quantifying the advatnge of being a bigs stack?
Here is a question that I have been struggling with and I thought this esteemed group may have some thoughts.
I believe that there is a point in a tournament in which the consequences of loss or more severe than the advantage gained from the win. But, I do not have a useful quantification of this point. I am even struggling to get my head around exactly what I am talking about. A couple examples…
Example 1:
You are the average stack size $10,000. Blinds $50-100. When faced with an edge for $400 chips, you probably should take it. Being $400 closer to having all of the chips is, instinctively, more important than losing the $400. At least, if you think you probably have an edge, but aren’t sure you might go with it since the loss is not devastating.
Example 2:
You are the average stack size of $10,000. Blinds $500-1000. You have a small edge for $4,000 chips, should you take it? My instinct is that a win of $4,000 is great, but a loss of $4,000 is much worse. My instinct is that $14,000 chips slightly increases my chance of winning, but a stack of $6,000 considerably reduces my chance. In other words, the loss is worse than the gain.
How do I quantify this? How does one quantify the advantage/disadvantage of big stack/small stack compared to blind size.
It seems to me that if a person could arrive at a “formula†then they would be better prepared to hit the brakes at the right moment.
Thoughts?
I believe that there is a point in a tournament in which the consequences of loss or more severe than the advantage gained from the win. But, I do not have a useful quantification of this point. I am even struggling to get my head around exactly what I am talking about. A couple examples…
Example 1:
You are the average stack size $10,000. Blinds $50-100. When faced with an edge for $400 chips, you probably should take it. Being $400 closer to having all of the chips is, instinctively, more important than losing the $400. At least, if you think you probably have an edge, but aren’t sure you might go with it since the loss is not devastating.
Example 2:
You are the average stack size of $10,000. Blinds $500-1000. You have a small edge for $4,000 chips, should you take it? My instinct is that a win of $4,000 is great, but a loss of $4,000 is much worse. My instinct is that $14,000 chips slightly increases my chance of winning, but a stack of $6,000 considerably reduces my chance. In other words, the loss is worse than the gain.
How do I quantify this? How does one quantify the advantage/disadvantage of big stack/small stack compared to blind size.
It seems to me that if a person could arrive at a “formula†then they would be better prepared to hit the brakes at the right moment.
Thoughts?
Comments
Once you established a type of system where you could identify a number of different styles (loose, passive, agressive...) that could be represented as varibles and the same could be done for the stages of a tounrnament. You could then equate that and apply it to the situation that is presented.
Sorry if this doesnt make sense, im still trying to figure out a better way to say what im thinking....I will repost when i can develop this idea a little further.
I need to give this some heavy thought. I am not sure I may even come up with an answer. Thanks for the challenge, Dave. You have helped to convince my wife that I am completely obsessed with the game. Bwawawawawawawa.
If you divide stack size into roughly 5 categories, from 1 to 5, with 1 being a huge dominating stack and 5 being a short short stack, you have to look at the difference in moving between categories. The advantages and disadvantages gained from moving between categories 2 through 4 are minor. So if you're sitting in category 3 (avg. stack) ... any decision that may only move you up one level (2) but if it doesn't work out pushes you all the way down to level 5 (short stack) should be avoided. On the other hand an edge that can leave you no worse than say level 4 (below average but not a short stack) can likely be persued because the lose doesn't move you out of that middle range where your flexibility to play is roughly similar.
Essentially unless that edge has the potential to get me to tier 1 where having lots of extra chips provides you much more leverage pushing that small edge isn't worth the risk of ending up in tier 5.
Suppose there are 10 players left. Each player has $10K. OK, it's a tie. All other things being equal, each player has a 10% chance of winning.
Now, suppose one player leaps ahead to $15K, another falls to $5K,and the others remain at $10K. Does the $15K player now have a 15% chance of winning? Knowing nothing else, you would have to say "yes, he does." But, there are other factors. The two that come to mind are "size of blinds" and "generalities of human behaviour." If we make certain assumptions, we can reach certain conclusions about how much the extra $5K will help you to win.
My strong feeling (instinctive, I admit) is that the $5K guy has less than 5% chance. And, the $15K guy does not have more than 15%. If I am right, then the consequences of losing the $5K is more severe than the benefit of winning. If I am right, what are the circumstances that make me correct? If the circumstances can be identified then one could identify the "danger zone" in which one should strongly choose "avoidance of loss" over "garnering of a win."
On the other hand, this could all be malarky and I could be out to lunch.
Just kidding obviously. I simply couldn't resist a joke where a comma was basically the punch line.
I seem to be in opposite-land on this one. I think I prefer taking the slim +EV shot in Example 2 over Example 1. The reasoning is that with the 10*BB stack of Example 2, I am feeling much more pressure to build chips than I would be in Example 1.
Whenever I get below around 15*BB (or so) in a tournament I'm far more willing to take slim +EV high Variance shots. Why? The theory of avoiding such plays is related to the fact that a good player can wait patiently and build better +EV and/or lower variance opportunities in the future. When I am short on chips relative to the blinds (as in Example 2), there seems to be no more time for this kind of waiting game.
Although risking 40% of your stack on a slim +EV shot may seem harsh, so to may be the alternative of possibly facing a barage of multiple -EV opportunities at a cost of 15% of your stack per orbit in blinds. It's not so clear to even a rocky-rock like me how much patience can be a virtue at this stage.
On the other hand, when I am comfortably stacked at 100*BB, I have loads of time to pass on slim +EV shots now (even if, or possibly especially if, they represent a small percentage of my stack) in order to wait for greener EV/Variance pastures down the road.
Example #1: No thanks, I think I can find a better spot for these 400 simoleons in the next few rounds.
Example #2: Okay, I'm desparate to get some more simoleons. Let's race.
I'm dying to know what Harrington has to say about his so called "inflection points" in his next book. From the clues he has given so far, I think he has in mind something along the lines of the quantification that Dave is looking for here.
BTW, thank goodness for online dictionaries. I never would have guessed the spelling of 'simoleon' in a milloleon years.
ScottyZ
Are you assuming the blinds are small or big here?
The common (though, I have no idea where it comes from) theory of tournament deal-making is that when the blinds are big (as they generally are near the end of a tourney) is that a big stack should give up equity to the small stack. That is, Mr. 15% o' the chips has less than 15% equity, and short stacked guy has more than 5% equity.
My guesses as to why this might be correct thinking are:
1. The big stack has less time to make use of the big stack.
2. The small stacks can gain certain advantages by being often all-in. (See TPFAP, Pg. 67)
My guesses as to why this particular deal-making theory might be a load of hooey are:
1. The small stacks are often forced (by the blinds) to go all-in against their will.
2. The small stacks usually have their poker skill set taken away from them, and have to degenerate into move-in specialists.
Of course, there is no parallel deal-making theory when blinds are small since players rarely make deals when the tourney has lots of play left (i.e., the blinds are small). I think (apart from the "human nature" you mentioned) all else being equal with the blinds small, we have 15% = 15%, 5% = 5%, and let's shuffle up and deal like it's 1999... erm, like it's hand #1.
ScottyZ
I still haven't wrapped my head around what I am trying to sort through. I will try again...
At some point in the tournament, although stealing shows a long term positive EV, the down side of variance makes short term fluctuations critical. Since you hate losing more than you love winning, you should bend over backwards to avoid REALLY high variance play.
I think I'd still prefer making this kind of slim +EV/high downside Variance play in the Example 2 situation. However, in Example 2 I'd want to quite aware of the chances that a steal would actually work against the players (particularly the BB of course) who are left in the hand. Reason: I'm teetering on the edge of pot-stuck country by making it $4,000 to go in Example 2.
Hmmm... I suppose I'm essentially saying that I'd enjoy the play in Example 2 more if it had lower varaince. Please let me get back to you on this one once I finish running around in circles.
But I'll mostly stick with my earlier thoughts on the risk $400/$4,000 to win $400/$4,000 situation. That is, I think I'd be more inclined to make the play with the Example 2 short stack.
ScottyZ
For fun lets say Zone 1 = 30BB and up, Zone 2 = 11-29 BB, Zone 3 7- 10 BB, and Zone 4 6BB or less.
In example one I am in Zone 1 and feel like I have a lot of play in my stack. The 400 chips does not move me into another zone so the play is simple...if I think I'm ahead (regardless by how much) I make the play.
In example two I am in Zone 3 and making the play will move me down into Zone 4 if I lose but moves me to Zone 2 if I win. So it boils down to where do I feel comfortable playing. For me losing here puts me into my least comfortable situation but winning moves me into a much more comfortable zone. So with an edge I make the play and hope to move into a more comfortable zone.
Sorry if this makes no sense at all. It kinda goes with what has been said above but is a step closer to coming up with an equation for quantifying these situations...I think...lol...my head hurts.
Oh, just thought of something else to consider in every situation. What level will winning/losing put your opponent in? Where are they before this play? Then we need to look at each players skill levels....oh my...my head hurts more now...LoL!
At any given point in a tournament you have X% chance of winning.
Assuming that all players are of equal skill, is the % chance of winning a direct correlation to the percentage of chips that you have?
All other things being equal, that is the proper way to look at it.
But, my feeling is that "the size of the blinds in relation to the size of the stack" does -- in fact -- alter this formula such that a slightly higher percentage stack does not correlate directly to the same percentage chance of winning. And, going one step further, my feeling is that if you get a big enough stack you might then "wrap the parabola" and exceed your percentage.
An example... 4 players of equal skill.
First hand of the WSOP final table. They each have $250K chips. One would have to conclude that they each had a 25% chance of winning.
Second hand of the WSOP final table (still DEEP stacks) and one player now has $100K, one $400K, and the other two at $250K. Probably 10%, 40%, 25% and 25% feels about right.
But, what happens when those blinds become oppressive. If the split is still the same it doesn't feel, to me, like the $100K player still has a 10% chance. It feels to me like the fact that he has had many of his weapons removed because of the oppressive blinds. So much so that this more than offsets the advantages he gains (e.g. frequent all ins).
If I am right, then the question is: (1) At what point do blinds "become oppressive"; and (2) What is the human element to poker that causes this phenomenon.
On the other hand...
Suppose it's head up. They start at 50/50 but after a single hand it's 90/10. Given what I have been feeling, the 10 player now has less than 10% chance, but that gives the 90 player MORE than a 90% chance which is a good reason to take the gamble... and not pass on it.
Aha! New theory...
When there are still multiple players at the table, preservation of stack is paramount. In a multi player environ being short stacked is DEADLY because there are too many foxes in the henhouse and you will have your options SEVERELY limited. But, when it gets heads up, get ready to gamble baby. This is starting to feel right to me and is, I note, based upon a "human assumption" about the game... namely, that most pots will be raised which severely limits that moves available to a small stacked player. But, when it's heads up, you don't care, because your moves are not limited anymore.
I don't think you can ever find equally skilled players. Even if you're looking at a normal WPT final table, all players have different skills. In last month's Cardplayer Magazine Negraneu talks about his rival (can't remember the guy) and how he's much better than he is pre-flop and how his skills shine post flop. So, even the top two tournament players last year have different skills. So, give Negraneu the 400K and the other guy 250, and I would say they were about even. If they were both even stacked, I'd give the edge to the other guy.
So, I'm trying to sort through the problem from the perspective of what the added chips buy me. Sure stack preservation is important, but for a pre-flop player it's not as important. If you're someone who likes to get deep into the streets, then a big stack is Huge. So give Negraneu the big stack with regular WPT players, and he's got a bigger edge than the percentage of chips he's currently holding.
I think the question is what do the added chips do for your particular strength. If you're a good pre-flop player, then deep chips are really not that essential. An above average stack will do just the same, as does a medium stack. I've watched many of the pros playing the stars tournies and they do so well as medium stacks, but really suck when they have the big stack. They end up doubling most players because they can't get their foot off the gas pedal and concentrate only on pre-flop play.
I'm still rambling. I'll post later.
Cheers
Magi
Perhaps you have laid your finger more and more upon preference. I have come to be a big beliver is Ralph "The Hurricane" Mair's favourite poker tip. First person to reproduce that tip here will get the first Team Canuck Poker Ball Cap made. It is at www.CanadianPoker.com
Start typing...
Mike
Hat will be in the mail shortly. PM me your snail mail address.
WOW !!!!! that's sincerly some of the best advise i've ever read.
Kill Bill: Vol 2 goes down as the movie that cost me a Team Canuck hat.
ScottyZ