ICM for fuddy duddies.

[thetank]

ICM for fuddy duddies

In these next few posts I'm going to explain what ICM is, how we use it, why we need it, and give a first lesson in using a program called sitngo wiz.

If at any point it becomes sickeningly patronizing, please assume that's some sort of ironic comedy thing I'm going for.



First things First

First of all, a couple of definitions...

Defⁿ : Fuddie duddie

If you play online poker tournaments that involve sitting and/or going, and you do not know, or have not previously been interested in, this ICM thing that all the kidz seem to rave about, then you are a "fuddie duddie" and this post is for you. 

Defⁿ : ICM

ICM is short for independant chip modelling.
It is a mathematical* model that attempts to assign a cash value to each of your tournament chips. When relative stack sizes are low in relation to the blinds, sitngo players typically use this model to help evaluate which pre-flop decision will maximize their equity.


Don't worry, all will be explained.





Equity

Imagine you are halfway through playing a sitngo and you want to stop. You've just found Jesus and he's convinced you that gambling is a horrible sin.

We could log off and go immediately to hang out with Jesus and help sick people and wotnot, but we've paid good money to buy in to this sitngo and being wasteful is also a sin.

As luck should have it, our fallen brother Jeramijah is on hand and recognizes this predicament. He kindly offers to buy this tournament from us. (Jesus is right there and he ok's that minor breaches in a poker site's terms and conditions isn't really a sin) He'll give us some cash for our seat, continue to play in our place, and in return he'll pocket any winnings from the tournament.

The question is, what would be the fairest price to charge Jeramijah for this privilege? We paid £100 to enter the tournament so how about £100?
The problem is what if we have already lost some chips? Jeramijah would be getting a rough deal for his £100 and Jesus would be cross.
What if we have already won some chips? Jeramijah would be short changing us if he only paid £100 and that's not what we want.
What if we had neither gained, nor lost chips, but so many players have been knocked out that we are in the money already, or very close to being in the money. Again £100 would not be a good price to give up our seat to Jeramijah.

So Jesus phones up his omniscient friend Dan and explains the predicament.

Dan is a helpful fellow so he freezes time, gets the bus over there, and takes his poker playing puppet Polly out of his toolbox.
He has Polly play the tournament from that point. When Polly is finished, Dan notes the amount of money Polly cashed for (between £0 for no cash and £500 for first place) in his special notepad. He then rewinds time to the point where Polly first took over (he's a clever man in Dan) and presses play, so that Polly can finish the sitngo again.

Dan repeats this process again and again until Polly has finished the sitngo five million squillion billion times. He puts Polly back in his box, and after turning back the clock one last time, declares that a fair price for Jeramijah to pay for taking over this tournament is the total amount that Polly cashed for overall divided by five million squillion billion.

This figure is our equity in the tournament at that point.





Back to ICM

We don't have a toolbelt or a bus pass or any of the other special things that Dan has to work out what our equity would be to such a high degree of accuracy. Instead we have ICM.

ICM helps us to estimate our equity in a tournament at any given point.

It's based on our stack size relative to all the other stack sizes in play, and from that the model estimates our percentage chance of finishing in each position. (eg, 1st, 2nd or 3rd etc) After it has assigned these percentages, if the model knows what each place pays (or doesn't pay) it's one last quick and relatively easy sum to work out what our equity might be.





Note

* I mentioned the word 'mathematical' back there, and that's where a lot of people understandably switch off.

Your fuddie duddie might argue that...

-Poker isn't all about crunching numbers and complicated theortical mathematics. It's a game of psychology, of cunning, of mental toughness and all sorts of other things that don't involve algebra.

-Any mathematical model you have is going to be fraught with problems and won't really help in the real world.

Rather than argue these points, I'm going to agree whole heartedly with the fuddie duddie. He has too strong a case. Poker certainly is a rich and complex game, there are many succseful players who are not number crunching boffins, ICM certainly does have it's limits, and it won't really help us all that much in the real world when we sit down and play a poker tournament.

So why all the fuss?

1. These are not poker tournaments; these are sitngos.
2. This is not the real world; this is the internet.

Is we look at things like this, we can move forward and maybe learn something new without upsetting our well established world view.







Coming soon

Coming very soon in fact, I'll be finishing this three post series tonight, in between trips to my fridge.

In the next post. I'll look at the applications of ICM and how we use it to make more money playing sitngos. I'll look at why we need ICM. The benefits of it, and some of its problems and limitations.

In the final post I'll walk through how to manually enter a hand into a program called sitngo wiz and how to go about playing around and experimenting with ICM to "hone your instincts" and increase the chances that you'll make better decisions while playing sitngos.
Hopefully the hand I choose will be a one that will demonstrates an instance where our intuition can lead us to make the "wrong" move, and thusly convince all and sundry to join the cult.

[byronkincaid]

sweet, i've never understood how to use wiz properly

[MC]

LOL, enjoying the dummies style guide, very well done. I have always had difficulty explaining ICM to other people. Look forward to the rest!

[TheChipPrince]

Fair play, I'm sure many will appreciate these posts, and 99% of ppl (obv everyone bar Longy) will be able to learn something.

[EvilPie]

Best equity explanation ever!!

[RED-DOG]

Cheers Tank.

Signed F Duddie.

[RED-DOG]

It must be bloody good, I understand it.

[roscopiko]

so good, eagerly awaiting part 2 & 3 so that i can steal them and reproduce

[thetank]

ICM, as we recall from the last post, is simply a mathmatical model that lets us estimate the equity our stack has at any given point in a sitngo. To understand why this brought about a strategic revolution in the way we think about sitngos, perhaps it's best if I first explain a little of the history.

What we already knew about sitngos before all this ICM stuff came along.

Sklansky talks about the 'gap concept' in his theory of poker, of requiring a better hand to call a raise with than we need to put in the raise ourselves. This is due to our chances of picking up the pot immediately when it's us who's doing the raising.
We know that this 'gap' is signifacantly widened in tournament poker where more than one place is paid, because of the disparity between the gain in our equity when we win chips and the reduction in our equity when we lose chips.

Even if we don't follow the mathematical logic, we've definately all absorbed through our collective cultural consiousness the practical consequences of this. Namely that we can raise with mince, but we need the goods to call.

In sitngos, with the ever increasing blind structure, people's stack sizes in terms of the number of big blinds they have goes down and down, and the number of chips available to win uncontested each hand if you raise and everybody else folds goes up and up.

So while everyone is getting gradually more and more desperate, the potential rewards of putting in a pre flop raise get more and more tempting.

Before long, we reach the point whereby any reasonably sized raise (ie, 2.5 or 3 times the big blind) will involve us putting a quarter of our stack in the middle and commiting us to the pot.

Note : Players still do sometimes fold pre-flop after they've raise a quarter of their stack (or more!)
Even some winning players do this (it's almost always a leak when they do) We're not going to, and are proceeding with the belief that it's weak, it's a leak and that we are to just say no!
Anybody who thinks otherwise, please see me after class.

Raising and calling a re-raise is an option, but generally players will reraise you with cards that they wouldn't call you with had you gone all-in pre flop. We might know we're never going to fold, but they think there's still a chance. They're using Sklansky's gap concept too!

Most of the time we would much prefer to pick up the nice pot that contains just the blinds and antes, rather than flip a coin for our tournament life. To discourage your opponents from reraising you then, we just go all-in straight away. They now can't kid themselves that there's any chance of them winning t'pot without beating your ass in a showdown. They have to tighten up accordingly, and we get our wish of winning an uncontested pot more often.


Pushbots

Pushbotting, this strategy became known as. The bot being short for robot, ie the sitngo player employing this strategy is just playing robotically.
 
The desicion the pushbot has to make on each hand looked really simple, you either went all-in or you folded. (If someone else had gone all-in before you, you could call or you could fold.) Other poker professionals would look down on the push botter, "it's not proper poker" they would remark. I was a pushbotter for a long time and it never used to bother me. I was making money playing some sort of 52 card game, I wasn't too bothered what people called it.

Other players at the table would get frustrated by the push bot; I recall an angry chatbox comment made in my direction back in 2006 "Do you want to actually play some poker?"

"Ok" I replied, "but let's finish this sitngo first."


Enough guff about the good old days; you'll be pining for the Tribeca network next. Tell me about ICM ffs.

I do beg your pardon, buisness will be resumed.
Sigh, this might take more than 3 posts.

Anyway, the pushbot strategy that sitngos necessitated was hardly the highly complex, multi faceted, minute to learn, lifetime to master beast that 'proper poker' puports to be. There was only one desicion, to push or to fold. Nevertheless a decision is still a descision, and any descion depends on...



Factors!

Yes, the factors. Where would we be without them in poker? (it depends)

When weighing up whether to push or not to push, among the things a good push bot would consider were

- What winning the blinds is worth to them.
- How often they are going to get called by the opponents still to act.
- When they are called, what hands their opponent is likely to have.
- How often they are going to be able to beat those hands.
- What winning that all-in coup will be worth to them.
- What consequences will losing that all-in coup have for them.


You can think about these things at the table, and use our intuition, common sense and experience or (latent mathematical subconcious prowess even) to try to come to the best descion.

Away from the table though, it's always good to be able to quantify things, put some actual numbers onto some of our factors to help us make a more informed judgement. This is where some poker calculators came along, a pariticularly fine one still going strong today is called Pokerstove.



Pokerstove.

Available to download (for free!) from http://www.pokerstove.com/download/

Here I have entered two hands to see how my fairs against the mighty when we're both all-in pre flop. I know I'm in bad shape, but I want to know how often I can expect to win the pot.
 
Very simple to do, anyone who has been apprenhensive about using poker software I would encourage to have a play about with a Pokerstove as they don't come simpler.

To replicate this experiment, after downloading and installing the latest version of Pokerstove, just click on the "Player 1" box, click on your two cards from the list of 52 and click 'OK'.

Then we click on the "Player 2" box and enter the two cards you want to run your cards against. After clicking OK again, press the big 'Evaluate' and then you'll get to where we are in this picture.

Click to see full-size image.

It has swiftly run through all the 1,712,304 possible combinations that five cards can be dealt from the remaining 48 cards (in 0.002 seconds) and calculates the equity that each hand has. Here we see my 96s has a win% of just under 40%, so we're going to bink about 4 times in 10. (As an aside, that's about the same frequency that a good player can expect a top 3 finish in a single table tournament)

Our chip equity it lists as 39.825% of the pot. We don't want to confuse this with the win% figure. The reason for the difference between the two is the occasional split pot.
 
We'd multiply our chip equity % figure, 39.825, by the size of the pot and divide by 100 to get our equity in terms of the number of chips we can expect to average.
Note : We don't want to confuse this chip equity with the equity we get from using the ICM model, so we'll call it cEV. (chip expected value)

All very nice and pretty, but in practise, we're never going to be in a situation where we know that if our opponent calls us, he has the exact hand .


Range Rovers

What we might have though, is a good idea of the range of cards our opponent might call us with. This idea of a "putting someone on a range" is central to the application of the ICM in sitngos.

As an example of a range, we might feel we'll get looked up by 77+ (which is shorthand for pocket 8's and all bigger pairs), A9s+, AJo+, KTs+, KQo+, QTs+ (which is the hands A9s, ATs, AJs, AQs, AKs, AJo, AQo, AKo... you get the idea)

This is an easy peasy job for Pokerstove to evaluate too. We click on 'Player 2', then 'Clear', then the 'Preflop' bar at the top. We can then select all the possible hands we think he'll call us with. (or in this case, slide the bar at the to 10.3%, meaning he'll call us with the top 10.3% of hands according to some hand ranking system, more on this later)

After we click 'OK' and 'Evaluate' we now get the following screen.

Click to see full-size image.

This time it's looked at over 226 million hands (in a quarter of a second!)
All the possibilities of the hands, and the resultant figures it spits out at us will be a weighted average* of how we will fare with our bold 96s against this range of hands.

*There are more ways to make AQo than there are to make AA. Pokeystove knows this. It also knows that it can't use (ducy? )

So, we can now see that 96s isn't quite so hot as before. When called by this range, we're only going to win just over 3 times in 10.



I'm breaking this post up into two parts now to make it a little more manageable. We continue below by going back to look at the main factors a push bot will have to consider when making his decision, and see how we're getting on attaching some good solid numbers to as many of them as we can.

[EvilPie]

Brilliant stuff Tank.

[GreekStein]

tank im not in a good enough state to remember it if i read it now but it looks damn impressive.

Look forward to it.

[thetank]

tank im not in a good enough state to remember it if i read it now but it looks damn impressive.

Look forward to it.

Probably best to wait a few days.

I'm really not happy with the second bit, especially the last part. It was rushed because it was getting late and I wanted to get something down. There's an important part that I want to fit in, and probably not so important parts that could be left out. It wants proof read and neatened up. (and probably broken up into two seperate posts, gg 3 part series, you're now a 5 part series.)

[thetank]

Back to our factors.

I'll just copy and paste them here, and see how we're getting on quantifying them.

- What winning the blinds is worth to them. We'd need to guesstimate our equity with our new stack size after we've chomped the blinds.
- How often they are going to get called by the opponents still to act.  We can use our experience, observation and knowledge of opponent to get this down.
- When they are called, what hands their opponent is likely to have. As above, we can have a good stab at this, hand rankings, like the 'top 10.3%' we just put into Pokerstove are quite helpful. So much so that the convention now is to think about what hands the opponent will call with, and that answers the previous question at same time
- How often they are going to be able to beat those hands. We've done that, Pokerstove, piece of piss.
- What winning that all-in coup will be worth to them. Needing to make a guesstimate at what our equity would be.
- What consequences will losing that all-in coup have for them. Again, another equity guesstimate required. Unless we were the shorter stack, in which case it's pretty easy to calculate our equity exactly. (ducy)



So the numbers helped a little. Intuition and judgement was still required because too many of these numbers were guesstimates. There were plenty of successful pushbots going about so it wasn't like we were a million miles away from what is now thought of as optimal strategy. It was tough to be sure if something was right or not though, too many things above highlighted in red that could not be reliably quantified.

The figures in red all had something in common though, they all had to do with equity. The sitngo boffins who worked hard to drive this strategy forward worked hard to find a reliable way of calculating your equity at a given point in a tournament as they knew that then everything would slot into place. There would only be one variable in the picture, how often your opponent called you.


The Hunt for Red October

[ x ] artistic licence heavily employed in the following section

Attempts were made to put figures on tournament equity based on empirical observations of many tournaments played (although somewhat less rigorously completed than the 5 million billion squillion trials of the previous post) It was a noble attempt, and probably better than picking numbers for your equity at a given point out of thin air (which was also tried in hand analysis, quite a lot)

It was too hard though, it was too big a job. They knew other players stack sizes had such a huge influence on things, and so to measure equity empirically they'd need to do all sorts different trials for all sorts of different stack size scenarios. It was hard enough to do one. A lot of them just forgot about it, used whatever made up numbers for equity they liked the best and continued their analysis. (They didn't do too badly)

When ICM was developed, the mathmatical model to estimate equity (and estimate it quite well) based on purely quantifiable factors, it was to sitngo strategy what the industrial revolution was to erm... industry I guess.



The Dawning of the Age of Aquarius

Now that they could put good numbers on all the main factors invloved in this push fold desicion. It wasn't long before people made a program that combined the work of Pokerstove with an program that used the ICM mathematical model to calculate equitys, bosch it all together, and after inputing a likely range for your opponent calling, come out with a single and simple instruction... push or fold.

One of the first (possibly the first?) program of this type (that we now call ICM calculators) was Sitngo Power Tools. It had a bit of a dark history as I recall, it's inital function was to run the calculator in game, so the push bot really would be a push bot. The poker sites didn't like this idea (and quite rightly too!) so made it difficult for sitngo power tools.

It was soon discovered though, that this ability to run the calculator 'in game' wasn't really necessary. If you looked at enough scenarios, you soon developed a feel for what was right and what wrong "according to ICM" and could employ the strategies it recommended without the need to run dodgy software at the same time as you were playing.

This was all around about the 2005/2006 sort of time. ICM was gradually being adopted by pushbots everywhere. The reason was simple, it worked! People who used it had more success than people who didn't.

Not only were they achieving higher ROIs, but the simplification of the (already quite simple) desicion making process meant that people were finding it possible to play more and more tables simulataneously. In 2006 players like The_Ventian on Pokerstars were considered amazingly gifted to play 10 turbo STT tables at a time. When Elky achieved Supernova status in a month it was headline news around the poker world and the man. Today, I would expect anyone to be capable of playing 10 tables, and if someone wanted to make a prop bet that they could get Supernova in a two weeks, they'd be lucky to find any action whatsoever.

Gifted players are now playing 20 tables profitably, and your concert pianist standard guys can manage to hold down 40. 

Through a Darwinian-like evolutionary process, we now find ourselves in a situation where I think it's safe to say that studying ICM is a categorical imperative for anyone serious about playing online sitngos as a way of making money.



Fuddy duddies.

The reason I'm taking the time to write this for the fuddy duddies is that I was a fuddy duddie too!
It wasn't until 2008 that I finally accepted that there might be something to this ICM lark and it was worth my while having a look.

I'd like to kid myself that what turned me off it so long was the early attempts at an 'in game' ICM calculator and me finding the very notion of such a thing morally repugnant. The truth is though, I was just arrogant and myopic. I remeber insisting that "the only sitngo power tool I need is between my shoulders."

I guess it's kind of typical of poker players, once they're making money they assume they're doing everything right and don't entertain the notion that they could make much more if they invested some time in looking into the latest strategy developments and working on their game.

I was happily plugging away and grinding some coin on the Tribeca network's sitngos in late 2006 and 2007. It wasn't until the network disbanded and I moved back to Pokerstars that it hit my how much the game had evolved in such a short space of time. The year prior I was able to beat the games comfortably. I was making loads of mistakes, but the games were forgiving and I kept up a healthy ROI. With the same game the following year, I suddenly went from being a 'decent reg' to a 'rakeback pro'
Life factors came along and I decided gg professional poker career, I'll try my luck in the real world.

I made a comeback to online poker in mid 2008, but first armed myself with a good working knowledge ICM, that I try and keep up. I'm doing ok, nothing spectacular but it's steady-ish money by professional gambler standings, I'm yet to have a losing month since returning to the cyber-felt.



That took me a little longer than I thought it would.

It's a difficult concept to try and sell this ICM buisness. It's now 1am and I've covered half of what I wanted to in the second post. (I thought I'd be done all 3 by about 9pm)
I think it's important though, to understand where ICM came from, it will help us properly apply it.

I need to go back and edit bits, tidy it up, come up with a simile that isn't as kak as that industrial revolution one, but I can do that another day.



Coming soon-ish

Still to come, the limits of ICM, the problems of ICM, and how I recommend you go about learning how to use it yourself (sitngowiz tutorial!)

I'm away on the train tomorrow morning and might get some done then. In all likelyhood it will be tomorrow night before I'm done though.

I will say this at the moment, for all I rave about Wiz, I don't recommend anyone actually buys the thing. It's easy to use, very pretty and 30 day free trials are nice things, but $100 is too pricey for something that essentially just does the job of an ICM calculator. (That I believe can be picked up for free)
I do not rate most of the bells and whistles it comes with to justify the pricetag. More on that when we continue...

[RED-DOG]

See, I don't understand why the player 1 hand, (6s 9s) has an equity of 60.175%, while the player 2 hand, (Ac Kd) has an equity of 39.825%. (Highlighted below)


Yours
F Duddy.

Click to see full-size image.

[MTT DESTROYER]

Exceptional thread