The old coin-flip debate

[PrayingMantis]

What you're saying is correct, but in a way it is (or should be) embodied in Hero's $EV (or rather: the $EV of calling / folding). Because the "general" $EV the whole field (all 4 players) gains by a specific move done by any player, is always 0. Therefore, if you're making a -$EV, the rest of the field (i.e, all others, as a "collective"), has gained, since it's by definition +$EV for them (however, it's possible, of course, that it's +$EV for some of them, but -$EV for others).

An implication from your point, goes something like this:

When you're making a -EV move at a certain point (by folding, in the cases we're taking about), you are making it based on the assumption that some other player will "soon enough" make a bigger -EV mistake, or you, for that matter, will get an opportunity to make a higher EV move (by applying aggression, for instance). But how much can you wait? How many negative EV decisions can you make against these equally skilled, equally stacked, players, during the bubble time? (also notice, that if the stacks were equal at the begining of the hand, and if everyone included you folded to the aggressor, at the end of the hand he has the chip lead. If you were on the BB, for instance, you're now 4th stack.)

[AleoMagus]

[ QUOTE ]

...he's consistently making -CEV moves... By doing so (folding), he is *by definition*, increasing his opponent (aggressor) $EV, and by that reducing his own. Another point (that really complicates it, IMO), is that we can no longer assume all players have equal ability, if Hero is making a consistent CEV mistake against his opponents.

if all opponenets are equally skilled, Hero should take ANY +CEV opportunity he has, since he hasn't got any skill advantage. Not taking even the slightest +CEV opportunity is, according to our "equally skilled" assumption, a mistake. Therefore - our Hero should call all-in even if he's less than a coin-flip, if the pot-odds justify it.

[/ QUOTE ]

From what I can tell, these and a few other points seem to confuse two issues that are not directly related.

Chip EV (CEV) and Dollar EV ($EV)

Making consistent -CEV plays in a tournament does not 'by definition' imply an increase in opponent $EV and does not imply an decrease in one's own $EV. Extending this, I think it is safe to say that even though equally skilled, we should not be inclined to take ANY +CEV edge we can get if $EV is what we are really concerned about.

$EV is a kind of a strange thing to even talk about in the context of a single play though I and others attempt to do it all the time. It would seem though (strange as it is) that -CEV plays can be +$EV in the context of tournament play.

Imagine for example a four handed situation like this

You (BB) have t3600
SB has t3600
Button has t400
UTG has t400

Blinds are 200/400 and antes are 50. After UTG and button pass, SB pushes all-in. You hold TT. SB is not a wild player, but is certainly capable of a push in this situation with less than premium hands. In fact, lets just assume you know his hand is JQo.

This is clearly a +CEV call, and may even be a +CEV situation for both you AND the SB even after you have called.

Strangely though, the two small stacks experience a major boost in $EV if the two of you collide and one of you is eliminated here. What this does imply is that despite your +CEV situation, both you and the SB have just lost $EV by getting into this big confrontation.

This actually brings me to an interesting thought. On any all-in steal on the bubble, the move itself does not seem to have a $EV independent of your opponent's reaction. If, for example, you are stealing with A7s and your opponent calls with KJo, it may be +CEV for both the steal and the call, and may even in some sense be +$EV for the steal and a fold, but if your opponent decides to call anyways (playing according to CEV concerns), he effectively lowers BOTH of your actual $EV in the tournament and increases the $EV of the small stacks.

Well, this may be unclear (or simply flawed) so before I ramble anymore, I'll see how this goes over first.

Regards
Brad S

-edit. In rereading this and the previous posts, I think I have noticed something that may be more accurate in describing what I mean. Making -CEV plays may actually increase your opponents $EV, but less than if you called. More importantly, avoiding slight +CEV situations on the bubble when facing elimination, though it will almost certainly lessen your $EV may still be better than making the +CEV play which will lower your $EV by even more.

[PrayingMantis]

Brad,

Yes, you are right of course that $EV and CEV can be 2 very different entities, and in my last post I got a bit carried away comparing them. Sure it's possible to make a -CEV move, that is +$EV, especially around the bubble. I was wrong when I stated that making consistently -CEV moves is by definition a mistake, since I wasn't refering to the $EV.

Regarding calculating $EV of specific moves: this is tough and vague, but doable. There was a thread here, a few months ago, with participation of eastbay and Bozeman, in which different approaches to calculate $EV were discussed. This $EV value of any move in a tournament was also discussed.

About your new thoughts that you mention: they are very interesting, and I must say that this is exactly where I'm going with my thinking about this subject, especially after reading and thinking about the replies in this thread.

To summerize some of my thoughts:

(On the bubble, equal stacks) If you're pushing against an opponent, who will call as a slight-medium dog (i.e: loose but not SO loose caller), you should definitely tighten-up your raising criteria, since his call will reduce yours and his $EV, and increase the two other player's $EV. This is, of course, a different perspective on the "gap" concept: If you take in $EV, you should normally need a much better hand to raise than to call, since almost ANY showdown will help the other two players more than the 2 involved in the showdown. And by that logic, if your pushing against a player who does not understand that, you are making a $EV mistake (and actually, if this player is sitting at your immidiate left, you have a rather problematic position, in regard to stealing, so you *might* need to adjust your calling strategy).

Some of what I'm saying here is pretty obvious, but it can have some very important implications on different bubble strategies.

For instance, we can try and think about different approaches (loose/tight, passive/aggressive) to deal with different mixtures of players, divided into 4 rough and extreme types:

1) almost always folds (weak-tight, almost never pushes or calls all-in)
2) Sometimes pushes, but never calls (a smart LAG, 2+2 type?)
3) sometimes calls, but almost never pushes (loose-passive?)
4) sometimes pushes and sometimes calls (loose in general)

1,2 and 4 are more common than 3, but I see all these behaviours on the bubble. 1 is, of course, the type of player you'd always want to have around you...

It is also extremely important to see what is your position in relation to these players (for example, you'd better have 1 or 2 at your immidiate left, than 3 or 4) in order to decide what is the best strategy.

Certain decisions in a strategy will have to be taken in regard to making calls, as x:y favorite, against specific opponent. If we'd have a more clear understanding of what is our advanage against any relevant field, including our position, I think we'll have a better chance to solve these "calling criteria" problems.

So there's still a lot of work...

[Benal]

Party Poker MTT Qualifier - 30 left, top 7 qualify. Blinds 150/300. Average stack is t5000

I have t2700 and get KJo on the button. MP1 (t4500) limps, MP2 (t4800) limps, I push.

I have a very tight table image, having played maybe 1 hand over the last 4 orbits. My thinking was that pushing would increase my stack by approx 30% if everyone folded, and would cut any other stack in half if called and they lost.

SB (t5400) folds, BB (t5000) folds, MP1 (t4500) folds, and MP2 (t4800) calls after a long pause.

MP2 flips over 66.

Whether I won or lost is irrelevant.

Did MP2 make a mistake calling with 66 knowing he’s probably in a coin-flip or a huge dog?

Did I make a mistake by pushing with two limpers behind me? Should limpers impact your decision when trying to steal blinds? If there is always a limp or raise behind you, should you (generally) never attempt to steal blinds? (I realize this is read dependant)

[Tharpab]

Lets consider the example:

1st - $50
2nd - $30
3rd - $20
Total Prize $80

Total chips 2000
Other guy 500 25%
Other guy 500 25%

Villain 500 chips 25%
You 500 chips
You 'own' 25% of the chips and therefore $20(of the total prize) After coin Flip $40/2(half of the time you lose) = You will 'own' $20 of the total prize

So in this case we have an $EV+-(Actually its + since the blinds will hurt an low stacked and therefore hurt the chances of winning than a bigger stacked) call, but it also must be took in account the skill of the players in their equity(like in a scale from 0 to 10 how much is likely they to win) as a way to creating their equities. Looks good on paper, but some math genius could comment this

[PrayingMantis]

[ QUOTE ]
1st - $50
2nd - $30
3rd - $20
Total Prize $80


[/ QUOTE ]

50+30+20=100.

[ QUOTE ]
You 'own' 25% of the chips and therefore $20(of the total prize) After coin Flip $40/2(half of the time you lose) = You will 'own' $20 of the total prize


[/ QUOTE ]

When you own 25% of the chips (in case of 2x,x,x), you "own" 25% of the prize pool, only when it's "winner-takes-all". Otherwise, (for instance: 3 places get paid 50/30/20), the calculation is more complicated.

[Bozeman]

I am not regularly reading the forum now, but PM sent me a pm about this thread, so I think I should try to respond.

General points about near bubble play:

1) -CEV is essentially always -$EV.

2) +CEV is often -$EV

3) The $ value of the various stacks will depend on the way other people play. For example, suppose stacks of 5x, 3x, 1x. If the 3x wants first, the 5x stack will have less $EV than if the 3x is playing to outlast the 1x.

4) Better calculations than AM's are available, but there will always be debate, mostly because of (3).

5) Small stacks are worth more per chip than large stacks.

6) When two stacks tangle, the stacks not involved gain $EV. Possible exception to this for VERY large stacks.

7) Reasonable players should not call big bets even with some hands that are better than the hand they are facing.


Now more detail: Suppose you are playing with 4 equal players with equal stacks, and everyone is aiming for 1st. Now you have 25% chance of each place. With three players that have 2x, 1x, 1x, and payouts of 50%, 30%, 20%, the big stack is worth 38.6% ($38.6 for a $10 tourney) (P1=50%, P2=35.8%, P3=14.2%). This is very close to the method used by PvSexton, which I have called the independent chip method (slight advantage to smaller stacks). In fact, this is the method used in my PalmApp for calculating fair deals ( DealCalc ), since the more accurate method I used above is very intensive for more than 4 places ( 4 way and independent chip source code ). A review of my research on this subject is at ( Tourney finish place probability ).

Given that the two smaller stacks may want to try to wait each other out, the big stack may be worth slightly more than 38.6%, so PM's $40 estimate is reasonable.

As for not knowing what hand the other player may have, this is mostly a strawman, because it is not usually difficult to place bounds on what sort of hand this player would need to make this move. Then instead of your win % against this particular hand, you can look at your weighted average % against his range of hands (twodimes doesn't do this, but many other showdown calculators do).

This brings up one mistake that I see many players make: they call when they think they are better than the worst hand that this player needs to make this move, even though they are -EV (and often even -CEV) against the range of hands.

The difference of hands chosen by AM and Pitcher (for example) is accounted for by the difference in level of play. If a good player knows (or even suspects) you will fold 99, you will be blinded off very often. But if several players will call with many hands, as often happens at lower limits, you can be virtually assured of a money finish with no risk if you fold. At higher levels, generally fewer players make the mistake of calling too often, AND generally fewer players make the mistake of raising too infrequently. Also, at lower limits the bubble occurs at lower blinds.

Finally, you must sometimes make -$EV plays because the alternative is even more -$EV. For example, going allin with a small stack and a bad hand UTG may be better than waiting for your BB even though you have only a small chance of picking upthe blinds and you are virtually certain to be an underdog when called. I think that some of the +CEV, -$EV calls fall into this category.

What have I forgotten?
Craig

PS Is it possible to search for posts more than 7 months old? It is not returning my older posts.

[donkeyradish]

I'm on the avoid confrontation side of the fence, ever since a couple of weeks ago I improved from 10th to 4th in a 300-player tournament by simply folding every hand!

At the final table I had the smallest number of chips I could have without dropping out a round. I fully expected to be 10th, but it seemed like everyone else wanted to win at all costs and the chips were flying around the place as everyone put themselves all-in.