Not sure why I didn't offer a deal... I think I should have. I was kinda swept up in the whole 'headsup' thing, so I didn't really think of it. No observer chat to prompt me, either.
Not sure why I didn't offer a deal... I think I should have.
Why?
(Note that by asking why, I'm not trying to imply that you either should or shouldn't have offered a deal.)
I think a lot of people have a knee-jerk reaction when it gets down to 2 or 3 players that the players should make a deal. Making a deal depends on a lot of factors, and isn't nearly as automatic as a lot of people seem to think.
I'd consider:
1. Am I particularly good or bad as heads-up (or whatever stage you're at) player?
2. How is my opponent's overall skill level comapred to my own? (Possibly you might even be able to guage your opponent's short-handed skill level.)
3. How big are the blinds relative to the stacks? In other words, how much is skill going to determine the outcome?
Supplementary question: If the blinds are "too big" heads-up and the players are equal in skill, does the short stack or the large stack have a greater advantage than if the blinds were typical?
4. How am I feeling at this point? Tired? Feel like doing something else? Feel like playing in some other game instead?
5. Use Dave's middle finger. (No, I don't mean just give your opponent the middle finger.) What does a deal mean to me?
6. What is the nature of the proposed deal? Are you getting a far better than fair or far worse than fair deal? (*ahem* Casino Regina *ahem*) In short, will this deal make you air guitar out into the lobby? 8)
1. Am I particularly good or bad as heads-up (or whatever stage you're at) player?
I'm pretty good... lots of h/u tourneys with my cousin, and lots of shorthanded online play in which most pots are contested headsup.
2. How is my opponent's overall skill level comapred to my own?
I didn't have much of a read on him. Every time I saw his cards, they were the goods, but I didn't always see them.
3. How big are the blinds relative to the stacks?
Blinds 20,000/40,000 ante 2,000
all aces: 792,527
homero: 2,309,973
So, I have almost 20 times the BB. I can afford to wait a bit (not that I did... lol)
Supplementary question: I'll have to think on that for a moment, but my immediate instinct tells me this is better for the shortstack.
4. How am I feeling at this point? Tired? Feel like doing something else? Feel like playing in some other game instead?
Lol it's hard to imagine wanting to play in any other game than heads-up on Stars at that moment, but I know what you mean. After beating out 1239 people, I might have already been in 'celebration' mode, instead of being completely focused on my final task. This is a lesson I will take with me for next time.
What does a deal mean to me?
Probably an extra 7K or so, which isn't small change. The reason I'm second-guessing myself lately about not making a deal is because I should have been more aware of the wide berth between 1st and 2nd place money. With that awareness I might have made a better decision, or at least a more informed one.
For some reason I got a little superstitious, and didn't look at the prize scale after I made the money. I didn't want to know that it was only, say, 3 people to go to the next prize level, because I was afraid I'd subconsciously set a false goal for myself; that is, making it to the next prize level instead of winning the damn thing.
(*ahem* Casino Regina *ahem*)
Lol.
In short, will this deal make you air guitar out into the lobby?
I was air-guitaring my ass off, deal or no deal. In actual fact, what you would have seen towards the end of the tournament was a lot of me jumping out of my computer chair and walking in slow silent circles with my arms way over my head.
My girlfriend was watching it all go down from the other side of the room, but not hovering if you know what I mean. Everytime I went all-in with the best of it (usually--though not always--the case) I would say 'I'm good...' when the cards went over pre-flop, then 'I'm good...' on the flop, again on the turn, and then the arms-raised-circle-walk if I won by the end of the hand. Also, I did smaller versions of the victory circle every time I bluffed at a pot and won it.
When it finished, I walked around in a kind of pseudo-daze for a couple of hours. I know 47K isn't really life-changing money--not in and of itself--but it's the biggest money I've won in a day, and I was completely, totally, thrilled and dumbfounded.
Regards,
all_aces
ps: Mark, the 500 + on Sunday, I'm not sure... I protect my poker bankroll like it is all of my chips in the mid-stages of a tournament, so I might actually try to win my way in, like you did. My general plan is to cash out 30K USD, leaving me with 4K or so to play in various tournaments (including the pokerforum ones) throughout the summer, and maybe beyond.
Supplementary question: I'll have to think on that for a moment, but my immediate instinct tells me this is better for the shortstack.
That was my instinct too, but I couldn't really come up with any good reasons why.
I think both players have to be more impatient (generally this means looser, but aggression and risk taking are involved too) with bigger blinds. I think (in general) the shorter stack needs to be a little more impatient than the large stack regardless of the blinds. What's unclear to me is deciding whether either
1. the large blinds somehow support or play into the short stack's natural style (possibly the short stack likes the fact that the large stack must take more chances?)
or
2. the large blinds make the small stack even more impatient than usual, which makes a bad thing worse.
Thanks very much guys. It's been a very good year for me. Between Pokerroom, then Regina, then the WSOP (although I didn't really make any money in Vegas) and now this, I feel very VERY lucky.
It's nice to be able to share these experiences with people who understand: basically, poker players.
I look forward to hearing about your big wins as well, which I'm sure will come in the not-too-distant future.
Supplementary question: If the blinds are "too big" heads-up and the players are equal in skill, does the short stack or the large stack have a greater advantage than if the blinds were typical?
ScottyZ
It depends who the better player is. The smaller the blinds, the more of an advantage to the better player (regardless if he is the big or small stack). The larger the blinds, the closer you get to your chances of winning being equal to the percentage of chips in your stack, with skill becoming more irrelevant. UNLESS (and this is a big exception) the more skilled player derives his advantage from his opponent throwing away too many hands.
Sklansky talks about this in his tournament book. It's a good read. He gives a concrete example of that exception too... he says that once, he was heads-up in a draw tournament, and his opponent was playing so tightly that Skalnsky said he would not have wanted to risk playing a big pot against him, even with 4 of a kind.
Supplementary question: If the blinds are "too big" heads-up and the players are equal in skill, does the short stack or the large stack have a greater advantage than if the blinds were typical?
ScottyZ
It depends who the better player is. The smaller the blinds, the more of an advantage to the better player (regardless if he is the big or small stack). The larger the blinds, the closer you get to your chances of winning being equal to the percentage of chips in your stack, with skill becoming more irrelevant. UNLESS (and this is a big exception) the more skilled player derives his advantage from his opponent throwing away too many hands.
Sklansky talks about this in his tournament book. It's a good read. He gives a concrete example of that exception too... he says that once, he was heads-up in a draw tournament, and his opponent was playing so tightly that Skalnsky said he would not have wanted to risk playing a big pot against him, even with 4 of a kind.
Keith
Okay, I'd agree with that assessment.
How about:
Supplementary question: If...the players are equal in skill...
I believe the shortstack would have the advantage if they are equal in skill and the blinds are huge. Obviously, the big stack has a better chance of winning the thing, but on a *per hand* basis I think the shortstack has the edge.
The reason is this: I *hate* playing against people who are legitimately shortstacked if I'm on a decent stack. If I have a *huge* lead, I don't mind at all. But if I'm average or just above average, I tend to fold a lot of hands to a shortstack in situations where I'd usually try to steal.
This is obviously because every time you enter a pot with a shortstack, you're basically assuming it will cost you all of their chips to play the hand. A good player with a shortstack will make sure that you are put to this decision more often that not. So, assuming two good players, I think the shortstack feeling the pressure of the blinds has the tactical advantage. Basically, the larger stack will steal less, and play less hands, because the shortstack should often be threatening to move in on him. And the last thing the big stack wants is to double the shortstack up.
This is why I bet all of my chips into the big stack with A3o on the flop on Sunday. I wanted him to start folding more hands to me preflop, and if I'd made it through that hand, I believe that would have been the case.
I believe the shortstack would have the advantage if they are equal in skill and the blinds are huge. Obviously, the big stack has a better chance of winning the thing, but on a *per hand* basis I think the shortstack has the edge.
Yes. I think we are trying to get the question, "If the blinds are big, does the short stack have more or less of a chance of winning the tournament than usual for the short stack."
So, I guess the idea is that if the blinds are too big then the short stack (mmmm...pancakes) is often pot-committed much more often than usual.
Seems to be another double-edged sword. I get your point about some of the large stack's weapons being taken away; the short stack might call or raise more of the large stack's steal attempts than usual. But, perhaps the same like of thinking might lead us to believe that the short stack has even more of his weapons taken away, being so often in pot-committed situations.
Yes. I think we are trying to get the question, "If the blinds are big, does the short stack have more or less of a chance of winning the tournament than usual for the short stack."
Tough question. 8)
ScottyZ
Ummm... Not too tough I don't think. I think that the answer is, the size of the blinds has no effect. In other words, if two players A and B are equal in skill, and A has x% of the chips, and B has (100-x)% of the chips, then player A has an x% chance of winning, and player B has a (100-x)% chance of winning the tournament, regardless of the size of the blinds.
This is covered in Skalnsky's tournament book too. Really, it's a good read. He doesn't really prove it but he sort of explains why it's true, and gives some hand-wavy arguments. Would probably be acceptable as a "proof" to someone who is not a math geek.
My own little hand-wavy argument to show that the blinds increasing does not favour either stack: Just look at the extreme case (this is often a useful little trick) where the blinds are SO BIG that the small blind is more than the total number of chips on the table. So no matter what, both players are all in for their blinds each hand. If the small stack wins a hand, he doubles up, and if the big stack wins a hand, he wins the tournament. In this case, it is not too hard to show that a players probability of winning is exactly the fraction of the total chips which are in his stack (at least I assume that it's not hard to show... I haven't actually bothered but it looks kind of obvious)
So, we know that when the blinds are extremely large, your probability of winning is the same as your percentage of chips. Same when the blinds are extremely small. This alone is enough to convince me that the same is probably true for medium-sized blinds. I am sure that we are dealing with some sort of nice-looking continuous function here, and I seriously doubt if it peaks and then dips again, ending up back where it started. I mean, I can't prove it, but come on... it's so obviously constant.
This is covered in Skalnsky's tournament book too. Really, it's a good read.
I have this, and have read it a few times. I'm sure ScottyZ has too. Don't you find that it encourages players to be a little too tight? I do... It is helpful to take some of his principles from the book and then loosen them up, though. HPFAP is better IMHO.
Ummm... Not too tough I don't think. I think that the answer is, the size of the blinds has no effect. In other words, if two players A and B are equal in skill, and A has x% of the chips, and B has (100-x)% of the chips, then player A has an x% chance of winning, and player B has a (100-x)% chance of winning the tournament, regardless of the size of the blinds.
This is covered in Skalnsky's tournament book too. Really, it's a good read. He doesn't really prove it but he sort of explains why it's true, and gives some hand-wavy arguments. Would probably be acceptable as a "proof" to someone who is not a math geek.
Actually, it's funny that someone has referenced this chapter specifically. This is the *only* part of any book that Sklansky has written that I don't buy.
If you read his second argument extremely carefully, I think you'll find that he argues that the fair value of a chip stack in a heads-up freezeout is proportional to the chip stack size, by assuming that the fair entry fee into such a tournament is proportional to the chip stack size. That's a circular argument, since the fair value of a chip stack and the fair entry fee into a tournament with that same chip stack (against an equally skilled opponent) are the same thing.
The main difficulity with his first argument is the idea that the short stack must double up repeatedly to win the tournament. This is only true if the blinds are very huge. (Like Keith said, when the small blind is larger than the total chip count.)
However, if the blinds are still very small (this nicely gets us back more on topic, actually), the small stack size will undergo some sort of complicated random walk based on all the cards to be dealt, and all of the decisions about plays each player will get to make. This random walk seems to me to be incredibly hard to analyze or simulate, and my intuition is that it will probably *not* be well approximated by a "doubling up or busting" random walk.
So, we know that when the blinds are extremely large, your probability of winning is the same as your percentage of chips.
Agreed. And this *is* exactly what Sklansky did show in TPFAP.
Same when the blinds are extremely small.
This is not at all obvious to me, and it's the very heart of the original question.
It's not clear to me how to determine the probability of winning a heads-up freezeout when the blinds are small.
However, if the blinds are still very small (this nicely gets us back more on topic, actually), the small stack size will undergo some sort of complicated random walk based on all the cards to be dealt, and all of the decisions about plays each player will get to make. This random walk seems to me to be incredibly hard to analyze or simulate, and my intuition is that it will probably *not* be well approximated by a "doubling up or busting" random walk.
Ok, look at it this way. Say I am small stack, and you are big stack, and we are exactly evenly matched. Since we are evenly matched, my EV on each hand is 0 chips. That is, before the cards are dealt, the answer to the question "how much is your expected win for the upcoming hand?" is "0 chips". The fact that you have a larger stack than I do is irrelevant. If I have $500 and you have $1500, the scenario plays out exactly the same as if we both had $500 (your excess $1000 is essentially not in play for this hand).
EV has this nice property of being additive. You can vary bet sizes and manipulate variance, but EV remains additive. Which is, of course, why people who try to beat roulette by doubling their bet each time they lose just don't get it (some people think that this doesn't work because the casino has a maximum bet. They are wrong. It wouldn't work even if there WAS no max bet).
So. My EV is additive. If we play 1 hand, 100, or 1 million, my EV remains 0. The fact that we agree to stop at some predetermined point (ie, when one person runs out of chips) is completely irrelevant. You can't manipulate coin flips by starting and stopping according to some system. My EV remains 0.
If I start with 1/x of the chips, and we agree to stop when one person runs out of chips, then, since my EV over all the hands is 0 chips, the probability that I end up with all the chips must be exactly 1/x. If it were any other value, my EV would not work out to 0 chips.
Since we are evenly matched, my EV on each hand is 0 chips. That is, before the cards are dealt, the answer to the question "how much is your expected win for the upcoming hand?" is "0 chips".
I don't think so. When it's heads-up (always assume players of equal skill), the small blind (button) will have +EV and the big blind will have -EV.
Making the analysis more difficult still, these EV's *change* each hand as the stack sizes change.
The fact that we agree to stop at some predetermined point (ie, when one person runs out of chips) is completely irrelevant.
Not at all. In fact, this is precisely what distinguishes a tournament from a cash game.
Without the agreement to stop when a player reaches 0 chips, questions like "What's the probability of the short stack winning the tournament?" can't even be posed.
If I start with 1/x of the chips, and we agree to stop when one person runs out of chips, then, since my EV over all the hands is 0 chips, the probability that I end up with all the chips must be exactly 1/x. If it were any other value, my EV would not work out to 0 chips.
I think what you might be getting at here is the Gambler's Ruin problem. If I have 10 chips, and you have 90 chips, and we bet one chip on tossing a fair coin until one of us goes broke, then it is true that the probability that I win all of the chips is 10% (my stack size as a proportion of the total chips).
What's not clear to me is whether or not poker game can be well approximated by this sort of coin tossing set-up. In poker, players can bet different amounts, are making multiple decisions per hand, must post two unequal blinds each hand, have two unequal positions within each individual hand, etc.
I don't think so. When it's heads-up (always assume players of equal skill), the small blind (button) will have +EV and the big blind will have -EV.
Fine. We will look at groups of two consecutive hands then. Nothing changes.
Making the analysis more difficult still, these EV's *change* each hand as the stack sizes change.
No they don't. This is exactly my point. As I said, the hand is no different than if the large stack had exactly the same number of chips as the small stack... the large stacks excess chips are (effectively) not in play for that hand.
The fact that we agree to stop at some predetermined point (ie, when one person runs out of chips) is completely irrelevant.
Not at all. In fact, this is precisely what distinguishes a tournament from a cash game.
No. It makes no difference. EV is additive. Your EV (in terms of number of chips) at the end of the tournament is whatever you started with, plus the sum of the EV of all your hands that you have played over the course of the tournament. The fact that you agree to stop at some predetermined point is IRRELEVANT to EV. This is basic statistics.
If I start with 1/x of the chips, and we agree to stop when one person runs out of chips, then, since my EV over all the hands is 0 chips, the probability that I end up with all the chips must be exactly 1/x. If it were any other value, my EV would not work out to 0 chips.
I think what you might be getting at here is the Gambler's Ruin problem. If I have 10 chips, and you have 90 chips, and we bet one chip on tossing a fair coin until one of us goes broke, then it is true that the probability that I win all of the chips is 10% (my stack size as a proportion of the total chips).
What's not clear to me is whether or not poker game can be well approximated by this sort of coin tossing set-up. In poker, players can bet different amounts, are making multiple decisions per hand, must post two unequal blinds each hand, have two unequal positions within each individual hand, etc.
The point is, that poker CAN be be approximated this way if both players are of equal skill. I mean, it's not as simple as a coin flip, but the EV is still zero. The positional considerations can be taken care of by looking at sets of two consecutive hands, rather than individual hands. So, a players EV over 2 hands is 0 chips.
Now, there is a little "blip" here. It is possible for the tournament to end after an odd number of hands. But, this is negligible with small blinds (the difference in EV can be no more than 1 BB, since the player in the big blind can just throw away his first hand blind, giving up 1BB worth of EV, and reverse the situation)
Simply put, to take care of all the problems that you are worried about, just add EVs. If player A and player B are equally skilled, and they play heads up, with player A getting the button first, then:
If they stop playing after an even number of hands, player A's expected number of chips (ie the EV of his chip stack size) is the same as the number of chips he started with. If they play an odd number of hands, his expected number of chips is some value between the number of chips he started with, and the number of chips he started with + 1 big blind. The fact that they agree to stop after precisely 1 hour, or 2 hours, or 1000 hours, or when 1 person has 100% of the chips, or when 1 person has 73% of the chips, or when the Cubs win the world series, is irrelevant to EV. It only affects variance.
Here is the key point: YOU CAN NOT change EV by agreeing to stop, after a fixed amount of time, or according to some system. It simply can't be done. This is why stop-loss methods at poker don't do anything (assuming that you always have the same EV whenever you sit down). This is why the gambler's ruin problem yields the result that it does. This is why varying your bets at casino games doesn't work. With these methods, you can control variance, but you CAN NOT change EV. No matter what, your EV is the sum of the EVs of all your plays. There's no getting around it.
Stack sizes certainly affect pre-deal +EV and -EV, so you can't just pair them to get 0. [If you could, we would have the result.] If the small stack has 1 chip and the large stack has 999,999 chips, the maximum +EV for the small blind is +1 for the next hand. If each player has 500,000 chips, the +EV of the small blind is probably much higher than +1.
The fact that you agree to stop at some predetermined point is IRRELEVANT to EV.
The stopping time of a freezeout tournament is not predetermined. It is a random variable.
I understand what you're trying to say when you point out that betting systems don't affect your expected outcome after a sequence of betting. The sequence of bankroll sizes while betting on a fair coin toss is a martingale under all possible betting strategies. This follows from the so called Optional Stopping Theorem.
Betting systems (or optimal stopping strategy) have nothing to do with the conditions for ending a poker tournament. Poker players in tournaments are *not* trying to determine an optimal stopping strategy--- they are simply confined by the rules of the game.
A heads-up tournament is like a random walk with two absorbing barriers, the barriers being the bust-out points of each player.
The presence (and location) of absorbing barriers *does* affect the expected outcome of a random walk. Namely, whether you're playing a tournament with a player, or a cash game with the same player, can affect the expected outcome.
As a silly example, suppose one player is so good that he is guaranteed to get the other player's chips. If these players decide to play in exactly one $100 buy-in tournament, the good player has EV of +$100. The good player's random walk is guaranteed to hit the +$100 absorbing barrier. If they play a cash game instead, the good player's EV cannot even be computed without more information. If the bad player decides in advance that he will play until he is either up or down $1,000, then the good player's EV turns out to be +$1,000. If the bad player does not decide on any stopping condition before they begin playing, the good player's EV is unknown.
Stack sizes certainly affect pre-deal +EV and -EV, so you can't just pair them to get 0. [If you could, we would have the result.] If the small stack has 1 chip and the large stack has 999,999 chips, the maximum +EV for the small blind is +1 for the next hand. If each player has 500,000 chips, the +EV of the small blind is probably much higher than +1.
The fact that you agree to stop at some predetermined point is IRRELEVANT to EV.
The stopping time of a freezeout tournament is not predetermined. It is a random variable.
I understand what you're trying to say when you point out that betting systems don't affect your expected outcome after a sequence of betting. The sequence of bankroll sizes while betting on a fair coin toss is a martingale under all possible betting strategies. This follows from the so called Optional Stopping Theorem.
Betting systems (or optimal stopping strategy) have nothing to do with the conditions for ending a poker tournament. Poker players in tournaments are *not* trying to determine an optimal stopping strategy--- they are simply confined by the rules of the game.
A heads-up tournament is like a random walk with two absorbing barriers, the barriers being the bust-out points of each player.
The presence (and location) of absorbing barriers *does* affect the expected outcome of a random walk. Namely, whether you're playing a tournament with a player, or a cash game with the same player, can affect the expected outcome.
As a silly example, suppose one player is so good that he is guaranteed to get the other player's chips. If these players decide to play in exactly one $100 buy-in tournament, the good player has EV of +$100. The good player's random walk is guaranteed to hit the +$100 absorbing barrier. If they play a cash game instead, the good player's EV cannot even be computed without more information. If the bad player decides in advance that he will play until he is either up or down $1,000, then the good player's EV turns out to be +$1,000. If the bad player does not decide on any stopping condition before they begin playing, the good player's EV is unknown.
ScottyZ
I am not sure what you find so difficult to understand here. For each orbit, each player's EV is 0 chips. Add zero as many times as you want. Stop adding zero after a fixed number of times. Stop after a random number of times. Stop when you fall asleep. It doesn't matter. You still get 0.
The example which you give is positional. It has nothing to do with stack size. In the hand where one person only has one chip, BOTH players have a maximum EV of +1. Because of the presence of blinds (which are presumably at least 1 chip each) the small stack is all in for his blind, and so both players have an EV of 0, regardless of skill level. But, really, you are changing the subject when bringing up this case, since we were talking about cases where the blinds are small. The blinds cannot be considered small if they put a player all in for his blind.
If you don't like the EV argument (even though I am SURE that it is valid), think about it this way. In a winner-take-all tournament, your optimal strategy is the same as your strategy in a cash game (assuming that all players are of equal skill. If you are a better player than most, you still probably want to avoid close gambles, since losing would prevent you from being able to make a better-EV bet later, or limit the volume of that bet. But we can ignor these considerations if we assume that all players are equal, since you are just as likely to make a bad bet later as you are to make a good bet, if the opposition is equal)
This is mentioned in Sklansky's book, and it's pretty obvious. Despite what you say a few posts back, the actual reason that tournament strategy differs from ring game strategy is that you make money by outlasting people, even if you eventually lose all your chips. If you started the WSOP with $1000 in chips (and equity) and lost all your chips right away, you get nothing. But it you lose all your chips AFTER everyone else except for one player, you get $4 million. Obviously, then, variance becomes important, possibly more so than EV. Like Sklansky says, it is (theoretically) possible to finish 2nd in a tournament without ever having more chips than you started with.
Anyway, the point is, in a winner-take-all tournament, things revert to being pretty much the same as a cash game. And, a heads-up situation is a winner-take-all tournament (effectively... you pay both players 2nd place and they are playing winner-take-all for the difference between first and second). So, in this situation, there is really not much difference between the tourney and a cash game. Your (cash) EV is simply the fraction of the number of chips you have, times the prize.
By the way, when I first read Skalnsky's book, I thought that his EV argument was circular too. But then I realized that he was not talking about EV in terms of money... he was talking about EV in terms of tournament chips. THEN it all makes sense. As is often the case with Skalnsky's writing, it's terse and a bit hard to read, but if you think about it for a while, you realize that he's right. It's a simple EV argument.
I am not sure what you find so difficult to understand here. For each orbit, each player's EV is 0 chips. Add zero as many times as you want. Stop adding zero after a fixed number of times. Stop after a random number of times. Stop when you fall asleep. It doesn't matter. You still get 0.
I simply don't think that the +EV for the short stack on the small blind is necessarily equal to (with opposite sign) the -EV for the same player on the big blind next hand because the stack sizes may change between hands.
I simply don't think that the +EV for the short stack on the small blind is necessarily equal to (with opposite sign) the -EV for the same player on the big blind next hand because the stack sizes may change between hands.
You could make the exact same argument about a cash game. Are you saying that a player's equity in a heads up cash game is not the number of chips he has in front of him?
I for one think it is GREAT that Keith has joined this forum.
Scotty finaly has someone who can keep up with his posts!!!
Hey Keith do you wanna post for me so I can get a free Mag since Scotty
won't? ppppppppppplllllllllleeeeeeeeeeeaaaaaaaaasssssssseeeeeeeee:) :?:
I for one think it is GREAT that Keith has joined this forum.
Scotty finaly has someone who can keep up with his posts!!!
Hey Keith do you wanna post for me so I can get a free Mag since Scotty
won't? ppppppppppplllllllllleeeeeeeeeeeaaaaaaaaasssssssseeeeeeeee:) :?:
Yeah, well, being unemp... umm.. a PROFESSIONAL POKER PLAYER 8) helps too.
Are you saying that a player's equity in a heads up cash game is not the number of chips he has in front of him?
I guess it would be, but the argument I could think of for this depends heavily on the fact that it is a cash game instead of a tournament.
A lower bound for a (sensible) player's equity in a cash game is the chips in front of him, because he could leave immediately with those chips. A sensible player would chose to not play if the expected outcome is worse than that. (Unless for some reason this person favours something else besides EV, like variance, or entertainment value, etc.) The same goes for the opponent, so an *upper* bound for the original player's stack must be
Total chips - Opponent's chips = Original player's chips.
So, I'd say that in a cash game between equal (and sensible) players, the equity equals the chips.
Also, by "sensible" I guess I mean some super-brain who can perfectly assess the opponent's skill level relative to their own.
Comments
Not sure why I didn't offer a deal... I think I should have. I was kinda swept up in the whole 'headsup' thing, so I didn't really think of it. No observer chat to prompt me, either.
Oh well, like you said, 2nd place pay gOOt!
Thanks!!!
all_aces
Why?
(Note that by asking why, I'm not trying to imply that you either should or shouldn't have offered a deal.)
I think a lot of people have a knee-jerk reaction when it gets down to 2 or 3 players that the players should make a deal. Making a deal depends on a lot of factors, and isn't nearly as automatic as a lot of people seem to think.
I'd consider:
1. Am I particularly good or bad as heads-up (or whatever stage you're at) player?
2. How is my opponent's overall skill level comapred to my own? (Possibly you might even be able to guage your opponent's short-handed skill level.)
3. How big are the blinds relative to the stacks? In other words, how much is skill going to determine the outcome?
Supplementary question: If the blinds are "too big" heads-up and the players are equal in skill, does the short stack or the large stack have a greater advantage than if the blinds were typical?
4. How am I feeling at this point? Tired? Feel like doing something else? Feel like playing in some other game instead?
5. Use Dave's middle finger. (No, I don't mean just give your opponent the middle finger.) What does a deal mean to me?
6. What is the nature of the proposed deal? Are you getting a far better than fair or far worse than fair deal? (*ahem* Casino Regina *ahem*) In short, will this deal make you air guitar out into the lobby? 8)
ScottyZ
I'm pretty good... lots of h/u tourneys with my cousin, and lots of shorthanded online play in which most pots are contested headsup.
I didn't have much of a read on him. Every time I saw his cards, they were the goods, but I didn't always see them.
Blinds 20,000/40,000 ante 2,000
all aces: 792,527
homero: 2,309,973
So, I have almost 20 times the BB. I can afford to wait a bit (not that I did... lol)
Supplementary question: I'll have to think on that for a moment, but my immediate instinct tells me this is better for the shortstack.
Lol it's hard to imagine wanting to play in any other game than heads-up on Stars at that moment, but I know what you mean. After beating out 1239 people, I might have already been in 'celebration' mode, instead of being completely focused on my final task. This is a lesson I will take with me for next time.
Probably an extra 7K or so, which isn't small change. The reason I'm second-guessing myself lately about not making a deal is because I should have been more aware of the wide berth between 1st and 2nd place money. With that awareness I might have made a better decision, or at least a more informed one.
For some reason I got a little superstitious, and didn't look at the prize scale after I made the money. I didn't want to know that it was only, say, 3 people to go to the next prize level, because I was afraid I'd subconsciously set a false goal for myself; that is, making it to the next prize level instead of winning the damn thing.
Lol.
I was air-guitaring my ass off, deal or no deal.
My girlfriend was watching it all go down from the other side of the room, but not hovering if you know what I mean. Everytime I went all-in with the best of it (usually--though not always--the case) I would say 'I'm good...' when the cards went over pre-flop, then 'I'm good...' on the flop, again on the turn, and then the arms-raised-circle-walk if I won by the end of the hand. Also, I did smaller versions of the victory circle every time I bluffed at a pot and won it.
When it finished, I walked around in a kind of pseudo-daze for a couple of hours. I know 47K isn't really life-changing money--not in and of itself--but it's the biggest money I've won in a day, and I was completely, totally, thrilled and dumbfounded.
Regards,
all_aces
ps: Mark, the 500 + on Sunday, I'm not sure... I protect my poker bankroll like it is all of my chips in the mid-stages of a tournament, so I might actually try to win my way in, like you did. My general plan is to cash out 30K USD, leaving me with 4K or so to play in various tournaments (including the pokerforum ones) throughout the summer, and maybe beyond.
That was my instinct too, but I couldn't really come up with any good reasons why.
I think both players have to be more impatient (generally this means looser, but aggression and risk taking are involved too) with bigger blinds. I think (in general) the shorter stack needs to be a little more impatient than the large stack regardless of the blinds. What's unclear to me is deciding whether either
1. the large blinds somehow support or play into the short stack's natural style (possibly the short stack likes the fact that the large stack must take more chances?)
or
2. the large blinds make the small stack even more impatient than usual, which makes a bad thing worse.
An interesting dilemna I think.
ScottyZ
Hmm...Mark and I getting buy-ins to big events, you doing well at this one, Dave kicking ass at the WSOP...gotta be something in the water.
It's nice to be able to share these experiences with people who understand: basically, poker players.
I look forward to hearing about your big wins as well, which I'm sure will come in the not-too-distant future.
Regards,
all_aces
This is probably simply some degree of modesty, but don't sell yourself short here. From what I've seen so far, I think you're very good.
Luck helps, but it can't help the helpless.
Man, try saying that ten times fast.
ScottyZ
It depends who the better player is. The smaller the blinds, the more of an advantage to the better player (regardless if he is the big or small stack). The larger the blinds, the closer you get to your chances of winning being equal to the percentage of chips in your stack, with skill becoming more irrelevant. UNLESS (and this is a big exception) the more skilled player derives his advantage from his opponent throwing away too many hands.
Sklansky talks about this in his tournament book. It's a good read. He gives a concrete example of that exception too... he says that once, he was heads-up in a draw tournament, and his opponent was playing so tightly that Skalnsky said he would not have wanted to risk playing a big pot against him, even with 4 of a kind.
Keith
Okay, I'd agree with that assessment.
How about:
ScottyZ
The reason is this: I *hate* playing against people who are legitimately shortstacked if I'm on a decent stack. If I have a *huge* lead, I don't mind at all. But if I'm average or just above average, I tend to fold a lot of hands to a shortstack in situations where I'd usually try to steal.
This is obviously because every time you enter a pot with a shortstack, you're basically assuming it will cost you all of their chips to play the hand. A good player with a shortstack will make sure that you are put to this decision more often that not. So, assuming two good players, I think the shortstack feeling the pressure of the blinds has the tactical advantage. Basically, the larger stack will steal less, and play less hands, because the shortstack should often be threatening to move in on him. And the last thing the big stack wants is to double the shortstack up.
This is why I bet all of my chips into the big stack with A3o on the flop on Sunday. I wanted him to start folding more hands to me preflop, and if I'd made it through that hand, I believe that would have been the case.
Regards,
all_aces
Yes. I think we are trying to get the question, "If the blinds are big, does the short stack have more or less of a chance of winning the tournament than usual for the short stack."
So, I guess the idea is that if the blinds are too big then the short stack (mmmm...pancakes) is often pot-committed much more often than usual.
Seems to be another double-edged sword. I get your point about some of the large stack's weapons being taken away; the short stack might call or raise more of the large stack's steal attempts than usual. But, perhaps the same like of thinking might lead us to believe that the short stack has even more of his weapons taken away, being so often in pot-committed situations.
Tough question. 8)
ScottyZ
LOL
Ummm... Not too tough I don't think. I think that the answer is, the size of the blinds has no effect. In other words, if two players A and B are equal in skill, and A has x% of the chips, and B has (100-x)% of the chips, then player A has an x% chance of winning, and player B has a (100-x)% chance of winning the tournament, regardless of the size of the blinds.
This is covered in Skalnsky's tournament book too. Really, it's a good read. He doesn't really prove it but he sort of explains why it's true, and gives some hand-wavy arguments. Would probably be acceptable as a "proof" to someone who is not a math geek.
My own little hand-wavy argument to show that the blinds increasing does not favour either stack: Just look at the extreme case (this is often a useful little trick) where the blinds are SO BIG that the small blind is more than the total number of chips on the table. So no matter what, both players are all in for their blinds each hand. If the small stack wins a hand, he doubles up, and if the big stack wins a hand, he wins the tournament. In this case, it is not too hard to show that a players probability of winning is exactly the fraction of the total chips which are in his stack (at least I assume that it's not hard to show... I haven't actually bothered but it looks kind of obvious)
So, we know that when the blinds are extremely large, your probability of winning is the same as your percentage of chips. Same when the blinds are extremely small. This alone is enough to convince me that the same is probably true for medium-sized blinds. I am sure that we are dealing with some sort of nice-looking continuous function here, and I seriously doubt if it peaks and then dips again, ending up back where it started. I mean, I can't prove it, but come on... it's so obviously constant.
Keith
I have this, and have read it a few times. I'm sure ScottyZ has too. Don't you find that it encourages players to be a little too tight? I do... It is helpful to take some of his principles from the book and then loosen them up, though. HPFAP is better IMHO.
Regards,
all_aces
Actually, it's funny that someone has referenced this chapter specifically. This is the *only* part of any book that Sklansky has written that I don't buy.
If you read his second argument extremely carefully, I think you'll find that he argues that the fair value of a chip stack in a heads-up freezeout is proportional to the chip stack size, by assuming that the fair entry fee into such a tournament is proportional to the chip stack size. That's a circular argument, since the fair value of a chip stack and the fair entry fee into a tournament with that same chip stack (against an equally skilled opponent) are the same thing.
The main difficulity with his first argument is the idea that the short stack must double up repeatedly to win the tournament. This is only true if the blinds are very huge. (Like Keith said, when the small blind is larger than the total chip count.)
However, if the blinds are still very small (this nicely gets us back more on topic, actually), the small stack size will undergo some sort of complicated random walk based on all the cards to be dealt, and all of the decisions about plays each player will get to make. This random walk seems to me to be incredibly hard to analyze or simulate, and my intuition is that it will probably *not* be well approximated by a "doubling up or busting" random walk.
Agreed. And this *is* exactly what Sklansky did show in TPFAP.
This is not at all obvious to me, and it's the very heart of the original question.
It's not clear to me how to determine the probability of winning a heads-up freezeout when the blinds are small.
ScottyZ
Ok, look at it this way. Say I am small stack, and you are big stack, and we are exactly evenly matched. Since we are evenly matched, my EV on each hand is 0 chips. That is, before the cards are dealt, the answer to the question "how much is your expected win for the upcoming hand?" is "0 chips". The fact that you have a larger stack than I do is irrelevant. If I have $500 and you have $1500, the scenario plays out exactly the same as if we both had $500 (your excess $1000 is essentially not in play for this hand).
EV has this nice property of being additive. You can vary bet sizes and manipulate variance, but EV remains additive. Which is, of course, why people who try to beat roulette by doubling their bet each time they lose just don't get it (some people think that this doesn't work because the casino has a maximum bet. They are wrong. It wouldn't work even if there WAS no max bet).
So. My EV is additive. If we play 1 hand, 100, or 1 million, my EV remains 0. The fact that we agree to stop at some predetermined point (ie, when one person runs out of chips) is completely irrelevant. You can't manipulate coin flips by starting and stopping according to some system. My EV remains 0.
If I start with 1/x of the chips, and we agree to stop when one person runs out of chips, then, since my EV over all the hands is 0 chips, the probability that I end up with all the chips must be exactly 1/x. If it were any other value, my EV would not work out to 0 chips.
Keith
I don't think so. When it's heads-up (always assume players of equal skill), the small blind (button) will have +EV and the big blind will have -EV.
Making the analysis more difficult still, these EV's *change* each hand as the stack sizes change.
Not at all. In fact, this is precisely what distinguishes a tournament from a cash game.
Without the agreement to stop when a player reaches 0 chips, questions like "What's the probability of the short stack winning the tournament?" can't even be posed.
I think what you might be getting at here is the Gambler's Ruin problem. If I have 10 chips, and you have 90 chips, and we bet one chip on tossing a fair coin until one of us goes broke, then it is true that the probability that I win all of the chips is 10% (my stack size as a proportion of the total chips).
What's not clear to me is whether or not poker game can be well approximated by this sort of coin tossing set-up. In poker, players can bet different amounts, are making multiple decisions per hand, must post two unequal blinds each hand, have two unequal positions within each individual hand, etc.
ScottyZ
Fine. We will look at groups of two consecutive hands then. Nothing changes.
No they don't. This is exactly my point. As I said, the hand is no different than if the large stack had exactly the same number of chips as the small stack... the large stacks excess chips are (effectively) not in play for that hand.
No. It makes no difference. EV is additive. Your EV (in terms of number of chips) at the end of the tournament is whatever you started with, plus the sum of the EV of all your hands that you have played over the course of the tournament. The fact that you agree to stop at some predetermined point is IRRELEVANT to EV. This is basic statistics.
The point is, that poker CAN be be approximated this way if both players are of equal skill. I mean, it's not as simple as a coin flip, but the EV is still zero. The positional considerations can be taken care of by looking at sets of two consecutive hands, rather than individual hands. So, a players EV over 2 hands is 0 chips.
Now, there is a little "blip" here. It is possible for the tournament to end after an odd number of hands. But, this is negligible with small blinds (the difference in EV can be no more than 1 BB, since the player in the big blind can just throw away his first hand blind, giving up 1BB worth of EV, and reverse the situation)
Simply put, to take care of all the problems that you are worried about, just add EVs. If player A and player B are equally skilled, and they play heads up, with player A getting the button first, then:
If they stop playing after an even number of hands, player A's expected number of chips (ie the EV of his chip stack size) is the same as the number of chips he started with. If they play an odd number of hands, his expected number of chips is some value between the number of chips he started with, and the number of chips he started with + 1 big blind. The fact that they agree to stop after precisely 1 hour, or 2 hours, or 1000 hours, or when 1 person has 100% of the chips, or when 1 person has 73% of the chips, or when the Cubs win the world series, is irrelevant to EV. It only affects variance.
Here is the key point: YOU CAN NOT change EV by agreeing to stop, after a fixed amount of time, or according to some system. It simply can't be done. This is why stop-loss methods at poker don't do anything (assuming that you always have the same EV whenever you sit down). This is why the gambler's ruin problem yields the result that it does. This is why varying your bets at casino games doesn't work. With these methods, you can control variance, but you CAN NOT change EV. No matter what, your EV is the sum of the EVs of all your plays. There's no getting around it.
Keith
The stopping time of a freezeout tournament is not predetermined. It is a random variable.
I understand what you're trying to say when you point out that betting systems don't affect your expected outcome after a sequence of betting. The sequence of bankroll sizes while betting on a fair coin toss is a martingale under all possible betting strategies. This follows from the so called Optional Stopping Theorem.
Betting systems (or optimal stopping strategy) have nothing to do with the conditions for ending a poker tournament. Poker players in tournaments are *not* trying to determine an optimal stopping strategy--- they are simply confined by the rules of the game.
A heads-up tournament is like a random walk with two absorbing barriers, the barriers being the bust-out points of each player.
The presence (and location) of absorbing barriers *does* affect the expected outcome of a random walk. Namely, whether you're playing a tournament with a player, or a cash game with the same player, can affect the expected outcome.
As a silly example, suppose one player is so good that he is guaranteed to get the other player's chips. If these players decide to play in exactly one $100 buy-in tournament, the good player has EV of +$100. The good player's random walk is guaranteed to hit the +$100 absorbing barrier. If they play a cash game instead, the good player's EV cannot even be computed without more information. If the bad player decides in advance that he will play until he is either up or down $1,000, then the good player's EV turns out to be +$1,000. If the bad player does not decide on any stopping condition before they begin playing, the good player's EV is unknown.
ScottyZ
I am not sure what you find so difficult to understand here. For each orbit, each player's EV is 0 chips. Add zero as many times as you want. Stop adding zero after a fixed number of times. Stop after a random number of times. Stop when you fall asleep. It doesn't matter. You still get 0.
The example which you give is positional. It has nothing to do with stack size. In the hand where one person only has one chip, BOTH players have a maximum EV of +1. Because of the presence of blinds (which are presumably at least 1 chip each) the small stack is all in for his blind, and so both players have an EV of 0, regardless of skill level. But, really, you are changing the subject when bringing up this case, since we were talking about cases where the blinds are small. The blinds cannot be considered small if they put a player all in for his blind.
If you don't like the EV argument (even though I am SURE that it is valid), think about it this way. In a winner-take-all tournament, your optimal strategy is the same as your strategy in a cash game (assuming that all players are of equal skill. If you are a better player than most, you still probably want to avoid close gambles, since losing would prevent you from being able to make a better-EV bet later, or limit the volume of that bet. But we can ignor these considerations if we assume that all players are equal, since you are just as likely to make a bad bet later as you are to make a good bet, if the opposition is equal)
This is mentioned in Sklansky's book, and it's pretty obvious. Despite what you say a few posts back, the actual reason that tournament strategy differs from ring game strategy is that you make money by outlasting people, even if you eventually lose all your chips. If you started the WSOP with $1000 in chips (and equity) and lost all your chips right away, you get nothing. But it you lose all your chips AFTER everyone else except for one player, you get $4 million. Obviously, then, variance becomes important, possibly more so than EV. Like Sklansky says, it is (theoretically) possible to finish 2nd in a tournament without ever having more chips than you started with.
Anyway, the point is, in a winner-take-all tournament, things revert to being pretty much the same as a cash game. And, a heads-up situation is a winner-take-all tournament (effectively... you pay both players 2nd place and they are playing winner-take-all for the difference between first and second). So, in this situation, there is really not much difference between the tourney and a cash game. Your (cash) EV is simply the fraction of the number of chips you have, times the prize.
By the way, when I first read Skalnsky's book, I thought that his EV argument was circular too. But then I realized that he was not talking about EV in terms of money... he was talking about EV in terms of tournament chips. THEN it all makes sense. As is often the case with Skalnsky's writing, it's terse and a bit hard to read, but if you think about it for a while, you realize that he's right. It's a simple EV argument.
Keith
I simply don't think that the +EV for the short stack on the small blind is necessarily equal to (with opposite sign) the -EV for the same player on the big blind next hand because the stack sizes may change between hands.
And thanks for the lesson in adding 0.
ScottyZ
You could make the exact same argument about a cash game. Are you saying that a player's equity in a heads up cash game is not the number of chips he has in front of him?
Keith
Scotty finaly has someone who can keep up with his posts!!!
Hey Keith do you wanna post for me so I can get a free Mag since Scotty
won't? ppppppppppplllllllllleeeeeeeeeeeaaaaaaaaasssssssseeeeeeeee:) :?:
Yeah, well, being unemp... umm.. a PROFESSIONAL POKER PLAYER 8) helps too.
It's a fine line....
Keith
I guess it would be, but the argument I could think of for this depends heavily on the fact that it is a cash game instead of a tournament.
A lower bound for a (sensible) player's equity in a cash game is the chips in front of him, because he could leave immediately with those chips. A sensible player would chose to not play if the expected outcome is worse than that. (Unless for some reason this person favours something else besides EV, like variance, or entertainment value, etc.) The same goes for the opponent, so an *upper* bound for the original player's stack must be
Total chips - Opponent's chips = Original player's chips.
So, I'd say that in a cash game between equal (and sensible) players, the equity equals the chips.
Also, by "sensible" I guess I mean some super-brain who can perfectly assess the opponent's skill level relative to their own.
ScottyZ
Regards,
all_aces