Theoretical question that's driving me nuts

[parappa]

A hypothetical player playing sngs:

a) has unerring judgment and only puts chips into the pot when he has positive ev, but;
b) goes all-in every single time he has +EV, even if his +EV is 1 tournament chip.

I'm assuming that this player must be a winner over the long-term in a cash game, but will have huge variance. Is the same true of Sngs? Is it possible for him to actually be a losing player even though he makes only +EV bets, because he busts himself out more often? Or will his results simply take a longer time to even out?

[PrayingMantis]

interesting post. But there's something that bothers me about this player.

[ QUOTE ]
a) has unerring judgment and only puts chips into the pot when he has positive ev, but;
b) goes all-in every single time he has +EV, even if his +EV is 1 tournament chip.

[/ QUOTE ]

I think that it's not so simple. In other words, these two criteria do not really help to understand how he plays. Let's take b first. Saying that he pushes every time he's +EV (do you mean CEV or $EV? it's very imporant), you assume that he takes in folding-equity, for instance. Otherwise it's not a complete EV assessment. So for b to be true, this player must have a PERFECT read: he should know exactly what cards everybody holds AND how they will react in any situation. Otherwise he can't make these decisions you say he makes.

Now, if we take a, a means that he also makes CALLS (not only pushes), if it's even slightly +EV. Again, he must know exactly what the cards are AND have a perfect knowledge of how players will react on next streets, for instance. Perfect information (except of the outcome of the cards).

SO, if this opponent must have perfect information in order to play as described in a and b, why would he act in such a way as described (specifically) in b, but not in a MUCH more adjusted way, that will allow him to maximze all the possible edges, he's aware of?

In other words, for this particular player, pushing in every +EV situation will be EXTREMELY stupid, and highly -EV, in regard to other options. And therefore, if you say that he has a perfect judgement (a) and only put chips in when it's +EV, it's in (some) contradiction with (b), according to which he's not playing a perfect game, but VERY far from it. So where did his "perfect judgement" go?

In a way, it's like saying someone is very short, but also very tall.

I'm not sure this answers your specific questions, but these are some thoughts.

BTW, a few months ago, a poster called Hood (if I remember correctly), started a thread about similar matters. It was in regard to the FTOP, and why it doesn't mean much in real poker, and specifically in SNG. Some of the thinking was similar to what you want to discuss here, I think.

[Irieguy]

If I somehow acquired the ability to know for certainty when I was ahead 100% of the time... I would push all-in every time too.

This hypothetical player would destroy the SNGs. Besides always being ahead, he would get people to fold coin flips often, and would never lay down the best hand.

Imagine playing somebody who would only bet with the best of it, and whom you could never push off of a hand. He's super tight-aggressive and unbluffable. I would tag him with a note and never play with him.

Irieguy

[parappa]

[ QUOTE ]
I think that it's not so simple. In other words, these two chriteria do not really help to understand how he plays. Let's take b first. Saying that he pushes every time he's +EV (do you mean CEV or $EV? it's very imporant), you assume that he takes in folding-equity, for instance. Otherwise it's not a complete EV assessment. So for b to be true, this player must have a PERFECT read: he should know exactly what cards everybody holds AND how they will react in any situation. Otherwise he can't make these decisions you say he makes.

[/ QUOTE ]

I mean ChipEv. Whether it's possible to make all positive ChipEV plays in such a manner as to get a negative $EV is the question I'm asking.

The sense in which I meant "only positive EV plays" was in the sense of some preflop plays being +EV even if you know your opponent will only call when he has a better hand, but it's really just a (bad) means to an end of asking the question above.


[ QUOTE ]
Now, if we take a, a means that he also makes CALLS (not only pushes), if it's even slightly +EV. Again, he must know exactly what the cards are AND have a perfect knowledge of how players will react on next streets, for instance. Perfect information (except of the outcome of the cards).

SO, if this opponent must have perfect information in order to play as described in a and b, why would he act in such a way as described (specifically) in b, but not in a MUCH more adjusted way, that will allow him to maximze all the possible edges, he's aware of?

In other words, for this particular player, pushing in every +EV situation will be EXTREMELY stupid, and highly -EV, in regard to other options. And therefore, if you say that he has a perfect judgement (a) and only put chips in when it's +EV, it's in (some) contradiction with (b), according to which he's not playing a perfect game, but VERY far from it. So where did his "perfect judgement" go?

[/ QUOTE ]

Yes, I meant "perfect judgment" only to apply to his assessment of whether his play is +EV or not. Otherwise he's an idiot. The real question that I'm trying to ask is whether Chip Variance in an Sng, assuming (I know there are problems with this assumption) only +ChipEV plays, can make $EV negative.

[PrayingMantis]

[ QUOTE ]
The real question that I'm trying to ask is whether Chip Variance in an Sng, assuming (I know there are problems with this assumption) only +ChipEV plays, can make $EV negative.

[/ QUOTE ]

OK, now it's a more clear. but then, why not ask it "backwards?". I'll try:

Let's say player X has played N (pretty big number. How big? who knows. /images/graemlins/grin.gif ) number of SNGs.

Now, is it possible that in retrospect ALL his decisions were +CEV, and still he has lost money?

I think this might be an easier way to ask it.

However, before trying to answer this very complicated question, I just wanted to note, again, that for judging whether a decision is +CEV or not, you need to take into calculation SO MANY factors, about how people actually reacted or would react, "now" and on next possible streets, that it's actually pretty much impossible to judge whether EVERY decision was indeed +CEV. This is true especially for marginal situations, which are very very common (you don't know if it's somewhat +CEV, or somewhat -CEV. Making a lot of somewhat -CEV, could be catastrophical, but you might have VERY difficult time realizing you're making somewhat -CEV decisions).

I know I'm making things difficult, but when asking theoretical questions, I believe we must understand exactly what we are talking about, because we don't have much else... /images/graemlins/grin.gif

[parappa]

[ QUOTE ]
Let's say player X has played N (pretty big number. How big? who knows. /images/graemlins/grin.gif ) number of SNGs.

Now, is it possible that in retrospect ALL his decisions were +CEV, and still he has lost money?

[/ QUOTE ]

Yes! That's the one! /images/graemlins/smile.gif


[ QUOTE ]
However, before trying to answer this very complicated question, I just wanted to note, again, that for judging whether a decision is +CEV or not, you need to take into calculation SO MANY factors, about how people actually reacted or would react, "now" and on next possible streets, that it's actually pretty much impossible to judge whether EVERY decision was indeed +CEV. This is true especially for marginal situations, which are very very common (you don't know if it's somewhat +CEV, or somewhat -CEV. Making a lot of somewhat -CEV, could be catastrophical, but you might have VERY difficult time realizing you're making somewhat -CEV decisions).

I know I'm making things difficult, but when asking theoretical questions, I believe we must understand exactly what we are talking about, because we don't have much else... /images/graemlins/grin.gif

[/ QUOTE ]

Yes, I agree. The above is a much clearer formulation of the question that's driving me bananas. I'm comfortable with the answer for something like craps, and even something like a ring game and I want the answer to be the same in an Sng, but it just doesn't feel right and I can't get a handle on where to start figuring out an answer.

[PrayingMantis]

Some more thoughts:

I think that if all the decisions a player is doing are indeed +CEV (regardless of how we judge whether something is +CEV or not), this player is by definition killing the games. Absolutely killing them (Edit: even if some of his +EV decisions are actually -$EV in some way). So if he has lost money over a long stretch, it's only some VERY VERY bad luck. /images/graemlins/grin.gif

[parappa]

[ QUOTE ]
Some more thoughts:

I think that if all the decisions a player is doing are indeed +CEV (regardless of how we judge whether something is +CEV or not), this player is by defintion killing the games. Absolutely killing them. So if he has lost money over a long stretch, it's only some VERY VERY bad luck. /images/graemlins/grin.gif

[/ QUOTE ]

No, I can't go along with this, because it assumes an answer to the question that I'm trying to ask. He could, perhaps, be making tons of marginally +ChipEV pre-flop allins repeatedly and going out of tournaments out of the money often enough to make him a net money loser. Or at least that's what I'm wondering.

[PrayingMantis]

[ QUOTE ]
No, I can't go along with this, because it assumes an answer to the question.

[/ QUOTE ]

I'm not sure I understand what exactly you mean here. What "question"? The one about judging whether a move is indeed +CEV? Please explain.

[ QUOTE ]
He could, perhaps, be making tons of marginally +ChipEV pre-flop allins repeatedly and going out of tournaments out of the money often enough to make him a net money loser.

[/ QUOTE ]

I think you should look for a post by eastbay, about some simulations he did recently (from 3 weeks ago?). I'll try to find it. His simulation showed in an extremely clear way, that even a very small (repeated) advantage, while going all-in, of even a few %, results in a HUGE difference in ROI for different opponents. For instance, the player that always had the PP's against the over-cards, was winning at about 40% ROI IIRC, while the one who holds the overcards was a huge loser (The structure is of an SNG, not a ring game, so it's not about simply accumulating chips. "Busting early" is completely a part of it. )

It's only a simulation, very far from real SNG, and I don't know too much about it, but the results are very relevant to the theoretical question you're asking, IMO.

[LinusKS]

[ QUOTE ]
A hypothetical player playing sngs:

a) has unerring judgment and only puts chips into the pot when he has positive ev, but;
b) goes all-in every single time he has +EV, even if his +EV is 1 tournament chip.

I'm assuming that this player must be a winner over the long-term in a cash game, but will have huge variance. Is the same true of Sngs? Is it possible for him to actually be a losing player even though he makes only +EV bets, because he busts himself out more often? Or will his results simply take a longer time to even out?

[/ QUOTE ]

I don't know the answer to either, parappa, although I agree it's a very interesting question.

My guess is that a player who pushed a lot of all-in edges in sng's would be a losing player - just based on simple math. IE, pushing two 51% edges in one tournament gives you a little better than 25% ITM.

I'd be interested to know the answer, since in my experience, one of the keys to being a winner is avoiding close situations.

Of course, if the perfect player were playing against people who more likely to fold, he'd do better than against looser players.

[PrayingMantis]

Here's the thread:

Eastbay's simulation (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=991448&page=&view=&sb =5&o=&vc=1)

[parappa]

[ QUOTE ]
[ QUOTE ]
No, I can't go along with this, because it assumes an answer to the question.

[/ QUOTE ]

I'm not sure I understand what exactly you mean here. What "question"? The one about judging whether a move is indeed +CEV? Please explain.

[/ QUOTE ]

No, no, I'm trying to avoid the whole question of whether a move is indeed +CEV. The thing that I'm trying to figure out is whether, because CEV and $EV are different, it's possible through having enough CEV variance to "add together all positives (CEV decisions)but still get a negative ($EV)" over the long term and whether SNGs are different from ring games in this respect.


[ QUOTE ]
I think you should look for a post by eastbay, about some simulations he did recently (from 3 weeks ago?). I'll try to find it. His simulation showed in an extremely clear way, that even a very small (repeated) advantage, while going all-in, of even a few %, results in a HUGE difference in ROI for different opponents. For instance, the player that always had the PP's against the over-cards, was winning at about 40% ROI IIRC, while the one who holds the overcards was a huge loser (The structure is of an SNG, not a ring game, so it's not about simply accumulating chips. "Busting early" is completely a part of it. )

It's only a simulation, very far from real SNG, and I don't know too much about it, but the results are very relevant to the theoretical question you're asking, IMO.

[/ QUOTE ]

Yes, I have seen it, and I'm not quite able to determine whether those results would necessarily contain the answer to my question or not. IIRC 2 players were randomly selected to go all-in each time. One was given an edge in his confrontations. It seems at first glance that whatever "bust-out variance" could skew results would be included in the final numbers, but I'm not sure.

[CrisBrown]

Hi parappa,

I'll take a shot....

[ QUOTE ]
a) has unerring judgment and only puts chips into the pot when he has positive ev, but;
b) goes all-in every single time he has +EV, even if his +EV is 1 tournament chip.

[/ QUOTE ]

I think the (b) part is probably a mistake. Yes, by pushing all-in every time he had the edge, this "perfect reader" would increase his steal equity. However, he'll also decrease his made hand equity, because opponents are far less likely to call him.

I played a SNG once where an opponent had AA six times in the first 40 hands. He went all-in pre-flop every single time. And he won nothing but the blinds ... every single time. He went out 5th in a 10-player SNG (this was on UB) and was never a serious threat to make the money.

It's not enough to simply get all of one's own chips in when you have a big edge. You also want to get all of your opponents chips in the pot, and pushing all-in whenever you feel you have an edge is less likely to get your opponents' money in the pot.

Obviously, with narrow edges, you'd probably rather just pick up what's in the pot right now, and not have callers, because when you're all-in again and again, the short side of the odds does add up. Of course, if you win the first one or two of such showdowns, you won't be covered in the future and you can afford to lose one or two all-in coups.

Basically, you can't separate EV decisions from the amount of your bet. Different situations call for different kinds of tactics, to maximize your EV for that specific pot. In some cases, yes, that will mean pushing all-in. But not in every case.

Cris

[PrayingMantis]

I'll attack it from a different angle.

"-CEV is essentially always -$EV." (Bozeman)

If we agree with this statement, our hero is playing in an enviroment where his opponents are making constant -$EV decisions against HIM (since he's basically making ONLY +CEV decisions, and therefore, their decisions are necessarily -CEV, in most usual cases).

He's ALWAYS ahead, in every hand he plays, against his opponent/s, in terms of $EV.

On the long run, I cannot see how this player will not be WAY ahead, in terms of ROI, against any player he played against, EVEN if some of his +CEV were -$EV, as it's sometimes the case (still, there was *at least* one opponent, at these particular -$EV situations for our hero, that made, possibly, an even worse -$EV mistake).

How about this?

[chill888]

Seems to me that since you can construct situations where playing +CEV is incorrect it proves that it is sub-optimal.
(extreme: the other 9 go allin 1st hand and you have AA.


Still if you are smart enough to do it every hand it is clearly profitable... just not optimal. The elimination aspect of S&Gs and the ever present bubble makes it less than optimal.

gl

[PrayingMantis]

[ QUOTE ]
Still if you are smart enough to do it every hand it is clearly profitable... just not optimal.

[/ QUOTE ]

That's a good point in regard to the *original* question, and to some of the paradoxes it presents. If our hero is good enough to recognize ANY +CEV spot, he's definitely good enough to choose among these only the somewhat better +CEV spots, and pass on the lower +EV, even though they are still +CEV. This looks like a *very* basic ability, especially when speaking about such a magnificent player.

However, even if his "current" strategy is not optimal (this strategy was not very clearly described, IMO, but I assume our hero simply plays ANY +CEV spot he can, even if its for his entire stack. Am I correct about this?), as chill says, I'd say it is still highly profitable.

(Note: with regard to our player's strategy. Playing ANY +CEV spot, or playing ONLY +CEV spots, are two very different things, and my restating of the problem didn't really deal with it either, or solved it.)

[Gator]

This post draws out my feeling about SNG's.
I want to end up in a position where I need to win one coin toss to finish in the money. Thus, if we are down to five players and I have about 1,500 in chips - If I get my medium PP all in against AK (or vice versa) - I feel like I maneuvered that SNG correctly to get to that point. If I win that one coin toss I'm virtually assured of finishing in the money - otherwise I'm out. I can't expect to endure more than one (to finish in the money). To get to that point in the tourney I need to blind steal effectively and/or get my chips in earlier when I am the clear favorite (i.e. 3:1 or better).
Depending on you you interpret your post, your fictious player endures several 52%/48% hands all in (in which case he would be a losing player) or doubles up early enough to build a chip bankroll that can endure losing hands that are slightly better than a coin toss.
Again, my goal is to get to a position where I only have to win one coin toss. If I do that, I consider it a successful tournament (regardless of outcome).
Please comment.

[parappa]

[ QUOTE ]
but I assume our hero simply plays ANY +CEV spot he can, even if its for his entire stack. Am I correct about this?

[/ QUOTE ]

Yes. Thanks very much to the responses to this. I'm still thinking about it, but when I started thinking about it, I was fairly convinced that it would be possible to make a series of 51/49 decisions that would lead to a negative ROI in Sngs. Actually, Eastbay's results might show this to be true, as his result for a player with a 2% advantage shows that player barely covering the vig.

I have a pretty good hunch from Eastbay's results that a player who always makes 60:40 bets must almost certainly be a winner. In a 55:45 case, it also seems tolerably clear.

But if our player constantly gets in at 51:49 over and over, I'm even more confused than when I started, due mostly to how difficult it is to state the problem correctly. I thought about approaches that raised the idea of gamblers' ruin, or about some kind of analogy to the martingale and other systems that try through progression to force an outcome out of short-term results, but both these analogies seem to have serious problems, so I haven't even brought them up. Imo a direct analogy to a ring game also falls down.

So, I'm a bit stuck. Linus and Gator make similar and reasonable points about the likely effect of multiple all-ins on your tournament chances, but it's hard to pin down. If the prize was for winner-take-all these arguments would be easier to make, but where multiple places are paid it's harder to maintain--e.g. the UB structure, 8-handed, 1st gets 70% 2nd gets 30%. It's easy to say that you have to double up three times to win and that your chances of doing so at 50/50 are 12.5%, but it ignores the fact that in order to double up the third time, the other player would have to also have 4000 chips and you'd be guaranteed 2d place. Expanding the idea to include real-world situations in which one or the other player has the other covered makes it impossibly complex, I think.

[PrayingMantis]

I believe the reason this problem drives you nuts, is, again, a result of the very vague nature of EV.

On these boards and elsewhere, we usualy speak about EV as if it's something we can define and understand. But actually, IMO, in *reality*, it is far from being an accurate concept.

It is rather easy to speak about EV in many gambling situations. We can apply rather basic probability calculation, and get to a satisfying result.

But in poker in general, and certainly in tournaments, it becomes very tough to deal with it with enough accuracy. So we use generalizations.

Very simple example:

Our hero plays an SNG. Early stages. It's folded to him in MP, and he holds KJo. Can you really say where is exacly the line between a +CEV move here, and a -CEV here? OK, let's even assume he knows all the cards the players behind him hold. They hold 84o, K8s, A9o, JTs, 33 and 87o. Well, what's +CEV for him now, and what's -CEV? Of course, you can not say that, without knowing how this table plays, and specifically, how *every* player will play in any given situation. You NEVER know all this, so you can only have a vague idea about what is +CEV and what is -CEV (That's why there are *endless* discussions between the the best poker authors, about playing, say, AQ from the blinds after a few limpers. But there are ENDLESS more example, for which you cannot say for certain where is the exact line between +CEV and -CEV. This is true for the endless marginal situations in poker, that come so often).

Until you are able to recognize the exact line between +CEV and -CEV for EVERY specific situation in poker, you can't really approach specific theoretical problems like the one you describe, because they are based upon unclear definitions.

And recognizing the exact line between +CEV and -CEV for EVERY specific situation is by definition impossible - because this game is very much about human psychology and behaviour. You can never simulate it accurately enough, and you can only speak about it in very general terms (that are usualy enough for making good money in this very complicated game).

I think that part of what is interesting about your question, is that it shows how difficult it is to fully understand EV.

[PrayingMantis]

Another shot at this interesting problem:

Thinking more about this, I'd like to ask the question again. parappa, tell me if you like this phrasing:

Hero is playing NL SNGs, *without knowing it's an SNG* (or without giving even the smallest thought to $EV consideration, bubble, etc, etc). i.e, For him, it's a cash NL ring game, with blinds that go up every fixed amount of time or hands, and he wants only to get as much chips as possible, not caring about chip-variance at all.

(Edit: Hero is playing *any* SNG as if it was practically a winner-takes-all. I believe this pretty much describes it, or very close to it.)

Now, Hero is a great NL ring player. He's especially good at playing short-stacks (small buy-ins on party, for instance. He's killing them). He's not a perfect player or anything, just a great one.

How will our imaginary hero's ROI will look, on the long run, and on different buy-ins?

[Nacarno]

This is fascinating to me, but I'm still kinda confused about some of the details. Maybe someone could help me out...

1) Does this player always push when he has a better hand?
2) What happens in situations where it's +CEV to call but not to go all-in? For example, what if there is some very loose player who min-raised with pocket 3s and our theoretical player has AK in the big blind?

[Nacarno]

You know what... I think it's actually pretty easy to show that because of the prize structure of SNGs that it is possible for our hypothetical player to make only +CEV moves and still be a losing player.

Suppose our player is at a 10 player SNG. Now suppose some hands have passed to that our player has 1 chip less than every other player. Now suppose on the following hand that he is last to act and everyone goes all-in before him regardless of their hands. He could easy hold a hand that would win say... 1/9 of the time at showdown and calling would be a +CEV move since the pot would be laying him 9:1. The times he won he would pretty much be assured of 50% of the prize pool but the 8/9 other times he lost he would lose his 10%.

Now supposed the prize pool was $100 from a $10 buy-in:

1/9 * $50 - 8/9 * $10 = -$3.33

He has made a +CEV move that guarantees he loses money in the long-run.

Of course this is not very likely, but neither is a player who only makes +CEV moves. So I guess the answer to the question of whether it is possible to only make +CEV moves and still be a losing player in SNGs is "yes".

[KJ o]

[ QUOTE ]
My guess is that a player who pushed a lot of all-in edges in sng's would be a losing player - just based on simple math. IE, pushing two 51% edges in one tournament gives you a little better than 25% ITM.

[/ QUOTE ]

Change "would" to could" and I can agree. But it's not very likely at all. For him to have a 25% ITM, he will
a) have to be called both times he pushes - in practice such a player would pick up a lot of blinds
b) have only a 51% edge - in practice, some edges will be 70% or more (remember this is the guy who never pushes kings and run into aces but always calls when someone pushes with queens and he has kings himself)
c) face a stack as large as his or larger both times - highly unrealistic.

Let's define the problem in this way: whenever it is hero's turn to act, he looks at his cards and thos of his remaining opponents. If he pushes and any combination of calls makes him net -EV on the play, he folds, otherwise he pushes. This player will kill the typical SnG because:
1) he will probably get called by "gamblers" (i.e. morons) early on which give him way better than 50% chance of doubling up.
2) once he has doubled up, people will be vary of calling him down, so he could pick up a lot of blinds with abandon
3) Late in the game, he would never have the bad luck of running into a higher pockt pair etc. Thus, once he gained a decent stack, he'd end up in the money with alarming frequency, IMO.

Would he always end up in the money? Of course not. And if his luck is bad enough, he'd lose money. But in reality, he'd make a killing.

This shouldn't be too hard to simulate, I guess...

[parappa]

[ QUOTE ]
You know what... I think it's actually pretty easy to show that because of the prize structure of SNGs that it is possible for our hypothetical player to make only +CEV moves and still be a losing player.

Suppose our player is at a 10 player SNG. Now suppose some hands have passed to that our player has 1 chip less than every other player. Now suppose on the following hand that he is last to act and everyone goes all-in before him regardless of their hands. He could easy hold a hand that would win say... 1/9 of the time at showdown and calling would be a +CEV move since the pot would be laying him 9:1. The times he won he would pretty much be assured of 50% of the prize pool but the 8/9 other times he lost he would lose his 10%.

Now supposed the prize pool was $100 from a $10 buy-in:

1/9 * $50 - 8/9 * $10 = -$3.33

He has made a +CEV move that guarantees he loses money in the long-run.

Of course this is not very likely, but neither is a player who only makes +CEV moves. So I guess the answer to the question of whether it is possible to only make +CEV moves and still be a losing player in SNGs is "yes".

[/ QUOTE ]

Yes, Aleomagus came up a while ago with the simple example of holding AA on the first hand in the big blind with 9 all-ins to you. You're guaranteed second if you fold; AA is still +CEV against 9 opponents, but doesn't have an appetizing win% against them.

[parappa]

[ QUOTE ]
Another shot at this interesting problem:

Thinking more about this, I'd like to ask the question again. parappa, tell me if you like this phrasing:

Hero is playing NL SNGs, *without knowing it's an SNG* (or without giving even the smallest thought to $EV consideration, bubble, etc, etc). i.e, For him, it's a cash NL ring game, with blinds that go up every fixed amount of time or hands, and he wants only to get as much chips as possible, not caring about chip-variance at all.

(Edit: Hero is playing *any* SNG as if it was practically a winner-takes-all. I believe this pretty much describes it, or very close to it.)

Now, Hero is a great NL ring player. He's especially good at playing short-stacks (small buy-ins on party, for instance. He's killing them). He's not a perfect player or anything, just a great one.

How will our imaginary hero's ROI will look, on the long
run, and on different buy-ins?

[/ QUOTE ]

I like this phrasing, but it feels as if it must be "slanted" in some way that it makes you want to ignore how huge a part variance could play. But if this is a fair formulation of the same question, it really makes me lean toward saying that such a player would find it difficult to lose.

[PrayingMantis]

[ QUOTE ]
I like this phrasing, but it feels as if it must be "slanted" in some way that it makes you want to ignore how huge a part variance could play.

[/ QUOTE ]

I don't think so. This player will not care at all about busting, for instance. He's only interested in CEV, and almost by definition his "chip-variance" will be rather huge.

[ QUOTE ]
But if this is a fair formulation of the same question, it really makes me lean toward saying that such a player would find it difficult to lose.

[/ QUOTE ]

it is not the exact same original question, but I think this question is more clear, and presensts basically the same theoretical problem, IMO.

I agree with you, that it's hard to see how this is a losing playier. I'd actually say he's a big winner. He might have a (significantly?) smaller ITM% than we are usualy happy about, but his proportion of 1/2/3 will be absolutley great. He'll probably have much much more 1sts than any other place. Actually, we are describing here a very strong player, that cares only about winning. 2nd and 3rd are not for him (and that's why he'll be making $EV mistakes in certain situations, and lose some opportunities to get ITM, for instance. But that will be "compensated" by his frequent wins).

You know, there *are* players who play in quite a similar way, most of the time (not always, of course). I's say Gus Hansen is one of them, and others who pretty much play as if CEV=$EV, at least in early-mid stages of tournaments. But SNGs are different in some aspects (you don't need to accumulate so many chips to win or money in a specific game).

This is a very interesting discussion, IMO, and it touches on the most fundumental aspects of SNG (and tournament) play. I'd be happy to see more opinions here, since these ideas about CEV and $EV are usualy discussed in the theory or MTT forums.

[PrayingMantis]

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ou know what... I think it's actually pretty easy to show that because of the prize structure of SNGs that it is possible for our hypothetical player to make only +CEV moves and still be a losing player.

Suppose our player is at a 10 player SNG. Now suppose some hands have passed to that our player has 1 chip less than every other player. Now suppose on the following hand that he is last to act and everyone goes all-in before him regardless of their hands. He could easy hold a hand that would win say... 1/9 of the time at showdown and calling would be a +CEV move since the pot would be laying him 9:1. The times he won he would pretty much be assured of 50% of the prize pool but the 8/9 other times he lost he would lose his 10%.

Now supposed the prize pool was $100 from a $10 buy-in:

1/9 * $50 - 8/9 * $10 = -$3.33

He has made a +CEV move that guarantees he loses money in the long-run.

Of course this is not very likely, but neither is a player who only makes +CEV moves. So I guess the answer to the question of whether it is possible to only make +CEV moves and still be a losing player in SNGs is "yes".


[/ QUOTE ]

I disagree. Of course: in certain situations this player will make a -$EV mistake by making a +CEV move, and will lose money at these points. HOWEVER, most of the time, making constant +CEV moves will result in making more (or much more) money than losing. It is hard to prove it, but the fact that in certain cases he'll lose money, does not mean that in the long run he isn't actually a huge winner.

[Lori]

If I somehow acquired the ability to know for certainty when I was ahead 100% of the time... I would push all-in every time too

This would not be optimal.

If you had that information, you would also be able to wait for a better spot and KNOW that it was a better spot.

Lori

[Nacarno]

I think we're actually in agreement here. I don't think it would ever be the case that he is a losing player in the real world, but in this hypothetical world where our player always knows when he is +CEV it is just as possible that the situation I describe, or a similar one, happens every time.

But in any case, I agree that he would be a huge winner in the long run 99.99999999999999% of the time.