Friday, May 30, 2008

Summer 2008 Vegas Gathering Plans

So this summer we have an "unofficial" blogger gathering in Vegas. It looks like it will be broken down to two weekends with the second weekend smaller and even less official. The second week is tough for me, as my son's B-Day party is Friday afternoon and that would mean a 1-2 am arrival in Vegas by car Friday night. So I will be out for the first unofficial weekend of the gathering. I am booked at the Tropicana Thursday June 5th through Sunday June 8th. The Trop is a great location for these and is as an inexpensive as the IP, but much nicer. Parking is a breeze as you don't need to go through a massive parking structure, and I just need to cross the bridge over to the MGM poker room, which is closer and easier than if you were actually staying at the MGM. You can also easily take the back roads to the IP as required from the Trop without ever crossing the strip. Even though there is almost no hype for this one in the bloggosphere, I still think it will be great fun. When the gathering is massive there is simply not enough time to spend with everyone and things get a bit "clicky". A smaller gathering means more quality time with your favorite bloggers, which will be a nice change. I think more people will be there for the first weekend than people think. I will list just a handful of A and B listers who should be there for the first weekend. More than enough for a great trip in my mind.

Dr. Pauly
Miami Don

Weak Player

That is a short list of who should be there. There are a bunch of others who are coming, but the silence on this event has been deafening so it is hard to put together a comprehensive list. Sorry if I left you off.

That is a pretty good crew. Zeem is my all time favorite blogger to play live poker with. He is so funny at the tables I can barely concentrate on playing. Miami Don is a baller. I will need to play some 2/5NL with him and watch him stack some tourists and build a bankroll to literally "blow" on an escort. I need to bitchout FallStaff for not playing Fantasy NASCAR on after he begged us to add it last year, and even helped develop the structure and scoring system that we use. And then there is Dr. Pauly. Since these gatherings are so large, and also happen when he is working the WSOP, it is difficult to spend quality time with him during these events. Should be easier this time around.

So it is week 1 for me. Let me know if anyone else is heading out for week one, or just look me up at the IP Hooker Bar Thursday night.


Wednesday, May 28, 2008

Digging Into MTT Example 1

"Most tournaments, it is just trying to play the cards you are dealt better than the rest of the field is."


The above is from Mookie's interview with lucko, when asked how much of his MTT game depends on the cards that he gets. I completely agree. This is all you can do in MTTs. You can try to play each and every starting hand you get better then the rest of the field plays theirs. This means that your EV graphs show a higher over all EV and are more adapted for MTT play by allowing for larger percentage swings when required late. Being able to play your cards better is enough to make you long term successful in MTTs, but it is never enough to get you a win in a specific MTT. To get a win in a specific MTT, you also need to catch some good cards at the right times and in the right situations. If you want to get better at MTTs all you can do is learn how to play specific hands better in specific situations. If you want to win 1000+ player MTTs you better play your cards better than the field does, and you will need to enter hundreds and hundreds of them (unless you are extra lucky). You can never expect to win a tournament of that size going in no matter how good you think you are. You can only expect to play your cards better and hope that will be enough. You simply can't control the other aspects of the MTT and those aspects outweigh your card playing advantage by a huge margin.

The graph of the first MTT example is not really readable. It will be impossible to show the details of each hand in a graph that also shows the results in all hands of an MTT. That is really not important though. I think if you understand what is going on for individual hands in the MTT you can see how this strings together to determine your MTT results. I am going to show in detail some individual hands below so you can really see what is happening. Lets start with AKs/AKo. You got that hand at the BB=50 and BB=100 levels of the example. Lets also assume for now that you picked it up on hand #1 as well, and also got it at the BB=500 level instead of the small pocket pair. Below is the cash game expectation value graph for AKs/AKo.

So now I am going to rotate it 90 degrees, get rid of the data bars, and fill in the starting and ending stack sizes and possible/actual results. For hand #1 you start with T1500, and could possibly get as high as T3000 or be eliminated. 45% of the time you will win about 2.5% of your stack and that's the result I show for this hand. You win T37 for an ending stack of T1537.

Now for the BB=50 hand shown below. Now you start with T2000 and could get to T4000. You are 40x deep now, and the graphs are set up for 100x deep stacks. This represents a 2.5x stretching out of the EV graph, as everything is relative to the blind levels. The most likely result now is a 12% increase in your stack size. There is a 12% chance of increasing your stack by 25% and this is what is shown for this hand. You end up with T2500 after the hand.

Now we are at the BB=100 level. You are still about 40x deep, so the EV graph shape is the same as the BB=50 hand, but now you start the hand with T3750, and can get up to T7500. I am showing the most likely result (45% of the time) of a stack increase of about 12% to T4200.

So now lets assume you catch AK again at the BB=500 level with a starting stack of T9500. You are only about 20x deep now so we will further stretch the EV curve vertically by a factor of 2x. The most likely result now is a 25% stack size move in either direction. About 10% of the time you will win 50% of your chips and that is what I am showing here. You end the hand with T14250.

You won money on all these hands, but that is not important. The curve determines the likelihood that something happens. Overtime everything shown on the curve will happen. During a specific MTT anything can happen. At BB=500 you are starting to face a significant elimination risk with AK that was not really there early on in the MTT.
These graphs assume that you are not making any adjustments to your play based on stack size. Stack size adjustments for AK will be pretty minor over the 100x to 20x range. Some poor MTT players may just play as if the stacks were deep the whole way, but good players will make adjustments as the stack sizes shrink. To keep things simple rather than a range of possible ways to play a hand, I will assume that there are only three ways hands are played based on stack depth. Deep stacks which would be for about 25x the blinds and up, middle stacks for about 8x to 25x the BB, and short stacks which is for 8x the BB or less. For short stacks I will assume a push or fold type strategy for most hands. In a later post I will show you how the EV graphs change for specific hands based on stack sizes.
I said in an earlier post that the cash game EV curves should be close to the most efficient way to play a hand. They should show the highest average EV. As you start to make MTT type adjustments to your play based on a small stack size relative to the blinds, you are moving away from ideal play and lowering your overall EV for the hand as a result. If you start pushing from the button with Ace little to steal the blinds this will be of a lower expectation value than a normal standard size raise that leaves you some options post flop. The curve will be radically different looking. The most likely result will be steal the blinds (a decent percentage move up), but the chance of losing all of your chips will be much higher, and your chance of doubling through goes up as well. Overall though you will lose more on average than before by playing Ace little in this way.
Now for an interesting result. While it is true that in general your overall EV will be lowered by making MTT types of adjustments late to specific hands, the overall EV value of the top hands (AA-TT, AK, AQ) will actually increase as stack sizes decrease relative to the blinds. This is a strange result. You play the hand in a less than ideal way, and your overall expectation goes up. I am not talking about a stretching of the curve. Top hands get stretched and shifted up in value late making wider swings more possible as well as increasing the overall Expectation Value of them. Anyone want to take a stab at why this may be true?


Thursday, May 22, 2008

Deterministic MTT Example #1

Above is my first example of what a deterministic MTT model would look like. The X-Axis shows the Big Blind Level, and the Y-Axis shows stack size. The blue bars show what the average stack size is at that point in the MTT. This one is simplified to show only two hands per level, and I left a bunch of hands out as well (where the blue bars remain). Its a bit hard to read, but this is what is going on. The Hole cards for the hand are shown at the top of the white bars. The white bar is the Expectation Value Graph for the hole card rotated 90 degrees. It is centered on the starting stack size for that hand, and the white bar represents the range of possible ending stack sizes. The EV graph indicated the likely results within the range of possible outcomes. The horizontal black line between hands represents your stack size.
For the first two hands shown you have about 1500 in chips with a BB of 20. You are 75x deep (close enough to 100x). The graphs at this point are not stretched out. When you pick up AA on hand 5, the BB is 40 and your stack is about 2k. You are 50x deep, and as a result the EV graph gets stretched vertically by a factor of 2x. This means that increasing your stack by say 30% on this hand becomes twice as likely as it was in round 1. For the AK hand you are 40x deep and the EV graph is stretched by a factor of 2.5x. When you catch 55 late the graph is stretched by a factor of 5x. Losing about 20% of your stack is the most likely result if you chose to play this hand normally at this point. Since you have an average stack, push or fold mode for this hand is probably not a great move just yet.
There are several takeaways from this very simple example. First off, the early hands played in an MTT are of little importance. The EV graphs are not stretched out yet, and you can't accumulate a significant amount of chips. As the MTT progresses, it becomes easier and easier to get big hands paid off in a big way. The range of possible stack size outcomes becomes much, much larger than before, and the stretching out of the EV curves make large percentage stack size moves much more likely. On the first hand of the MTT your ending stack can be 0-3000, but will tend to be little changed. For the 55 hand that comes late your stack size result will be 0-19,000 and a percentage change of +/-20% becomes a likely result. A minus 20% move here would negate a full-double up on an early hand. This also shows why the order of cards received in an MTT is so important (possibly the most important factor in determining the winner). If you are going to catch some big starting hands like AA or KK, you will be able to chip up easier, and by larger amounts later in the MTT vs. earlier. You would prefer to get these hands late if you had a choice.
What does this say about basic MTT strategy?
It really validates that tight early, loose late approach to MTTs. If you play tight and conservative early in an MTT it helps to keep you alive for later when larger percentage swings become much more likely. There is simply not much to be gained in the early stages of an MTT by risking your stack. The best MTT players have the best looking late game EV graphs, and play tight early on so that they will be alive to exploit their EV advantage later on. Its when the stacks and swings get larger late in an MTT that the winner is determined, and if your end game is good, you want to be alive when this happens. When you see top pros like Helmuth and A.C. strolling into a WSOP event two hours late, it is for a reason. The MTT can't be won in the first few rounds, and these guys can improve their hourly win rates, by skipping the early rounds and focusing on when their EV advantage gets largest over the field. This advantage kicks in when the stacks start to get short relative to the blinds.
This model is fully deterministic. It says you can't will your way into a win. All you can do is play your hole cards better on average than the rest of the field (improve your EV Graphs). Doing this will give you an edge, but in no way guarantees a win. When you play your hands better than others, get good starting cards, and get them at the right times (preferably late), that is when you will get the win. The most likely result for the best player in an MTT is that they will not win. This is because hole cards and hole card order are the primary factor in MTT success.


Monday, May 19, 2008

The Mathematics of Tournament Poker

I am probably taking on way more than I should here, but what can I really lose. You guys never agree with me anyway so let the hating begin.

I have a few topics to cover as a prelude to my attempt at a deterministic model for NL Holdem MTTs. I am basically trying to show that if you know what hole cards you will get (and in what order), how you personally play those hole cards in various situations, what hole cards your opponents will get and how they play them in general, then your MTT results are entirely determined in advance. Since you have no control of your opponents at the table and how they play their hands in general, and you also have no control of the hole cards you get and the order that you receive them in an MTT, you can't possibly control your own destiny in a large MTT. You are completely at the whims of the cards that you receive and the opponents and situations that you face. You can't win a MTT with air, and even the best MTT players need luck, cards, and situations on their side to actually get the win. This is something that I have felt for a longtime, but I am just starting to see the mathematical foundations for it. This does not mean at all that MTTs can't be beat for a profit, it just means that you can't beat them on skill alone.

While you can't control your starting cards or your opponents, you can control how you play them. This does not mean that you are inventing how to play your cards on the fly in an MTT. If you are a skilled MTT player, you know what you are doing and have a plan for nearly all situations that arise. Sure you will run into some strange and borderline situations from time to time, but even then you are relying on your experience to make the ultimate decision. You bring your poker game (hopefully your A-game) to an MTT. You do not create your game as a tournament progresses.

What this means is that when situations arise in an MTT you will play your cards as best as you can play them, based on what has been successful for you in the past (a rational model). Each unique starting hand has a weighted range of possible outcomes, based on how you play that hand and the various situations you will face with it. When you play a hand in an MTT, you are at the mercy of this range of possible outcomes. I will use expectation value graphs as a way of visualizing the EV ranges for specific hands. Rather than average all results into a total "Expectation Value" for a hand, these graphs show what really happens when you play a hand. If you double up 50% the time and lose your stack 50% of the time with a certain starting hand it will have an EV = 0, while the same hand will make or break you in an MTT. Raw EV values do not show this. What is much more important is the range of things that can happen when dealt a hand. And this range of possible outcomes is something that is stamped into your poker game before the MTT begins. A few more foundational ideas are below.

MTT stack sizes in large MTTs tend to form a Normal Gaussian Distribution

Above is a classic example of a normal distribution. This is a distribution of values where most values lie near the median value for the series, and values away from the median in both directions are progressively rarer to find. This chart puts things in terms of standard deviations, but that is not really important. What is important is that MTT stack size ranges will tend to follow this distribution throughout an MTT. Most stacks will be near the median stack size, and only a few will have a very large or near zero stack size. This was always obvious to me, but the reason why is not so obvious. If you started out 1000 players playing a limit holdem cash game with mega deepstacks, you would absolutely expect a distribution like this. Everybody starts with the same median amount, and your wins and losses overtime make your stack wonder around this median. Only a rare stack up of wins or losses can put you very far off of the median, and a nice perfect distribution would form naturally. But MTTs do not operate this way. The blinds are going up. People are getting eliminated. The average stack size is marching up as time goes by, yet the stack sizes still tend to follow a Gaussian distribution. Why is this? You would actually expect a lopsided saddle like distribution with the guys who have won some large pots on one side, and the guys who have bled down on the low side, and just a few people managing to stay near the median. This is not what happens. It becomes easier to "double-up" as your stack size shrinks relative to the median, while it gets tougher to double up as your stack size grows relative to the median. You get more action near the bottom, and you either get knocked out or pushed towards the median. From the perspective of the guy in the lead, the median is constantly growing with eliminations, but there are not enough chips in play at his table for him to easily keep pace. You simply can't fully double through when you are in the chip lead. So there is this force acting on everyone in the MTT pulling their stack sizes towards the median, and a Gaussian distribution overall. The main point here is that as you progress through an MTT and avoid elimination, you are most likely to stay near the median chip stack size. This will help to simplify a deterministic MTT model.

NL Holdem MTTs elimination rates are very predictable

If you know the blind schedule of an MTT and the average chip counts, you can easily predict how many people will be eliminated between breaks with a high level of accuracy. If you play an hour of NL Holdem a certain percentage of the players will be eliminated. Leaving you with a new blind schedule and average chip count to determine what percentage will go out the next round. Because the blinds march up in a steady way, and people are eliminated in a steady way, if you leave out the differences due to starting stack sizes (double or triple stacks), the same percentage of players will be eliminated in just about every hour of play. This is normally somewhere between 1/2 to 2/3s of the players who start the hour, or about 60% on average.

You can lose your entire stack or double through on any hand in an MTT

Since we will assume that in general you will be near an average stack while playing an MTT you will normally have a chance of doubling though or getting eliminated on any hand you are dealt. (based on your Expectation Value Graph for that hand)

Expectation value curves flatten out as the blinds go up in relation to your stack.

The EV graphs that I will use are based on database of actual hands at 1/2 NL holdem cash, with a $200 starting stack. The stack size is 100x the BB. In an MTT you will rarely be this deep. You will be playing for larger percentages of your stack when playing these same hands in an MTT, and this will tend to flatten out the graphs making larger percentage swings possible. The flattening of the graph will be entirely determined by the Stack size to BB ratio prior to being dealt a hand. You will see how this works when I show my first MTT example.

When you get to push or fold mode in an MTT the EV graphs will not be the same.

Good MTT players will be making adjustments as an MTT progresses and playing hands radically differently when necessary including going into "push or fold" mode. I do not dispute this, and my cash game EV graphs can't show this. However, you can make assumptions on what the changes will be and what the effect will be on overall expectation values. I will say that cash game play is near optimal, and that radical departures from a cash game style for a hand will lead to a reduction in overall expectation value for the hand. When you go into push or fold mode you are sacrificing some expectation value, by forcing the EV graph to change in a way that increases the chances for you to both chip up and be eliminated.

Good MTT players will adjust to the table and gain some additional EV.

While you can't choose who you will play against, good MTT players will exploit certain types of players at their table and raise the expectation value of certain hands as a result. While this is true, this is also fully reflected in a players EV graphs for their hands. Overtime they will play others of various styles and to the extent that those types of players are present and can be exploited an EV graph will adjust to this. So the idea of exploiting other specific playing styles to further your MTT chances is already fully baked into your A-game, and not adjusted for on the fly in an MTT. You either already now how to exploit the situation, or you don't. You do not learn how to exploit the situation during the MTT.

Expectation Value Graph Examples

Below are several Expectation Value Graphs for various NL Holdem starting hands. All based on a database of 100x deep 1/2 NL holdem hands. The graphs show the likelihood of increasing or decreasing your stack by various percentages based on your starting hand. The X axis represents winning or losing your stack in 5% increments. They are centered on EV=0 which most likely means that you folded preflop while not in a blind (or chopped heads-up). To the left is win 0-5% of your stack, to the right is lose 0-5% of your stack. The X-axis legend is offset a bit to the left. The Y-Axis shows the percentage likelihood of that result. A red line indicates the overall EV for the hand. During an MTT when you get dealt a hand, your starting stack size, plus the EV chart, plus an element of chance (which determines where you land on the chart) fully determines what your ending stack would be. This ending stack becomes the input for the next starting hand, and away you go until you lose all of your chips, or win all chips in play.

AA Expectation Value

77-99 Expectation Value (Middle Pocket Pairs)

22-66 Expectation Value (Small Pocket Pairs)
65s to T9s Expectation Value (Middle Suited Connectors)

AKo & AKs Expectation Value

Non-Suited, Non-Connected, No Paint (Throwaway Hand)

I think I need to stop now. I will put up my first example of an MTT progression fully determined by starting cards later in the week. All of this will start to come together at that point I hope.

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Wednesday, May 14, 2008

Runnin Like OJ

I watched tons of the OJ murder trial when it was going on. It was some fascinating stuff, and without online poker at the time, what else was I supposed to do. I was pretty convinced that OJ did it while watching the trial, but was also convinced that he was railroaded as well. I can't really say framed, because you can't frame a guilty man, but they definitely manufactured some evidence to help the DA's case. When the deliberations ended quickly, I went on record that he would be acquitted the night before the verdict was announced. I actually think the acquittal was the correct verdict. When it becomes clear that the evidence presented is a combination of real and manufactured, it calls all of the evidence into question, and you have easily enough reasonable doubt to acquit. There was no way that jury was going to convict OJ without thoroughly reexamining the critical evidence and a tough battle. A quick result was the easy one for the jury, acquittal. What came out about five years later which was not a national story was the "Rampart Division" scandal in the LAPD. It turns out that there was a huge culture of corruption, manufacturing evidence, and framing people by the same group of cops involved with the OJ case. A bunch of these cops went to jail for this or were thrown off the force. This convinced me once and for all that the cops had cheated aggressively to try to get OJ convicted.

The thing that bothered me the most about a premeditaited murder by OJ was the lameness of his plan. It was basically put the gloves and ski mask on, and head over to the wives house an hour or so before a flight to Chicago. Knowing that the your kids were home you would need to get her outside. Then slash her up good. Dump the bloody clothes and murder weapon while leaving your kids mother's dead body on their doorstep. Then race home beating the limo driver. Get cleaned up, and be in Chicago before anyone else is the wiser. Ron Goldman showing up was just a complication. I figured he dumped both gloves at the crime scene, and Mark Furman connected her with OJ, grabbed one of the gloves, and headed over to OJ's house. He smears some blood from the glove on OJ's car, giving them the probable cause to enter OJ's property and then dumps the same glove (to be found later) on the side yard. That's it in a nutshell. The cops had the right guy all along, but figured they would need some help getting a conviction against a popular celebrity.

So now someone claims OJ admitted it by saying that he had gone to Nicole's house, and she answered the door with a knife in her hand. OJ is quoted as saying something like 'If she does not bring the knife to the door she does not get murdered'. Now that's an interesting angle. If it was not premeditated that takes away my big issue with the lameness of the plan. He came by for some reason. She shows up with a knife. They get to arguing. She may even attack OJ with it. They struggle. She gets stabbed in the struggle. Ron Goldman shows up seeing all the blood and OJ fighting with Nichol. He comes to help. OJ does them both. This was not planned so he needs to dump the weapon and bloody clothes off somewhere, and does not beat the limo driver back to his house. This all makes perfect sense to me.

Except the bloody gloves

Why is he wearing Isotoner gloves in Brentwood unless this is premeditated and it is to hide his fingerprints. Brentwood is just a couple miles from the pacific ocean. It is never below 40 degrees there. You just don't see people wearing gloves near the beach in Southern California. OJ had the Isotoners for covering NFL games in Buffalo, not walking on the beach in California. So I think there are only three possible answers here.

1) The gloves were brought to the scene by the cops who bloodied them and planted one at the scene and one at OJs (they were not OJs gloves)

2) The murder was premeditated as thought, and this latest story of OJ claiming she brought the murder weapon to the door is just complete BS.

3) OJ is just a Ghey-ass Isotoner wearing ex-jock.
Thoughts anyone?


Tuesday, May 13, 2008

The Dank Escape

I have been in the "Dank Position" many a time. My MTT playing style tends to put me there at some point when things are not going my way. For those not in the know, the Dank Position is last place, but still alive in an MTT. Its the position at the bottom of the leaderboard for the one with the least amount of chips. Its not all bad though, and I tend not to panic when in the dank position. You need to think positive. You are in a better position than everyone who has been eliminated, and if you can settle down and stay alive you can only move up from the dank position. You can win a pot and move out of the dank and up the leaderboard, or somebody can bust above you, and you will slide up a position while remaining in the dank. There is only one way out of the dank position, and that is to bet your way out. If you are short and in the dank, then it is push or fold mode. If you have chips while in the dank, you pick your spot, but still you bet your way out.

This brings us to last night's MATH event. This would be my first MATH in all of 2008. I am not a big fan of 6-max, and when Hoy switched the format I decided to spend my limited poker time elsewhere. I was able to lock down a seat in the Bodog championship, and have put almost no effort into the BBT3. I have had a few decent runs in the Skillz events, and Riverchasers with a couple FTs in about 10 total events so far. I had a small window of opportunity, and decided to take a shot this week at the MATH, and possible skip Tuesday's bodonkey if I caught too much flack from the wifey.

We would get started 5-handed at my table with PokerBrian, MiamiDon, UpForPoker, and Joanne seated. The table was crazy aggressive from the beginning, and I was thrown totally off what little 6-max game I have. I try to play 6-max deepstacks like 9-max with almost no adjustments in the early going. I want to play small ball, and get money in post flop. With just about every pot getting raised preflop at this table, I found myself playing hands I should not be playing to stay active. Joanne was on my left and was absolutely pwning me. Every pot we played she won. Every time I bluffed (and I was bluffing way too much) she was all over it. I was bleeding chips like mad, and afraid of playing pots with her. She was picking up on this, I guess, and would come along every time I played a hand. I was getting reminded of why I hate 6-max, and was just plain uncomfortable at the table. Eventually, GCox would show up on my right, making the table 6-handed, and changed the dynamics of the table a bit. I started to get a walk once and a while, and the aggression level came down a bit. Through the first 65 hands, I had won just three pots (one a walk), which is just horrible for 6-max, and was down below 2000 in chips. I would bleed all the way down to the Dank position with about 60/70 players left, and just north of 1000 in chips. I wanted to just jam something to end my misery, but I decided to hold on, and at least try to get it in good when I pushed.

After about 20 minutes in the Dank, I started to work my way out. I got a double up, and won a few small pots, before getting involved with PokerBrian (table chip leader), in some big pots. With about 3500 in chips, I open raised with AKo, and Brian reraised preflop. I jammed, and he thought and called with AT and I doubled through. I would win a few more pots, before catching QQ and open raising. PokerBrian reraised, and I re-reraised for most of my chips. He jammed with 77 and I called. Doubling through would put me north of 20k in chips. At the second break the leaderboard would look like this, as I had gone from worst to first.

Things were starting to go my way, and I even flopped a straight against Gracie on the below hand. She would flop top-pair and a flush draw. On the turn she would hit trips, and we would get it all in. She was sitting on 19 outs to the river with 9 outs to the flush, 9 outs to a boat, and one out to Quads. All those outs beat my flopped straight, and she would hit the flush on the river, knocking me back down into the pack.

As we approached the FT I would play a massive coin flip with Gracie, with my AKo beating her QQ when an Ace flopped. I would take a nice chip lead to the final 6-handed table. At this point, I had survived the 6-max portion of the MTT, as once you get to the final 6, it becomes identical to a full ring MTT with 6 people left. Below is an image of the FT and the mighty Ace-Jack.

We would get down to four handed semi quick. The four handed battle would be a long and drawn out. I would hold the chip lead most of the way through four handed play that lasted about 1/2 hour. We would then get to three handed, and Shabazz would start to pull away with a large chip stack. I was also starting to tire of short handed play. I can play short handed pretty good, but it is such a mental game that it is tough to stay focused for a long period of time. I would pick up AA and get it in preflop against Shabazz's JJ.

A two-outer on the river would send me home in third, without a TOC seat. PokahDave was knocked out on the next hand. The double-up would have probably got me to heads-up, but I would have still been at about a 3-1 chip disadvantage with a bunch of work to do. I guess I will just have to let the $240+ cash make me feel better. That cash pushes me into profitability for the BBT3. I was also profitable over the BBT1 and BBT2 series which is not bad for a cash game specialist. I guess that's not really fair, as I am a bit of an MTT specialist nowadays. I should be able to take a few more shots at a TOC seat, but this one was pretty close. When you end up with 4 skilled players late, it is really anyone's game. You just need to keep putting yourself in those types of positions, and eventually you will get the win. The cash did move me ahead of Hoy in the MATH leaderboard which is sweet because I have played only one, and he probably has played them all.

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Wednesday, May 07, 2008

AA and 44-66 Expectation Value Graphs

I have refined a bit the Expectation Value graph and have ended up with what is below.

Expectation Value in Percentage for AA
This was data collected over 13k hands at FullTilt 1/2 NL Holdem. 63 instances of AA for the above graph. The vertical bar shows the percentage chance of the result each time you are dealt AA. Each bar represents 5% of your stack size. This shows that 33% of the time you will win 0-5% of your stack size (steal the blinds), and about 5% of the time you will win 45-50% of your stack size. I am also three times more likely to get stacked than to double up with AA based on the 63 hands. Keep in mind that this is my chart for how I play AA. Other player's charts will look different, but in general should show a similar shape. The blue line is a guess at what the long term results would average to if I had bigger sample size. Overall I win 7.5% of my stack size or about $15 on average when dealt AA at a 1/2 NL cash table. You win tons of small pots with it and have a significant chance of winning a decent pot. You only actually lose money on the hand about 13% of the time you are dealt it.

Below is the chart for 44-66 the semi-dangerous low to middle pair. Again this is for 1/2 NL Holdem at Full Tilt. In this case 180 hands are shown.

Expectation Value in Percentage for 44-66

For the small to middle pairs a full 66% of the time I am dealt them I will lose 0-5% of my stack. This is me limping in with them, and getting either bet off preflop or missing the set. About 4% of the time I will call a raise preflop, miss, and lose 5-10% of my stack. 15% of the time I will win 0-5% of my stack. This probably includes some late position plays where I am not limping or limp/calling the hand preflop. Outside of that I will win a bunch of decent sized pots, and not really lose too many big pots. Overall I will increase my stack size by 1.1% or $2.20 on average each time I am dealt 44-66.

Where am I going with all this? Its going to be a different way of looking at MTT results. If you take a chart like above and rotate it 90 degrees it becomes an operator on your chip stack. I want to build a few more of these charts before I get there, but you can take whatever your MTT chip stack is and then take the expectation value chart for the hand that you are dealt and line up the 0% mark on the Expectation Value axis with your stack size. Then rather than just give you the +7.5% in EV for AA you would get some result between +100 and -100% of your stack based on the likelihood of each occurrence. You can then simply map out your MTT chip stack size based on the hands you are dealt. This all sounds a bit crazy, but I think this is actually a very solid model of how MTTs work. The key is that each player has their own EV curves for each hand they are dealt in an MTT. They are also free to manipulate how they play certain hands to influence the EV curves as necessary. When you get into push or fold mode late in an MTT the curve for 44-66 will look a bunch different, but that is how you may want it to look late. Ultimately, I think this will show why we are more of a slave to the cards in an MTT than many would want to admit. Sure we can play each hand slightly better then the next guy, but is that enough to overcome the threat of elimination on any hand in an MTT significantly?


Bodonkey Insurance & Back to Back 5k Cashes

I played the Bodonkey, Bodog 5k and Skillz Razz last night. I have not pointed in the bodonkey since my win, and although I probably will not need it I wanted to point one more time just to make sure. I got off to a decent start in the bodonkey getting up to a quick 3700, but then I ran AK on a K high flop into High on Poker's well played AA, then ran 66 on a 554 flop into Byron's 5 to become DQBs by the turn. At this point I found myself with about 425 in chips, but I jammed a couple hands, and got back to a more comfortable 1200+ and held tight for an 8th place finish the insurance points and the bonus T11.

In the bodog 5k there were 455 runners. I caught an early double up and just cruised to the final three tables. There were some serious retards with stacks late, and I was chipping up pretty quick until I got it in with JJ vs. ATo and lost to a four flush on the river. The win there and I FT for sure, but I would end up flaming out in 26/455. I finished 14/430 in my last attempt. This MTT just seems too easy, and I will continue running it Tue/Thu whenever possible.

I was pretty excited about the Skillz Razz. I figure that is my best chance at a seat followed by Skillz HORSE, Skillz HA and River Chasers NL Holdem. I played my normal hyper aggressive RAZZ style, but the cards were never there for me when I needed them. My stack was all over the map (mostly below average), but I never could string any big pot wins together and flamed out mid-way. I was able to drop a few BOOMs at the table. Then I started the new whisper boom for RAZZ which gets dropped like this"b o o m". Pretty doubtful I will make the BBT3 TOC at this point, but I have less than 10 events in so far.

I am starting to work on the EV chart for AA. I am going to use cash game data from poker tracker rather as the basis. It will be much more interesting than the throwaway type hand that I already did. Stay tuned.


Monday, May 05, 2008

Visualizing Expectaion Value

Expectation Value is probably one of the more poorly understood terms in poker. While many will know what it means in general, few probably could calculate it for a specific hand. I have been playing mostly MTTs lately, and I started thinking about how important the series of cards that you are dealt in an MTT is to your odds of success. Think about the raw expectation value of each hand that you are dealt. If you get dealt a bunch of +EV hands your stack should move up, while a bunch of -EV hands should send you stack south. Its a lot more complicated that that though. Different people play the same hands differently and for different expectation. Also when you say a hand is +T207 in expectation value, that does not mean that that you win T207 each time you are dealt that hand, it means that's what you will win on average when playing the hand. The average is developed from all the times you fold preflop, and all the time you win or lose a small pot, get stacked or double up. T207 may be a small percentage of your stack but it includes the times you are stacked playing the hand as well as rare instances when you triple up.

Now lets look at Tournament poker. On any hand you can be eliminated, double or triple through, or win/lose a small or big pot. So even if the expectation value is small compared to your stack, playing any hand in a MTT has the potential to knock you out. What I am trying to get to is that the variance in expectation value is HUGE for all hands. Understanding this variance level is vastly important for success in MTTs. Folding a bunch early is not a great way to build a stack, but it is a great way to reduce the variance that can knock you out in an MTT before the cash payouts begin.

So now lets try to visualize Expectation Value for a simple throwaway type hand. I will use 84o as an example here, but any hand that you would autofold from outside the blinds and play with extreme caution from the blinds will have a similar curve. I am starting with a throwaway type hand because it will be easy to deal with. Playable hands will take much more work to figure out the expectation curve. Since I am developing this as a way to look at MTT results, I am going to use percentages instead of raw numbers. That way as the blinds go up, the curves stay the same. The pots get bigger later in MTTs because the stack size you are leveraging becomes bigger. To simplify things a bit I will assume that you can lose your entire stack on any given hand (somebody at the table has you covered), and you can win up to three times your starting stack (quadruple up). While in theory you can more than quadruple up, in practice that is so rare that we can simply ignore it. So you end up with a graph that goes from -100% of your stack to +300% of your stack. This is how much you can win or lose on a given hand relative to your stack. For each percentage that you may win or lose on a hand there is a percentage likelihood that that will happen. The sum of the product of percentage likelihood times percentage won/lost will give you the overall Expectation Value for the hand. Below is a chart for 84o.

Looking at the above chart you can see that 78% of the time you will be outside of a blind, and will autofold your 84o and have EV=0. In the SB you will fold most of the time, but play on when very priced in. From the BB you will play if you can limp, or could call a min raise with enough pot odds. When you fold your SB you will lose 1% of your stack (assuming a stack size of 50x the BB). When you fold your BB you will lose 2% of your stack. When you play on you are most likely to win or lose a small pot with this hand as shown by the small band around 0%. It is also more likely to double up or get eliminated than to win or lose 30-90% of your stack. You can see the small bumps at -100%, 100% and 200% showing this. When you sum up the EV for this hand, you will find you will lose 0.15% of your stack on average when dealt it, with a small chance to win or lose a massive pot. This is the chart for a conservative player who will not get out of line with this hand. An aggressive player who may steal from the button or cut-off with 84o would have a very different chart. The results would be more spread out indicating much higher variance. Playing aggressive simply increases the variance. Playing 84o aggressively will most likely reduce the expectation value to say -0.25% as well. I am going to stop here for now, but will try to put together charts for suited connectors, small pairs, big pairs, AK and other playable MTT hands. When I get enough of these complete I will start looking at how all of this actually determines your stack size as tournaments play themselves out which will be pretty interesting.