SnG Bubble Quiz

[eastbay]

You're on the button holding 66 with stacks, after posting 150/300 blinds, from BB moving left:

BB SB YOU CO
2500 2500 2500 2500

Let's considering options of push/fold here. It's possible there are other options, but assuming you're going to push/fold, what do you choose here?

What if BB is a shorter stack, with bigger stack behind?

1500 2500 2500 3500

Then let's say BB and SB are shorter stacked, with bigger stack behind?

1500 1500 2500 4500

are you more or less inclined to move in now?

What if there's two shorter stacks but big stack is in your way?

1500 4500 2500 1500

Does it matter if big stack is the BB?

4500 1500 2500 1500

Discuss.

eastbay

[chill888]

This is a complex and great topic. BUT /images/graemlins/smile.gif

If my choices are only push or fold, I would fold absolutely every time, regardless of players.

The only way I would push would be if my wife was in labor and her water broke and she was bitching cause my game was still going on.

You are covered in all situations. What are the odds that at least one of the 3 has a PP above 66? I don't know, but off top of my head it is in the area of 10%.

We haven't even started talking about other hands.
If I'm called I can only pray for a coin toss and must fear facing a 4-1 shot. Patience grasshopper.

One of the main ways to cash is to go make a sandwich and let two guys from this forum bet their 66 and 77. Every extra hand i play is another chance someone else busts or I get dealt AA.

Now, if smaller bets were allowed - depends on my opponents. But you wouldn't let me. /images/graemlins/wink.gif

[Daliman]

I'm not sure if you realize this, but the way you have structured the hand, you are removing the CO from play. Also, not to mince, but your scenario has 10450 chips in play...

Given those parameters, my decisions are..
1. Fold. There are better spots for your money.
2. Push. SB isn't calling with many hands, BB still has a foldable stack, and likely is behind if he calls.
3. Fold. You are more likely to be called here by either of the blinds, and folding will often spur a blind battle, where the SB will often push allin with a VERY wide range of hands, and the BB will call with a wider range of hands than usual, given that this is often a steal move by the SB and he will now be the only SS left at the table.
4. Fold. Let the big stack do his job. THe CO is about to pay 30% of his stack in blinds the next 2 hands, so opportunities abound.
5. Fold. The SB will push into the BB here with any ace, any 20, any pair, and many other hands on a steal attempt, and BB will call most of the time with same.

[chill888]

I must say i looked at the order and assumed Hero was CO and that CO was Button

[stupidsucker]

You're on the button holding 66 with stacks, after posting 150/300 blinds, from BB moving left:

BB SB YOU CO
2500 2500 2500 2500
---Here with complete even stacks(assuming its folded around to me)
I am going with Push. There is only about a 7% chance that one of the 2 players left has an over pair. This is my only main concern. I think everyone will be less inclined to call with crap with the stacks this even and I have great FE.


Let's considering options of push/fold here. It's possible there are other options, but assuming you're going to push/fold, what do you choose here?

What if BB is a shorter stack, with bigger stack behind?

1500 2500 2500 3500
---Push

Then let's say BB and SB are shorter stacked, with bigger stack behind?

1500 1500 2500 4500
--Push

are you more or less inclined to move in now?

What if there's two shorter stacks but big stack is in your way?

1500 4500 2500 1500
--Im still pushing here
Does it matter if big stack is the BB?

4500 1500 2500 1500
--I am still going to push my 2500 can take out a good chunk and the short stacks arent in dure trouble yet.


Discuss.

I push every time because I am out to win not get ITM. I cant see one time where the short stacks were too small to not push or the big stack was too big compared to my stack not to push. With two people left to act the chances of someone having an over pair is less then 8%. All other hands I am ahead slightly in a coinflip, but I have good FE. ALso I think there is a decent chance that 22-55 might call me. I am curious to see what others wrote.

Edit: Looks like I am too aggressive... good to know.
I will break down the odds and post my thoughts soon.

[Daliman]

I'd like to add that, even though myself use a much more reseved strategy, pushing in ANY of these situations is not a BAD play. I play them differently than most because I am trying to find a better way than ABC-aggressiveness.

[stupidsucker]

Ok..
What hands can call you?
what hands will call you?

77-AA 8%
A7-AK, KT-KQ,QT-QJ,JT 12%

These are the only hands I think you MIGHT get a call from.

To pose another question Lets say you are the BB or SB.. what hands do you make a call with if the Button pushes with those respective stacks?


Ok so 20% of the time we get a call and 12% of the time we are ahead. Lets also assume we never suck out when we face an overpair, and that we only win exactly 50% of the time when we face overcards.

80% of the time we suck up the blinds CHip EV is 450+
8% of the time we lose
12% of the time we coinflip so 6% of the time we lose 6% we win

that means we lose pushing here only 14% of the time(only when we are covered)

This doesnt even take into account the amount of times someone calls with 22-55 (You cant say no one will if they will call with hands like TJ or QT) Also the times they might call with A6-A2.

I am out to win, and with all stacks equal you only have a 75% chance to move on.

[RobGW]

I would push everytime as I want to win. The blinds are too high and are coming around too fast to wait for something better. The times I bust out in 4th will be made up for by the times I win. I think I see what you are trying to get at but imo it just makes more sense to be ultra aggressive and either take the blinds down or take someone out or be taken out.

[chill888]

[ QUOTE ]
Ok..



that means we lose pushing here only 14% of the time(only when we are covered)



[/ QUOTE ]


1. I agree that pushing is not a horrible play in any of these these positions.

2. Wow only a 14% chance of going broke on this one hand? I hate it. And use Bayes - you win the blinds when you are ahead and go broke (get called) when you are losing.


The greatest thing that ever helped good players was when bad players learned that 22 beats Ako heads up. All of a sudden a bunch of fools think that means that 22 is a good hand and better hand than Ak. LOL

Now I may be wrong on the analysis of this hand BUT let me give you a fallacy similar to 22 being a good hand.
People keep posting:

"I play to win, dude" thus I will be recklessly
aggressive.

"You are a rock dude" and don't play to win.

A very profitable fallacy.

[stupidsucker]

Why are we talking about 22?

Also pushing is a far cry from calling.

What hands are YOU as the BB going to call with if the button pushes?

Let me answer for you.

You arent going to call with most of the crap I figured in, thus making the FE even higher. I also didnt figure in the times 66 will suck out on an overpair either.

Also just exactly what hands are you pushing with. 66 has over a 90% chance of being the best hand and you throw it away.

Lets take it by each situation.

1)2500 2500 2500 2500
14% of the time we go broke
6% of the time we are ITM with a great chip lead
80% of the time we take the blinds

2)1500 2500 2500 3500
80% we take the blinds
3% we double up and are ITM
3% we gain 1650 and are ITM
7% we go broke
7% we lose 1500 chips and still have 1k left
(Only a 7% chance of going broke here)

3)1500 1500 2500 4500
80% to get the blinds
0% going broke
14% losing 1500 in chips
6% ITM now with a decent chip lead

4)1500 4500 2500 1500
80% we take the blinds
3% we double up but not ITM
3% we gain 1650 and are ITM
7% we go broke
7% we lose 1500 chips and still have 1k left
(Only a 7% chance of going broke here)

5)4500 1500 2500 1500
80% we take the blinds
3% we double up but not ITM
3% we gain 1650 and are ITM
7% we go broke
7% we lose 1500 chips and still have 1k left
(Only a 7% chance of going broke here)


In only 1 outa 5 of these situations do we have a 14% chance of going broke, and this is assuming that they would actualy call with hands as weak as TJ or even KJ with 4 EVEN stacks... they would have to be morons to do that.

in 3 outa 5 the chance is only 7% of oing broke.
in 1 outa 5 its 0%

I know these numbers are not perfect, but I skewed them not in favor of my argument.



Thanks Eastbay great topic. I am arguing ferociously because I truely want the answers. As of now my position is push, and I challenge anyone to show me mathmatically why its bad.

[chill888]

Sucker Good post I will give it some thought BUT...

I hate having any chance of going broke when I am in healthy position. It is tough to model but i play so many S&Gs where I never or rarely put my chips at risk. And in this situation, by folding I am giving myself the future to win and avoid this "opportunity" to put my chips at risk. How do you model that?

How do you model the fact that I have almost a 1% chance of getting AA or KK in the next single hand?

But I will reread your post a few times to digest the math.,

Stuff like this is important to maximizing ROI. So I disagree - but with respect and the knowledge that none of us are yet POSITIVE as to the right answer.

As a separate point, I take a lot of comfort in the extra player info I can gather by notes and tracking at Stars- and belive that watching table dynamics are hugely important to determining optimal bet size. Especially optimal steal size (big enough to work - and small enough to not be painful if they fail).

gl

[stupidsucker]

I would suggest keeping it simple, figure out what hands you would like to push with and your chances of getting that hand.

Sitting back and waiting for someone else to make a move and get called cant be a good strategy because this dooms you to 3rd place more often then not.

Here is another idea. Lets freeze it in time and play it as if it were a BJ hand or something.. Will you go broke before you get all the chips? Not quite sure how to model it or explain exactly what I mean, but its in my head.

I need to quit gabbing and play some poker instead.

[chill888]

Believe me I often get called crazy in the late games and can be super aggresive. I don't only wait for people to go broke - and I do quite well. But I am in no rush to find my hand.

I truly struggle with all the posts that talk about PUSH PUSH easy push etc. What about all the posts that talk about how they came back from no chips and won?

I think a super valuable skill in poker is estimating the maximum bet for a steal to be often profitable and avoiding any bets bigger than that. This is a skill that is hard to use when playing 8 table or playing at Party where you often don't know your opponents.

The extreme (and simple) example is when an opponent uses autofold when he has nothing. WOOHOOO I make a note of this instantly. If you are bluffing him how much should you bet? The minimum amount!! And if you are reraised by a supertight autofolder? FOLD!! Knowing your opponents is critical. I think a big part of my winninigs are from this knowledge of opponents. (thx Pokertracker and Stars for easy notes)

Another huge part of my winnings are from guys that keep pushing mid pairs mid game - or AQ or even AK when a smaller raise (or a fold) would suffice.

I push a lot - there is a time for it - but I am just not at the same place as many of you. Still: there is more than one way to win.

gl

[eastbay]

I said this is a "quiz" like there are cut-and-dried answers. Of course there aren't.

However, here is one line of analysis:

Assume $equity as given by the independent chip model. If you don't know what that is, google it.

The simplest push/fold criterion is to find the $equity of a fold and compare it to the $equity of a push, assuming calling standards for SB and/or BB. If $equity is higher for one or the other, choose that. If SB calls, assume BB folds (no multiway pots - doesn't happen often enough to matter anyway, IMO.)

For 2500 2500 2500 2500:

equity after fold: 0.243096
equity after push and fold: 0.269909
equity after push and win w/ sb: 0.382936
equity after push and win w/ bb: 0.376538
equity after push and lose w/ sb: 0
equity after push and lose w/ bb: 0

Assuming calls only with "premium hands" AA-JJ,AK,AQs:

PUSH ( 0.26) pc1 0.0359|pw1 0.351|pc2 0.0346|pw2 0.351|pnc 0.929

Key: (equity of push)
pc1: prob. of call from SB
pw1: prob. of win, given call from SB
pc2: prob. of call from BB
pw2: prob. of win, given call from BB
pnc: prob. of no call

Equity here is 0.26 which is bigger than the equity of a fold: 0.24.

Now here is, in my mind, the open question for tournament strategy: Does the ~8% increase in $equity justify the risk of the push? I simply don't know the answer to that question. It could be that one should always choose larget possible $equity decision available to them at any one time. Or it might be that they should choose smaller $equity decisions that carry less risk, in hopes of getting to bigger $equity decisions (like calling with AA) with less risk later on.

Anyway, continuing with the $equity line: imagine a crazier table, where you expect a call from any ace or pair, or a big king:

FOLD (0.241) pc1 0.262|pw1 0.541|pc2 0.193|pw2 0.541|pnc 0.545

Here it's a clear fold. Your $equity is lower than a fold, and you're risking everything to lower it. Note that your probability of a win if called is much higher in this case: .541 vs. .351, but it doesn't matter because you're not picking up enough blinds to justify the much higher risk of a call.

Going back to the premium calling hand assumption, which is probably a reasonable one, let's start adjusting the stacks like in the original question, and look at the push equity in each case:

1000 2500 2500 4000
$equity fold: 0.255
PUSH (0.278) pc1 0.0359|pw1 0.351|pc2 0.0346|pw2 0.351|pnc 0.929

~9% better equity by pushing. Worth it? Dunno.

1000 1000 2500 5500
$equity fold: 0.274
PUSH (0.299) pc1 0.0359|pw1 0.351|pc2 0.0346|pw2 0.351|pnc 0.929

Again, ~9% $equity increase, but less risk, since we're still alive in all cases. Worth it? Still dunno, but I'm pretty sure I push here.

Now let's increase the danger by putting big stack in our way:

1000 5500 2500 1000
$equity fold: 0.277
PUSH (0.295) pc1 0.0359|pw1 0.351|pc2 0.0346|pw2 0.351|pnc 0.929

Only 6.5% equity increase with a big risk. What happens if we lower big stack's calling standards? Let's say, any ace or pair?

PUSH (0.281) pc1 0.21|pw1 0.544|pc2 0.0284|pw2 0.351|pnc 0.762

1.4% equity increase. I don't like it, even though my program spits out "PUSH" since .281 > .277.

If the big stack is in the big blind, let's lower his standards to any ace, any pair, king-face:

5500 1000 2500 1000
$equity fold: .280
FOLD (0.276) pc1 0.0359|pw1 0.351|pc2 0.253|pw2 0.541|pnc 0.711

Pushing is a loss of $equity here. Clear fold.

Anywho, there are all kinds of rough edges on this whole line of analysis:

ICM doesn't consider positional advantage (who is about to take blinds, etc.)
ICM is just a model, and is considered by some experts to give too much equity to short stacks
ICM assumes "equal skill"
Nobody knows how to balance $equity gain with risk.
etc.

But it's certainly better than "hey, it's a pair, I'm all-in!"... I think. /images/graemlins/wink.gif

eastbay

[Daliman]

Your grasp of the mathematics amazes me, but yeah, you're going to see a LOT looser calls than you'f think, even at the $200 level. I cannot imagine a situation where 88-TT folds given equal stack sizes, and frequently see KTs and 22 call

[eastbay]

[ QUOTE ]
Your grasp of the mathematics amazes me, but yeah, you're going to see a LOT looser calls than you'f think, even at the $200 level. I cannot imagine a situation where 88-TT folds given equal stack sizes, and frequently see KTs and 22 call

[/ QUOTE ]

I pretty much agree. But you'll notice I showed some results for any ace, any pair, KQ-KT calling standards.

I just got tired of cutting/pasting...

eastbay

[doubleplus]

[ QUOTE ]
Assume $equity as given by the independent chip model. If you don't know what that is, google it.


[/ QUOTE ]

http://www.google.com/search?hl=en&lr=&ie=UTF-8&q="independent+chip+model" (http://www.google.com/search?hl=en&lr=&ie=UTF-8&q=)

[stupidsucker]

I am going to have to read that again.. and maybe again.

I will end up having to thank you later. After I understand what I just learned.

This may take a few days.

[tallstack]

I like this method of analysis. It is obviously quite dependant on the estimation of being called, but it appears to give pretty realistic answers.

I do have a question on how you arrived at the probability of a call from the sb and bb. In most cases, you have a higher probability of the sb calling than the bb calling. Why? This seems counter-intuitive to me.

I took a look at the chip equity to compare it to your $equity results. I wanted to see whether a chip equity calc and a $equity calc would suggest different actions (as they often should in a bubble situation). I tried your first two examples with equal stacks and used your call and win probabilities. When you calculated a $equity rise to .26 the chip equity rose from t2500 to t2941. When you calculated a $equity drop to .241 the chip equity again rose from t2500 to t2897. Here I think this is a situation where the chip EV is going to be positive with any probability of being called, whereas the increased risk of busting with a rise in the probability of being called is being considered in the $equity calc. I have not tried the other examples yet, but I do think that the $equity calc much more realistically considers the risk of a push situation.

As far as whether a small rise in $equity is worth the risk, well I don’t know either. I do think that here all the cases where you calculated a rise in $equity are realistic push/steal opportunities. However, I am sure that there are cases where knowing a player will be forced all-in soon, or where you think you have an edge to outplay your opponents may make it reasonable to pass on a marginally positive $equity situation.

Dave S

[dethgrind]

[ QUOTE ]
Equity here is 0.26 which is bigger than the equity of a fold: 0.24.

Now here is, in my mind, the open question for tournament strategy: Does the ~8% increase in $equity justify the risk of the push? I simply don't know the answer to that question. It could be that one should always choose larget possible $equity decision available to them at any one time. Or it might be that they should choose smaller $equity decisions that carry less risk, in hopes of getting to bigger $equity decisions (like calling with AA) with less risk later on.


[/ QUOTE ]

Doesn't the .24 equity for folding already take into account the possibility of getting AA later?

What I've been thinking about is how to adjust the ICM to account for skill level. Being a superior player, your actual equity here if you fold is probably more than .24. Then again, your actual equity if you push is probably more than .26. The problem is that the difference between your actual equity and the equity predicted by the model is probably not the same in both cases. I suspect that the difference is greater for folding than it is for pushing.

If there were a reasonable method to take into consideration the skill of the players, one could obtain more accurate $equities. Once you obtain these numbers, I think choosing the action which results in the highest equity would be correct, because they already take into account the risk factor.

Maybe giving your chips a multiplier, like 1.1?

[bones]

Make a small raise, call a re-raise, check dark, hit your set, finish 2nd.

[eastbay]

[ QUOTE ]
I like this method of analysis. It is obviously quite dependant on the estimation of being called, but it appears to give pretty realistic answers.

I do have a question on how you arrived at the probability of a call from the sb and bb. In most cases, you have a higher probability of the sb calling than the bb calling. Why? This seems counter-intuitive to me.


[/ QUOTE ]

The range of hands that SB and BB will call with is a user-input to the calculation. So just for simplicity, I chose the same range of hands in most cases.

The reason the BB has a slightly smaller probability of a call is that I assumed that if the SB called, the BB would fold, i.e., no multi-way pots. It's not perfect, as BB would call with AA, but I think it doesn't happen often enough to justify the extra complexity in the analysis.

So BB simply has fewer opportunities to call than SB, as SB can force him out with a call.

I agree with the rest of what you said.

eastbay