The old coin-flip debate

[PrayingMantis]

I reread recenly this interesting thread by Aleo ( A bad way to play on the bubble (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=711461&page=&view=&sb =5&o=&vc=1) ), and had some new thoughts.

I want to specifically adress this paragraph (and calculation):

[ QUOTE ]
If I take a coinflip, I have a 50% chance of busting and a 50% chance of being the big stack with three left.

So I have 50% chance of $0
and a 50% chance getting into the final 3 with about 4000 to 2000 to 2000

this should mean 1st 50% of the time I survive- $25 equity (10+1)
2nd 25% of the time - $7.5 equity (10+1)
3rd 25% of the time - $5 equity (10+1)

so all together this means .5(0)+.25(50)+.125(30)+.125(20)
or, $18.75 equity

BUT...

if I avoid confrontation when I know it's gonna mean a showdown I have the same equity (slightly less if I'm in the blind) as before. This is

1st 25% of the time - $12.5 equity
2nd 25% of the time - $7.5 equity
3rd 25% of the time - $5 equity
4th 25% of the time - $0

so all together this means .25(0)+.25(50)+.25(30)+.25(20)
or, $25 equity


[/ QUOTE ]

The point of Aleo here is, that getting into coin-flip situations on the bubble, with equal stacks and equal ability, is -$EV, since by folding you remain in a +$25 EV position, and taking the coin-flip reduces your EV to +$18.75.

However, according to this reasoning and evaluation, taking a 7:3 showdown, is only marginally +$EV:

Taking it:

0.7*37.5 (your overall portion of the prize pool, according to the same calculation, when stacks are 2x,x,x) = $26.25

Avoiding it: $25.

And of course, any situation where it's 66:33, is neutral in terms of $EV (about 0 $EV), for instance: AQ vs. KJ.

I believe that part of the problem is in the assumption of having "only" $37.5 EV, once in the money, with stacks at 2x,x,x.

I would suggest it's in the vicinity of $40, for a strong player (I'd hope someone who's very familiar with these calculations, like Bozeman, will help here), and on the other hand - a player that is constantly avoinding confrontation once it's 4 handed with equal stacks (I assume pretty massive blinds, of course), as suggested in the original post, has probably less than 25% of the prize pool as an approximate EV, especially if he's dealing with loose-aggressive players.

Any thoughts?

Edit: all the $EV numbers are calculated for a $10 SNG, but that's only for the sake of convinience, of course.

[stupidsucker]

These equations baffel me a little, but I understand them enough to get the jist of what you are saying. Forgive me for asking a stupid question, but how do you know its a "coinflip" without seeing the cards.

My calling hands are of a higher standard then my pushing cards. If I push I dont know if I am getting called. If I call then I know its going to be a race, but I have no idea what the % chance is. I may be on either side of a domination.

Please understand that I am not trying to belittle the thread. I really want to understand what you mean.

[PrayingMantis]

You can never *know* of course, if it's a coin-flip, until you see the other-opponent's cards (whether you called, or he called your push). But against most opponents, you might have a strong enough "feel" of their pushing (raising) and calling standards, and have a pretty good guess of where you would "normally" stand.

Aleo is saying, for instance (he would say it better than me, and I hope he'll reply in this thread), that calling all-in on the bubble, with equal stacks, when you hold 99, is a wrong move, because most of the time you'll be in a coin flip situation (i.e, against over-cards), or worse: bigger pair (However, since it's short handed, and high blinds, you can not put your opponents on big pair every time they push, and it's much more probable they are on over-cards. Hence, coin-flip). Calling with 99, according to some assumptions, is -$EV. You're losing money, despite the fact you're probably getting the right, if not good, pot-odds.

Now comes the more subtle point of what is your read on the raiser "looseness". With what Ax will he push? Will he push with any A? any pair? etc. If he will, many times you'll be in a far better than coin flip - 7:3 or much better. Does it worth the call? Do you still consider it as a coin-flip in normal circumstances? is it +$EV? Marginally +$EV? Auto-call? That was the point of my post (or some of it). I hope this is more clear.

[AleoMagus]

Hi PM

For anyone who hasn't seen that thread, it is here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=singletable&Number=711 461&Forum=,,,,,,,,All_Forums,,,,,,,,&Words=&Search page=1&Limit=25&Main=711461&Search=true&where=&Nam e=5278&daterange=&newerval=&newertype=&olderval=&o ldertype=&bodyprev=#Post711461)

I was toying with those ideas when I first posted this and I think it is important to read Phil Van Sexton's criticism, which I think is valid.

Still, The idea of calling equal stack ALL-IN raises on the bubble with equal stacks still seems like a horrible move to me. As I said in that original post, I wouldn't even do it if I knew myself to be slightly ahead.

What troubles me about the reasoning though is the thought that in some way, we hurt our chances of making the money when we start to play too timidly and it is hard to know where to draw the line between what hurts us most, especially on an agressive bubble where your blinds are constantly being challenged.

The implications of my original argument, if correct, run both ways after all. We should be raising a lot on the bubble, and maybe even all-in against good players, because there is very little they can actually call with that makes the move correct for them, even if they are ahead. In a really strong game this might mean players going all-in almost any chance they can be the first in the pot until one player finally gets a big pair and can call down the raiser.

In that original thread I never did get any responses from math types about my reasoning and I too, would love to see some.

I'm gonna write more about this, I promise

Regards
Brad S

edit - In re-reading your post, I think you may be touching on at least Part of where this reasoning might be flawed. Having 2x,x,x stacks may give you greater $EV than my assumption, but I am also not an expert on those approximations. That combined with the potential -$EV implications of playing too timidly on the bubble almost certainly lessens my original argument. To what degree remains to be seen.

[PrayingMantis]

[ QUOTE ]
Still, The idea of calling equal stack ALL-IN raises on the bubble with equal stacks still seems like a horrible move to me. As I said in that original post, I wouldn't even do it if I knew myself to be slightly ahead.

[/ QUOTE ]

How much is "slightly ahead"? That is the main problem here. I think that in this forum there is a big tendency to see everything in terms of aggression and folding equity (I do it many times myself). However, It seems that by not calling (all-ins, that is), consistently, when there's a good possibility you're around, say, 2:1 favorite, is giving the aggressor in that spot a very big advantage (I'm talking high blinds of course), and in these last stages of a tourney, that can be significantly -$EV for you.

Of course the gap still applies: you can raise with a much wider range of hands, but against certain strong opponents, especially in the higher buy-ins, big calls are a dangarous weapon too. The higher the blinds, the narrower the gap. Part of what you achieve (if you manage to survive) is tightening your opponents, which is also +$EV for you. I know many in this forum won't accept it, but your opponents might actually *fear* your calls.

[AleoMagus]

For me, slighltly ahead usually means small to medium pocket pairs. These hands will really only be behind against a bigger pair and as you have stated, you can't always be scared of that.

I have softened somewhat on hands like TT and JJ because that I think so many opponents will push with Ax on the button or even K7+. The possible addition of a small card makes hands like TT (and maybe even 99) better than perhaps I have first suggested.

88 or smaller pairs are trouble though and I think still are better folded in the situations we are discussing. I'm actually still folding 99-TT to big raises on the bubble and I like my bubble stats of late. I'm sure this is relative to opposition and may be different at higher or lower limits. I am playing mostly Party 30+3 these days with a few 50+5 thrown in to the mix. If I think a player begins repeatedly going after my blinds, I will lessen these requirements. If he lets me keep my blind a lot of the time, I'll be happy to give him the occasional one even if I do have 99.

Slightly ahead may also mean hands like AT or smaller aces if you think an opponent will push with any two cards over 9 or even with Kx. I'd never call an all in raise from a big (equal) stack with even AJ in these situations unless I knew a player was continuously gunning for my blinds and I needed to make a stand. Most times, if I can leave myself with 3-4 BB after a loss, I will call with more. Another problem with medium aces is that so often you will be dominated if you guess wrong.

As for opponents fearing calls, the problem is that if you survive, that opponent is eliminated or crippled and his fear is no longer very important. I just don't give credit to players for actually paying attention to what happens to other people. I definitely think players pay attention when they are in a hand, but not much otherwise. If I want fear or need to slow a guy down, I think re-raises all-in are still ideal. That's pretty obvious I guess.

Regards
Brad S

[stupidsucker]

Ok so correct me if I am wrong..

This pretains to calling only.

With hands like medium pairs where you are probably a coinflip with overcards. Or other situations where its probably a flip, like K9s or JQ.

I guess I agree for the most part, and the most important factor to me is stack size.(You did mention it was equal stacks) I would have a hard time laying down 99 when pushed against from the button or SB.(If I am BB) I already Have BB invested, and I know I personaly will push with a lot of hands on the bubble into an equal stack. Perhaps my standards for pushing are way to low. I guess if I feel I am up against a moron or a good player I have to call with 99. Because in either case they could have almost anything and I feel I am ahead enough to warrent the call. If the pusher seems passive and tight then I am more inclined to lay it down, but probably still wont.

I am curious what is the proper move, and thanks for the good post.

[Pitcher]

Hi Brad,

[ QUOTE ]
I have softened somewhat on hands like TT and JJ because that I think so many opponents will push with Ax on the button or even K7+. The possible addition of a small card makes hands like TT (and maybe even 99) better than perhaps I have first suggested.

[/ QUOTE ]

Bingo Brad,

At the higher buyins (200's) this is a borderline auto-call in some games because many very good players will push with Ax or K-7-8. You just can't give hands like 99-TT up in these situations, especially when the blinds are large. Plus, players pickup on the fact that you won't defend immediately and challenge you even more. I also almost always call with AJ (amazing how often this is dominant) and AQ-AK are near autocalls. Of course, some of this is read dependent (I know of one player who will only push with PP's 88 or above or AK, AQ. Of course, I won't call this player with overs in that situation. I would like to be on the "good side" of the flip...the guy with the 11-9 edge), but these are pretty standard for me at these levels. I like my bubble results but want just a few more 1sts /images/graemlins/smile.gif

Pitcher

[BradleyT]

I never fold 99-TT on the bubble when they come up.

You don't get push hands often enough on the bubble to wait for a stronger hand than 99 or TT. And the fact that you're only behind 4-5 hands (higher pairs) makes it even more reason to push with these hands.

[AleoMagus]

Yeah, we are talking about calling here only. 99 or TT is definitely a raise and probably a push if the blinds are big enough. these hands are often even re-raise pushes if you think an opponent might still be re-stolen from.

It is the fact that you are guaranteed a showdown that makes a all-in call so undesirable, even if you think you might be ahead.

As stated by many, folding 99-TT to all pushes might be too timid a play. There are times for calling, and many will always call (successful players).

Just one example I can think of where I think it is bad might be:

4-handed with all stacks at ~2000.
blinds are still only 100/200

you are in the BB and the SB (who has slightly more) pushes against you.

For me, I definitley fold 88 or smaller and unless it is a weak raiser who I know has been gunning for my blinds, I probably fold even 99 and TT.

basically what it comes down to is the thought that I am about 75% (more actually) to make the money when I find myself equal stacked in the final 4. If I suspect I will be facing two overcards, why would I want to take 50% odds on my survival here.

Yes, doubling up here increases the chance of a win, but that is what the calculation PM is speaking of addresses. I attempt to show that the $EV of folding is still greater than calling. As yet, no math gurus have commented (that I know of).

Regards
Brad S

[AleoMagus]

Yes, we are in agreement.

99 and TT are definitely strong enough hands to push with and a coinflip confrontation if you are called is ok, because you have the greatly added value of the steal attempt.

It is calling all-in raises against other decently sized stacks that this and the other thread is addressing

Regards
Brad S

[PrayingMantis]

Reading my original post again, I've realized that the point that seemed clear to me, wasn't too clear from the way I've written it. Although the discussion that origniated was exactly what I was looking for.

My point was, that according to the original calculation by AM, calling all-in as a 7:3, with equal stacks on the bubble, is only marginally +$EV. However, I cannot believe this is correct. I'm pretty much positive that calling all-in as such a favorite, is significantly +$EV, and the same probably goes for calling it as a 2:1 favorite.

For my thinking here to be true, we have to assume that by folding in that situation we are not securing an $EV of 25$ (but less), and by calling, we are gaining more than merely the $37.5 * P (while P is our probability of winning the showdown). So basically, I'm arguing against these 2 numbers (25$ and $37.5, for a $10 SNG), and my argument is that calling all-in as, say, 2:1, favorite, is higher +$EV (against certain, but not few, opponents) than was suggested by AM.

Some of the replies here (from Pitcher, and also AM), are in the line of what I'm thinking.

I think this is a very important discussion (and not because I started, or reopened it). It's possible we're talking here about a small but meaningful increase in ROI, although it's difficult to say exactly how much.

[BrettK]

[ QUOTE ]
I reread recenly this interesting thread by Aleo ( A bad way to play on the bubble (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=711461&page=&view=&sb =5&o=&vc=1) ), and had some new thoughts.

I want to specifically adress this paragraph (and calculation):

[ QUOTE ]
If I take a coinflip, I have a 50% chance of busting and a 50% chance of being the big stack with three left.

So I have 50% chance of $0
and a 50% chance getting into the final 3 with about 4000 to 2000 to 2000

this should mean 1st 50% of the time I survive- $25 equity (10+1)
2nd 25% of the time - $7.5 equity (10+1)
3rd 25% of the time - $5 equity (10+1)

so all together this means .5(0)+.25(50)+.125(30)+.125(20)
or, $18.75 equity

BUT...

if I avoid confrontation when I know it's gonna mean a showdown I have the same equity (slightly less if I'm in the blind) as before. This is

1st 25% of the time - $12.5 equity
2nd 25% of the time - $7.5 equity
3rd 25% of the time - $5 equity
4th 25% of the time - $0

so all together this means .25(0)+.25(50)+.25(30)+.25(20)
or, $25 equity


[/ QUOTE ]

The point of Aleo here is, that getting into coin-flip situations on the bubble, with equal stacks and equal ability, is -$EV, since by folding you remain in a +$25 EV position, and taking the coin-flip reduces your EV to +$18.75.

However, according to this reasoning and evaluation, taking a 7:3 showdown, is only marginally +$EV:

Taking it:

0.7*37.5 (your overall portion of the prize pool, according to the same calculation, when stacks are 2x,x,x) = $26.25

Avoiding it: $25.

And of course, any situation where it's 66:33, is neutral in terms of $EV (about 0 $EV), for instance: AQ vs. KJ.

I believe that part of the problem is in the assumption of having "only" $37.5 EV, once in the money, with stacks at 2x,x,x.

I would suggest it's in the vicinity of $40, for a strong player (I'd hope someone who's very familiar with these calculations, like Bozeman, will help here), and on the other hand - a player that is constantly avoinding confrontation once it's 4 handed with equal stacks (I assume pretty massive blinds, of course), as suggested in the original post, has probably less than 25% of the prize pool as an approximate EV, especially if he's dealing with loose-aggressive players.

Any thoughts?

Edit: all the $EV numbers are calculated for a $10 SNG, but that's only for the sake of convinience, of course.

[/ QUOTE ]

In TPFAP (Second Edition; P109) Sklansky discusses determining your chances of finishing in each place as part of the 'Making Deals' chapter. He explains that while, with equal skill levels, determining your chances of finishing in first place is easy, determining your chances of finishing in any other position is more difficult. However, he employs a method that he says gives you a reasonably good idea of the correct answer. With three people remaining, Sklansky suggests starting from the point of view of the last place player and working your way up. Using this method, here's the proof that AM's percentage calculations are correct:
After the hypothetical coin flip, Hero has 50% of the total chips, and Soandso and Whatshisface have 25% each. Since there isn't a last place player (Soandso and Whatshisface are tied for second), we'll compare them to one another. Each has a 25% chance of finishing in first, since that's their portion of the total chips. The ratio of last place player's chips to second place player's chips is 1:1, so they each have a 50% chance of finishing in second *if* they don't finish in first. Using this information, we know that Soandso and Whatshisface each have a 25% chance of finishing in first and a 37.5% chance of finishing in second, and therefore a 37.5% chance of finishing in third.
Combined, they have a 50% chance of finishing in first (which gives Hero a 50% chance), a 75% chance of finishing in second (which gives Hero a 25% chance), and a 75% chance of finishing in third (which gives Hero a 25% chance).

Using that information, AM's percentages and EV numbers are correct. (One must logically assume that with equal skill levels and equal stacks, there can be no difference between chances of finishing in different positions, so his percentages and EV numbers for the situation in which the coin flip was Not taken must also be obviously correct.) You mentioned in your post that you believe there are situations in which better players should take the odds (coin flip in the first example) because the difference in skill makes the chance at having many more chips a much better prospect. AM was assuming equal skill level, but let's look at examples with a major difference in skill between Hero and the other players. The most logical way to show this seems to be with a certain percentage boost for Hero, so that the more of the total chips he has, the greater his advantage.

Let's say that compared to his opponents, Hero is actually 10% better than his portion of the chips, and that the other players are equal to one another. After our coin flip, hero has 50% of the chips, but according to us has a 55% chance to win, which means that each of the other two players has a 22.5% chance to win, and an equal chance to come in second or third. This gives us 22.5%, 38.75% and 38.75% for first, second, and third respectively with regard to Soandso and Whatshisface, and 55%, 22.5% and 22.5% for Hero. Our equity is $27.50 + $6.75 + $4.50 = $38.75 after the coin flip, and $19.38(rounded) before.

If we can prove that there's a bigger increase in this number than in the number we get when not taking the coin flip, we'll know that there's a point at which skill outweighs the other factors. The hard part is figuring out Hero's percentages when he *doesn't* take the coin flip. There are still four people remaining, and I don't know that Sklansky meant to imply that his method will work with any number other than three. I'll give it a try, though.

When Hero doesn't take the coin flip, he's still 10% better than his stack would indicate, which means that he has a 27.5% chance for first. Soandso, Whatshisface, and Whatshisname (the player that wasn't in our calculations before) are still of equal skill level, so they each have a 24.17% (rounded) chance for first.

Here's where I hit a wall, and begin to think that I can't use the same method. I know that each of the three worse players has the same chances of finishing in each position, but how do I figure out what the chances are for second, third, and fourth? I would be willing to bet that because Hero is a certain *percentage* better than his stack, he can play hands closer to a coin flip in our hypothetical situation than one of the worse players. Does this make sense, or did I complicate something that should be simple? As always, take what I post with a grain of salt.

Brett

[Phil Van Sexton]

I just can't see how you can have an equal chance of finishing 2nd or 3rd. You would have to be more likely to finish 2nd.

Let's assume the one of the shortstacks is going to win. What are the chances that you finished 2nd? Well, you have 4000 and the other shortstack has 2000....so I'd say it's 67% (4000/6000) that you "win" 2nd place.

therefore...
33.33% * $30 = $10
16.67% * 20 = $3.33

So it's $38.33, not $37.50.

Did I just go through all that for 83 cents?

[BrettK]

[ QUOTE ]
I just can't see how you can have an equal chance of finishing 2nd or 3rd. You would have to be more likely to finish 2nd.

Let's assume the one of the shortstacks is going to win. What are the chances that you finished 2nd? Well, you have 4000 and the other shortstack has 2000....so I'd say it's 67% (4000/6000) that you "win" 2nd place.

[/ QUOTE ]

I'm not sure what you mean when you say that you're assuming that one of the short stacks is 'going to win'. Would you be more specific? It would help me respond. Using Sklansky's method for three people, the chances of the first player finishing in each position is determined by figuring out the chances of the second and third players finishing in each position and subtracting those from 100%.

Brett

[fnurt]

One thing that's missing here is the impact of the blinds. If you're somehow on the bubble with the blinds at 10/20 maybe it doesn't matter. But in the real world, the blinds are much higher, and you're either in the BB with money already in the pot, or in another position where the blinds provide you with an overlay. A model that basically assumes the blinds are 0/0 and you can keep this up forever doesn't reflect reality.

[Jsb]

in your calculations you came out with that Hero had a 55% chance of getting first, a 22.5% chance of second, and a 22.5% chance of third. i think Phil was talking about those percentages in particular. i don't know how to do most of this statistics stuff yet, but it seems against my intuition for hero to have an equal chance of catching second and third. In this case that one of the lesser players gets first, you say that Hero has an equal chance of getting either second or third, but my instinct is that he has a greater chance of getting second than third. my instinct could very well be wrong, it just strikes me as kind of odd. and i think that was what phil was saying as well.

[Phil Van Sexton]

We have already calculated that 50% of the time, one of the shortstacks will win.

In this case, you will be playing against the other shortstack for 2nd. Think of this as a 2 player tournament where the winner gets $30 and the loser gets $20. We know that your chance of winning a tournament is equal to your chip count, so the calculation is simple....4000/6000=66.67%.

Since we are only talking about the 50% of the time that you don't get first, you're chance of getting 2nd is 66.67% * 50% = 33.33%

The calculation is easy because the shortstacks both have the same amount. If they didn't, you'd have to do this calculation for each player and do a weighted average. This will get much messier for more than 3 players, but likely doable with a computer.

[PrayingMantis]

I completely understand the model AM has used in his calculation, and I'm familiar with Sklansky's statements in TPFAP. However, as other posters have stated here, and combined with other reasons, it seems to me as it's lacking in some respects. I don't have a better model (I know Bozeman has worked on simulating similar problems), and AM also admitted that his calculation is not perfect, but I can suggest a few different variables that can be added here:

1. (as was already said), It doesn't look reasonable that big-stack has the same probability for finishing 2nd as 3rd (with stacks at 2x,x,x). This has to do with the $EV of getting into the money as the big-stack.

2. In the title here I wrote "coin-flip", but I'm actually more interested in situation where hero is, say, 2:1, against someone who pushes against him (this has implications for coin-flips too, of course). According to the original model here, calling is only marginally +$EV. However, it seems that if hero is consistently avoiding 2:1 confrontations (over whatever long-run), he's consistently making -CEV moves. This is clear, especially if the blinds are significanly high, which means he's getting great pot-odds. 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.

3. That leads to another, similar, complication (or a "paradox"): 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. With high blinds, these spots are very common.

There are some other points to consider. For instance: how high and what is your position in relation to the blinds, when is the next level coming, etc.

Anyway, the main question remains: what are the criteria for judging whether a certain all-in call (equal stacks, on the bubble), is +$EV.

[fnurt]

What you didn't mention is that when two players go all-in, everyone who is not in the hand gains EV, because someone is going to get busted out.

So when you fold in a favorable situation, your opponent gains EV, but you don't take the corresponding negative EV hit all by yourself. The other players also lose significant EV that they would have realized if you had called.

So you lose EV by making these repeated decisions, but everyone else is in the same boat; either they lose the same EV when they're on the hot seat, in which case you're back to even, or they call and someone gets eliminated. You rate to gain EV when you force someone other than yourself to make the decision.

[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 (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=tourn&Number=761690&Forum= ,All_Forums,&Words=&Searchpage=0&Limit=25&Main=761 690&Search=true&where=&Name=134&daterange=&newerva l=&newertype=&olderval=&oldertype=&bodyprev=#Post7 61690) ), since the more accurate method I used above is very intensive for more than 4 places ( 4 way and independent chip source code (http://home.earthlink.net/~craighowald/FourWay/Source/) ). A review of my research on this subject is at ( Tourney finish place probability (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=369811& Forum=,All_Forums,&Words=tournament%20finish&Searc hpage=1&Limit=25&Main=369811&Search=true&where=bod ysub&Name=134&daterange=1&newerval=1&newertype=y&o lderval=&oldertype=&bodyprev=#Post369811) ).

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.