Stack Size Essay

[fnord_too]

Why does the value of chips change depending on how many you have?

Before we can get into the debate of what a non average stack is worth in cashing expectation, we need to establish the importance of chips in a tournament.

There are some famous essays discussing the marginal value of chips in a tournament. These essays discuss how the marginal value of chips drops as chips are accumulated. This argument is basically founded in the reality that tournaments are not winner take all events and that tournaments play out until one person has accumulated all the chips.

While the mentioned articles are quite correct, they really have no bearing on the tact I am taking. What I am talking about in this section are the tactical and strategic implications of having chips. Later I will look at their value in terms of cashing expectation using the actual pay out structure of a tournament (noted above).

Tactical consideration – options available:

A lot of times when one discusses stack size in a tournament, it is in terms of how many times the big blind (BB) a player has rather than the actual number of chips. Why is this? The number of BB in your stack determines the number of options you have. The more options you have, the more opportunity you have to exploit your skill advantage over opponents. Let me illustrate what I mean by stratifying the stack sizes. Note that the following discussion assumes that the average stack size is such that a 3BB standard raise is reasonable. At the stage of the tournament we are considering, this is almost always the case. Also, it assumes further that a 3BB open raise is in fact the table standard. If the standard is more or less, the following ranges may need to be adjusted.

One other important note: the number of options you have depends is limited by the number of options your opponent has. For instance, it does you no good to have enough chips for rich post flop play if your opponent’s only options are pushing or folding. This is the subject of the next section.

0 – 3 BB: You simply have no choice other than which hand you will take a stand with. You have next to no folding equity (that is there is next to zero chance that pushing will win you the pot by virtue of inducing all of your remaining opponents to fold). Realistically, you are looking at putting your last few chips in the pot pre flop and running your hand out against one or more opponents.

3 – 12ish BB: You have some folding equity here, but if you come in for a raise, you are basically committed to the hand, therefore, except under special circumstances, if you decide to play a hand not in one of the blinds you are pushing pre flop. (Sometimes you will be able to over limp into a pot and sometimes you will raise less than all in with a monster pre flop to try to get action, but these are really the exceptions, not the rule.)

12 – 15 BB: You can now raise a pot pre flop without being pot committed. This means that after your pre flop raise you still have options. Also, you could call a pre flop raise and still get away from your hand later. With this stack size though, any post flop action pretty much commits you to the hand. If you make a 4BB continuation bet or call after the flop, the pot will have 14 – 15.5 BB in it and you will have 5 – 8BB left in your stack. You really should not put yourself in this position if you are not willing to scoot the rest of your chips into the pot, and if you are willing to do that it is usually better to be the aggressor and push them in at first opportunity (except when you have a hand that welcomes a showdown, in which case you want to get called so you may want to slow down some to induce calls or raises.)

15 – 30 BB: With this many chips, you can make two post flop actions. You can reraise of check raise and have folding equity on the action. You can fire at the flop and the turn. Whatever the combination, you can handle one post flop action and still get away from the hand or have enough chips for an effective (i.e. one with folding equity) post flop action.

30 – 60 BB: Now you can engage in two standard post flop actions and still get away from your hand, or put in an effective third action. This affords almost a full range of options, and allows for very rich post flop play.

60+ BB: You will rarely be in a situation where both you and your opponent have more than 60BB in the middle stage of a tournament. There are two reasons for this: 60BB is usually well above the average stack size so the likelihood of two players having this big of a stack at the same table let alone both having a hand worth playing on the same deal is slim. Moreover, people with over 60BB stacks are loathe to put their whole stack at risk since it is such a huge asset.

Strategic consideration – stack domination:

We noted above how the larger stack in a confrontation really only has as many options as his shorter stacked opponent. There are other advantages to stack size beyond having more options to out play your opposition. These are the ability to survive losing a hand and the extra pressure you can apply by putting someone else’s tournament life in jeopardy while not risking yours.

Being able to survive losing hands is extremely important. Hold em is a high variation game that is blanketed in uncertainty. Losing hands is inevitable, so you need enough chips to be able to effectively continue after you lose a hand or be fortunate enough to avoid losing any hands until you do (that is, get lucky). You really want to be in a position where your opponents have to get lucky to survive and you have to get unlucky to get knocked out. That is in general (you have to lose a few hands to get knocked out where they are often all in) not just on specific hands (though it is very nice to be in a similar situation on specific hands, too).

The fact that when a shorter stack tangles with a bigger stack they put their tournament life on the line affords the bigger stack the opportunity to exert tremendous pressure on the shorter stack. That means that steals against shorter (though not desperately short) stacks succeed more often, and shorter stacks are more reluctant to attack bigger stacks blinds (assuming the bigger stack is not weak tight despite their chips).

Relationship of tactical and strategic considerations

So which factor is more important, available options or stack dominance? It really depends on the size of the average stack and the size of the difference between the two stacks in question.

When the average stack is over 15 or 20 BB, it is very important to have enough chips to have more options, since you will have more opportunity to exercise those options. That is, if the average stack is 25BB and you have 20BB, your chances of being in a hand against someone with at least as many options as you are a lot greater than if you had those same 20BB but the average stack size was 10BB. Also, it is important to understand that if a reasonable bet or raise from the bigger stack will not commit the opponent to a show down if called, the value of stack dominance is reduced. Unreasonable bets from the bigger stack are not a good idea since they make the risk to reward ratio unfavorable. That is not to say that stack dominance is not still important, it just delays when the bigger stack can threaten his opponents tournament with a reasonable action, which typically means the opponent will have more information when making his decision.

When the average stack size in relation to the big blind drops, stack size becomes the most important factor since hands will tend to played all in pre flop or on the flop if they are contested at all. In these cases, the ability to survive losing hands is extremely important.

[woodguy]

Good stuff Fnord.

Stack size implications are one of the NL considerations that many of our weak opponents do not take into consideration, and our ability to adjust our play based on stack sizes is an advantage that most of us do not utilize properly.

Ok, next can you please write an essay about how to combine stack size, distance from bubble, severity of bubble, PF action and position in determining which hands to play and how to play them? [img]/images/graemlins/laugh.gif[/img]

Regards,
Woodguy

[SossMan]

well stated, fnord.

[ZBTHorton]

Excellent post. Especially considering recent arguments.

[MLG]

Nice stuff. 30x-60x also includes the ability to reraise preflop without committing yourself to the hand.

[tek]

Here's my thoughts on a big stack betting out against a short stack. If your bet is such that the short stack will be all in to call, their rational will be to double up/or go home if they call. They know they can't survive much longer. Usually they will have a random hand and hopefully the big stack will not. Their is the possibility that you catch the short stack slowplaying a great hand and double him up.

He now has more chips and more strategic options, and a psychological boost.

One way I see to avoid this and simultaneously prolong the short stack's slow death is to bet half their stack. Instead of looking at a double or nothing possibility, he is looking at a 1.5 or 0.5 possibility. This would be strategically a bad play, thus he would fold and continue to get blinded down. But again, he could reraise himself all in if he has a better than random hand. So as always, you need to have a good hand and/or good read on your short stack target.

Now, I would like to add an essay I found at the Fish Forum we are all so enjoying making fun of. This essay is one that I had been thinking about, but never got around to writing. It's called the Highlander Effect by a poster there named Jon.

Fish Forum main page

The Highlander Effect

Ok, I'm writing this in the hopes that people will stop concentrating on tournament stack sizes and chip lead. I'll explain a little thing I call the "Highlander Effect". First, a little background for the Highlander unanimated.

Highlander is a popular TV show/Movie(s) about a group of immortal human beings whose only way to the grave is by being decapitated by another immortal. When death occurs the killer is bestowed upon them all the power of that immortal plus everyone he has killed. Kill and immortal with 100 kills under his belt and you now have 101 immortals worth of power. Eventually there will be only one left and with the power of thousands of immortals before him. That's the short and skinny of it.

Too many people believe that in order to get ahead in a tournament that they need to make power plays in the early stages and risk their chips. Tournaments are about survival and staying ahead of the blinds. A lot of players feel that they need to be at a stack size that is in relation to the average so they compare their stack against other players. This is the wrong mentality to get into. Your only focus should be to increase your stack only enough to stay ahead of the ever increasing blinds. You will only need to win enough to pay the blinds and one or two called bets each round. That's it. Only enter the pot with a statistical advantage and a hand worth calling an all-in bet. Obviously Cat 1 hands.

Now, here's where the "highlander Effect" comes into play. Remember this golden FACT: the chips never leave the table! Only players do. If there's 100K worth of tournament chips in the beginning, there will be the same at the end (Only exception being color changes and raced off chips. The principle doesn't change though). The chips represent immortal power and the players the immortals. Knowing this, it's obvious to see that a power play later in the tournament will be of much more equity than the same hand played early. When you go all-in on a player late in the tournament the wins are much greater and the balance of power shifts more drastically than if it were earlier. If chip equity is spread between say 4 players, taking a win at this point gives you at or more than 25% more total chip equity. You kill him off and you essentially take the chips of all before him. I've seen people, including myself, have the short stack all through the tournament; never bust anyone out; never go all-in; fold 95% of their hands; and make just enough to keep paying the blinds. On the final table they play one hand all-in with their short stack and steal a huge chunk of total equity. Then I watch as they aggressively lean on the other players with their new found stack and crush the remaining players. In one hand they gained enough stock in the game to do a hostile takeover. Risk your equity and bust a player out early and you gain practically no power because the tournament chips are spread too thin.

Think of this principle as you play. Be patient and don't concentrate on what other players have. It's an illusion that will have you impatiently calling too many hands to catch up. Play the blinds and wait for those good cat 1 hands that you will feel comfortable raising with. If you lose with a cat 1 hand, then you have most likely been a victim of a bad beat because somebody who had no business calling you just drew out on his statistical underdog. You can walk away feeling confident that you had the best hand going in, got your chips in while you had the best, and lost with a respectable hand.

[fnord_too]

[ QUOTE ]
Nice stuff. 30x-60x also includes the ability to reraise preflop without committing yourself to the hand.

[/ QUOTE ]

Right, I sort of ignored extra pre flop actions. In a lot of ways, an action is an action (in terms of bet size and it's implications) regardless of where it occurs. There are a couple of exceptions, though. One is that pre flop, the difference between two hands will almost always be less than it is post flop (that is to say, the equity difference on the flop tends to be greater than it is pre flop). So that is a long way of saying, yes! Just because you have enough chips to make a post flop action and get away from the hand does NOT mean you can necessarily reraise pre flop and still correctly get away from the hand.

The other difference is that raises are almost always more than minimum allowable raises. So it may be feasible and correct to bet say 4BB on the flop and 4BB on the turn, but there are not many instances where you would want to raise a 4BB flop bet to 8BB.

I just read what I posted for the first time since I wrote it (which was a few days ago) and I noticed a few typos. I didn't really proof read any of this before I posted it (which was really on a whim prompted by El Diablo's post), so please forgive the gramatical errors.

[fnord_too]

Here are my initial thoughts on the highlander article:

This is realy the way I thought as recently as a few months ago. I think that coasting until you find a good opportunity then striking, and then wielding your stack as a weapon is definitely a viable strategy.

The problem arrises in that you need to increase your stack greatly just to be in a position where doubling up will give you an effective weapon late in the tourney, so you need to be making those 5% of hands really pay off. (I don't think my played hands was ever less than 10 or 12%, but I digress). The implication is that you play big pots (relative to your stack), and when you do this you run the risk of being eliminated. Even if you are getting in as the favorite most of the time, your chances of survival can be quite low.

Lately I have been pondering the statement that it is better to increase variance early to mitigate it later. One of the key reasons being that the stakes (in terms of cashing equity) are much higher later.

I think developing a good stack early is extremely important. I have been increasing the range of situations I will try to exploit by a substantial ammount lately. (Additionally, I am continully amazed at just how big an asset agression is.)

At any rate, I keep the thoughts in your article as a reason not to force action. That is, I agressively seek chips early on, (and later on, too, though through different tacts), but if opportunities are not presenting themselves I know that waiting is a better alternative than forcing things. The edge I need to play a situation is inversely proportionate to the vulnerability of my stack size later in tournaments (to the point that I am pretty short stacked, then I am willing to gamble more).

[PktAcesSoWht]

At what point BB-wise relative to your own stack would you consider yourself pot committed? I do not feel that I have a good grasp of when I really should be pushing and making a move on the flop because I am going to be pot committed anyway. I am thinking mainly when the blinds have gotten above 100/200 level and moving up.

Also if this could be framed in relation to the average stack and big stack that would be great. I know that the closer I get to the final table the bigger the swings can be so I would like to have a frame of reference to when I should be pushing either PF or on the Flop to achieve maximum Fold Equity on the hand, since I am going to be pot committed anyway.

And I want to say thank your for this great essay.

[fnord_too]

Pre flop, I think almost all the time you have less than around 12BB, if you play in a raised pot you are committed. That means unless you are in the blinds or in an odd overlimp scenario, you should be putting all or none of your chips in.

Post flop, I don't think you should ever put more than 1/3-1/2 of your remaining stack into the pot if there is a chance you will fold to any future action. There are some cases where you may close the action getting odds, and the risk to reward is worth it to call off half your remaining stack. For instance, say by some odd series of events there is a 20BB in the pot on the turn, you have 9BB left, and there is a 5BB bet to you (not counted in the 20BB) and you are the last to act. Further suppose you have the nut flush draw on an unpaired board, but there is no chance you will win the hand without improving to a flush. Here you are getting the right odds to call, and losing the 5BB is no where near as detrimental to you as winning 20-24BB is benefitial. (You may not even need to be getting the correct odds here to make this correct, but that is a topic for another day).

I don't know if this really answers your question, but the idea is that when the pot gets big in relation to your stack, you are going to be getting good odds to call. If those odds are not good enough, you probably made a mistake earlier in the hand. Most of the time this mistake was calling. If it was in betting, than their are two cases: Either a smaller bet could have been made with folding equity or it couldn't. If it could, you bet to much, if it couldn't you needed to push or fold. (To not make the calling mistake, you would also have to push or fold. If you do not have folding equity, do not push unless you want to show down your hand. If you do want to show down your hand, calling is not bad if you think you DO have folding equity. In the cases where you trap and a very scary card comes, you just have to pay off on the end because good agressive players will bluff with scare cards enough to make calling correct.) (Also note, there are ALWAYS exceptions.)