personal remarks / insights here and there.

[jockney]

Thanks for taking the time to construct and deliver such an informative thread.

I have read ,and will re read and try to digest the points. Some of it I will be honest enough to say is slightly over my head but in essense I can understand the theory. There are some of the very good pointers that I am now going to attempt to apply to my game.

Thanks also for the links, which I am now going to delve back into.

[HopeImLucky]

This was extremely informative, but I'll probably have to read it several times before it all sinks in. In the meantime, I'll be trying to apply the essence to my game.

[lahambra2]

as usual you make something clear,applicable and interesting there stern, cheers bud

[CherryPie]

Must say am not keen on reading too many long-winded poker theories as i think they are based on common sense and can be worked out by figuring out the game yourself.. :/ ... find they tend to complicate simple concepts... BUT i did read all of this and i did appreciate it TY stern is straight-forward ideas but categorising into zones with figures could definitely b helpful i will remember the 1-5 for sure

n1 stern

[LfcFan]

Thank you very much for this Stern
A good write up and a good read.
Just like a couple of others here,it will take a couple more reads to get the majority of it to sink in.
I first came across this theory in street66's thread and have already loosely applied it to my game. I found using the calculator on my phone helpful to sum up my M ( how nerdy is that?lol ).
When you get some more time, please keep these quality stratigy threads coming.
Thanks again

[SternSwiss]

Well thanks a lot for the feedback.

I'll be glad to keep posting some more here and then as there is interest (and furthermore by dear friends here).

I find too little time to study to my taste, but anyway sum up stuff for myself (as quickly taken, elliptic notes).

It is true that taking the time to redact things to share with others (not to mention layout) does take quite a while and wanted to make sure there was some interest.

It is quite rewarding too, for one sees things from outside and might notice a blind spot or the other while doing so, not to mention possible debates. So done with double pleasure (sharing & learning)



@cherry: I both agree and disagree with your general comment, but that would bring us too far to debate (let's keep this for when we are both drunk in the same place in december, lolol).

I appreciate you taking the effort to read and the nice comment, hun .

[69kindagal]

tht is sooooooooooooo long :evil

[SternSwiss]

Originally Posted by LfcFan

Thank you very much for this Stern
A good write up and a good read.
Just like a couple of others here,it will take a couple more reads to get the majority of it to sink in.
I first came across this theory in street66's thread and have already loosely applied it to my game. I found using the calculator on my phone helpful to sum up my M ( how nerdy is that?lol ).
When you get some more time, please keep these quality stratigy threads coming.
Thanks again

Glad you found the post useful, m8

Btw, nerdy colleague:

Keep in mind that play here is a bit more wild and loose and that therefore you have to adjust things (just as you have to do with the steep raises or bets to avoid too manny call
ers, etc).

In my experience so far it makes the useful M zones a bit lower, actually, though it would be hard to quantify, as it really depends on the game / players. The overall logics and progession do still totally make sense to orient strategy, of course never mechanically

Cheerio!

[telboy]

im going green after reading this glad to help recycle others chips


great read stern,but trying to put this to use will be hard as you said lots of factors to consider

[BBOB]

This is must read advice for any serious tourney players I hope all on site read it. Well done Stern and well done "Action Dan" keep the poker stratagy tips coming Stern its much appreciated. Just today I waited a few hands too many too move in in a tourney and it cost me a final table a clear reason why we should all take this therory to heart. thanks Stern keep up the great work )