Interesting little trivia

[A_PLUS]

MTT, assume far enough away from the bubble that CEV=$EV. Also assume that opponents will call any push from you with a reasonable calling range of 77+, AJ+. You are at a full 10 person table.

Two players fold, you are next to act with ATs. How short would you be to make a push profitable here?

The answer suprised me a little bit.

[DonT77]

If we are playing 3-handed I should never have to push and I'll still be +EV when the first two players fold /images/graemlins/tongue.gif

[durron597]

This is why AT sucks in EP.

[SossMan]

I'll throw an intuitive guess out of 7xBB. No math attempted.

I assume that we are saying +EV in abolute terms, not in the tournament sense that we are "taking a less -EV bet now since we will soon be forced into a very -EV spot later".

[CardSharpCook]

intuitively, 12BBs. You're winning pots a lot of the time that you are called.

CSC

[stone_7]

5 Foot 3 is my guess. If I am right do I win a prize?

[A_PLUS]

Yes, no opportunity cost EV invloved. Just a pure CEV calculation.

But in your little thoughtless blurb (thoughtless, meaning you didnt even think about it), you just brought the single arguement that turned me onto the dark side of LAG poker. NH!

[ilya]

Intuitively, 8-9xBB

[A_PLUS]

[ QUOTE ]
intuitively, 12BBs. You're winning pots a lot of the time that you are called.

CSC

[/ QUOTE ]

Sorry, bro. Soss has better instincts than you....uhhh and just about everyone else here.

[CardSharpCook]

[ QUOTE ]
[ QUOTE ]
intuitively, 12BBs. You're winning pots a lot of the time that you are called.

CSC

[/ QUOTE ]

Sorry, bro. Soss has better instincts than you....uhhh and just about everyone else here.

[/ QUOTE ]

Aw, geez, that's a cheap shot. /images/graemlins/frown.gif

[A_PLUS]

My calculations were just under 8BB (and lower) to make this a +CEV move. I will post the details tomorrow if anyone is interested.

Put damn, if you have seen nothing but rage for 4-5 orbits, AT can look REALLY good.

[schwza]

very rough math: win 35% you get called, get called ~ 1/2.5, so you lose in EV ~1/3 of your stack when called, so 1/2.5*1/3 of your stack = 1.5 bb's, so ~12 bb's.

[schwza]

[ QUOTE ]
[ QUOTE ]
intuitively, 12BBs. You're winning pots a lot of the time that you are called.

CSC

[/ QUOTE ]

Sorry, bro. Soss has better instincts than you....uhhh and just about everyone else here.

[/ QUOTE ]

damn, really? you got actual numbers for us?

[A_PLUS]

I stand corrected, I caught an error in my program. The actual value is closer to 9.5xBB. My apologies for believing Sossman had better instincts than the rest of us.


Ok, here it goes

There are 78 hand combinations that will call you
AA-3, (KK-JJ)-18, TT-3, (99-77)-18, (AK-AJ)-36.

Then are 1225 or C(50,2) possible hand combos.

**in the next step I ignore the probability of having two players call, so EV will actuall be overestimated.

7 players left to act, 1225 possible hands. The number of ways those can be dealt is C(1225,7). The number that contain no hands that are in the calling range C(1147,7).

So C(1147,7) / C(1225,7) = .63 Which is the % of time you will steal the blinds.

Pot won with steal: 1.5
% success: .63
-----------------------
subtotal: .945

Pot at showdown: 20.285
Equity Range: .3434
EV of showdown: -2.5325
% of time: .37
-----------------------
subtotal: -.9365
TOTAL: .008

[A_PLUS]

[ QUOTE ]
very rough math: win 35% you get called, get called ~ 1/2.5, so you lose in EV ~1/3 of your stack when called, so 1/2.5*1/3 of your stack = 1.5 bb's, so ~12 bb's.

[/ QUOTE ]

Doesn't .35% equity mean that you will have 35% of your stack remaining when you get called, not that you will lose 35% of it?

[schwza]

[ QUOTE ]
[ QUOTE ]
very rough math: win 35% you get called, get called ~ 1/2.5, so you lose in EV ~1/3 of your stack when called, so 1/2.5*1/3 of your stack = 1.5 bb's, so ~12 bb's.

[/ QUOTE ]

Doesn't .35% equity mean that you will have 35% of your stack remaining when you get called, not that you will lose 35% of it?

[/ QUOTE ]

if i have 100 chips, push and get called, there's a 200 chip pot. if you are 33% to win, your EV of the 200 is 66, so it costs you 34 chips. it only works out that way for 33%. obviously 50% equity leads to a loss of 0.

[schwza]

[ QUOTE ]
very rough math: win 35% you get called, get called ~ 1/2.5, so you lose in EV ~1/3 of your stack when called, so 1/2.5*1/3 of your stack = 1.5 bb's, so ~12 bb's.

[/ QUOTE ]

i forgot to multiply the 1.5 bb's on the right side by chance of stealing (~60%). oops.

[durron597]

So I guess this is where the pros get the 10 BB allin/fold rule.

[A_PLUS]

[ QUOTE ]
i forgot to multiply the 1.5 bb's on the right side by chance of stealing (~60%). oops.

[/ QUOTE ]

How did you get an estimate for % of times you will be called? The ability to ballpark this number quickly would be great.

[A_PLUS]

If my math is right, it really drives home the importance of position. Check out the swings in stack sizes (in BB) as you move closer to the button.

Players left/ Max BB
9/ 7.4
8/ 8.3
7/ 9.6
6/ 11.2
5/ 13.6
4/ 17.1
3/ 23.0
2/ 34.9

[durron597]

[ QUOTE ]

4/ 17.1
3/ 23.0
2/ 34.9

[/ QUOTE ]

In later position there are higher +EV moves than pushing.

[A_PLUS]

Obviously, I am not advocating pushing with 35xBB from the button. Once you get over 15xBB this analysis is pretty useless anyway. I just thought it was cool to quantify the large jumps as you move around the table.

[PrayingMantis]

[ QUOTE ]
MTT, assume far enough away from the bubble that CEV=$EV. Also assume that opponents will call any push from you with a reasonable calling range of 77+, AJ+. You are at a full 10 person table.

Two players fold, you are next to act with ATs. How short would you be to make a push profitable here?

The answer suprised me a little bit.

[/ QUOTE ]

One problem with this question, is that you keep the calling range fixed, while your stack in term of BBs isn't. It's very reasonable to believe that the bigger your stack is, the narrower the calling range will be. And so it might be profitable to push ATs with bigger or even much bigger stacks than what your calculation shows. Not necessarily optimal, but still profitable, and your question is about profitability.

[A_PLUS]

Very good point. But I think in situations when this analysis would be useful (i.e. you are in the 13-8xBB range), that assuming a static calling range doesnt really hurt you. Sure, someone with 18xBB may call or fold 88 based on the difference, but I think overall the results will be close.

[schwza]

[ QUOTE ]
[ QUOTE ]
i forgot to multiply the 1.5 bb's on the right side by chance of stealing (~60%). oops.

[/ QUOTE ]

How did you get an estimate for % of times you will be called? The ability to ballpark this number quickly would be great.

[/ QUOTE ]

well, it wasn't that quick, here's what it was...

3 low pairs, 3 high pairs, count AA/TT as 1 pair b/c you have an A and a T. 7 pairs = 42 hands.

12 ways to have AK-AJ, so that 12x3 = 36 hands. that's about 80.

80 / 1250 (approx number of hands) = ~1/15. 7 left to act, so on average, there will be 1/2 of a calling hand. that overestimates the odds that at least one has a calling hand (because it overcounts when there are many), so reduce it to 1/2.5. it's pretty ballpark and i couldn't do it fast enough to actually do in a hand, but it came out reasonably close.

[SoBeDude]

[ QUOTE ]
If my math is right, it really drives home the importance of position. Check out the swings in stack sizes (in BB) as you move closer to the button.

Players left/ Max BB
9/ 7.4
8/ 8.3
7/ 9.6
6/ 11.2
5/ 13.6
4/ 17.1
3/ 23.0
2/ 34.9

[/ QUOTE ]

I'm having a dense moment so I'm not sure I'm following what this chart is actually saying. can u spell it out for me?

Thanks

-Scott

[schwza]

[ QUOTE ]
[ QUOTE ]
If my math is right, it really drives home the importance of position. Check out the swings in stack sizes (in BB) as you move closer to the button.

Players left/ Max BB
9/ 7.4
8/ 8.3
7/ 9.6
6/ 11.2
5/ 13.6
4/ 17.1
3/ 23.0
2/ 34.9

[/ QUOTE ]

I'm having a dense moment so I'm not sure I'm following what this chart is actually saying. can u spell it out for me?

Thanks

-Scott

[/ QUOTE ]

with 9 players left to act (i.e., utg), pushing ATs is +EV if you have < 7.4 bb's. with 4, it's +EV with <17.1 bb's. (limping/raising small are not allowed, and it assumes that no one ever overcalls).

[PrayingMantis]

I agree that this kind of theoretic "fixed" range calculation could be helpful in order to get some sort of feel for things, but in reality the non-static range is not the only problem you'll be facing: not only that for different table conditions (due to level of tightness, your image, etc) a certain push could be pretty significantly more or less profitable (this is obvious, of course), the somewhat less obvious thing is that calling ranges will always be tighter the closer the position is to yours (as the raiser).

So again, even if you're talking about a theoretical static range, it can't be the same range for all players who act behind you, and you can actually assume it is much tigter for the player who acts right behind you than for BB (if it's folded to him). So again, if your fixed range, as it is, is relevant for BB, pushing (in reality) becmoes profitable for bigger stacks than what the fixed-range-for-all-players calculation shows.

I'm not trying just to make things complicated, this is an interesting discussion regardless of how realistic it is.

[SoBeDude]

thank you!

[SoBeDude]

[ QUOTE ]
I stand corrected, I caught an error in my program. The actual value is closer to 9.5xBB. My apologies for believing Sossman had better instincts than the rest of us.


Ok, here it goes

There are 78 hand combinations that will call you
AA-3, (KK-JJ)-18, TT-3, (99-77)-18, (AK-AJ)-36.

Then are 1225 or C(50,2) possible hand combos.

**in the next step I ignore the probability of having two players call, so EV will actuall be overestimated.

7 players left to act, 1225 possible hands. The number of ways those can be dealt is C(1225,7). The number that contain no hands that are in the calling range C(1147,7).

So C(1147,7) / C(1225,7) = .63 Which is the % of time you will steal the blinds.

Pot won with steal: 1.5
% success: .63
-----------------------
subtotal: .945

Pot at showdown: 20.285
Equity Range: .3434
EV of showdown: -2.5325
% of time: .37
-----------------------
subtotal: -.9365
TOTAL: .008

[/ QUOTE ]

Could you do a chart that shows the reasonable probability that you'll get called (in %s) if you push first in from each position?

Of course I know that some of this is stack and read dependent, but just on hand value, a chart like this would be really useful.

Thanks in advance.

-Scott

[SoBeDude]

with 9 players left to act (i.e., utg), pushing ATs is +EV if you have < 7.4 bb's. with 4, it's +EV with <17.1 bb's. (limping/raising small are not allowed, and it assumes that no one ever overcalls).

Does the calculation include the times that you'll be called by a better hand, but still win the pot?

-Scott

[schwza]

yes.

[Luke]

Could you do a chart that shows the reasonable probability that you'll get called (in %s) if you push first in from each position?

Of course I know that some of this is stack and read dependent, but just on hand value, a chart like this would be really useful.

Given ATs vs { AA-77, AKs-AJs, AKo-AJo }, and the number players left to act behind you listed on the lefthand side, you'll get called in at least one spot:

9 44.68%
8 40.92%
7 36.91%
6 32.61%
5 28.03%
4 23.14%
3 17.91%
2 12.33%
1 6.37%

Luke

[A_PLUS]

something similar that I will be working on soon, is a baseline push analysis. Basically, if you are first to act, and opponents behind you called EVERY TIME that your expected value at showdown was negative, would a push be profitable, and what % of the these 'dominant hands' would you need them to fold to make a push profitable.

This way, you avoid the problems of estimating ranges, etc. and see your cards, and position for exactly what they are worth. Again, not something to base a game on. It will be something that will provoke thought / discussion, and hopefully improve intuition.

[PrayingMantis]

[ QUOTE ]
Basically, if you are first to act, and opponents behind you called EVERY TIME that your expected value at showdown was negative

[/ QUOTE ]

What exactly do you mean by that? It is not clear to me.

BTW, some very interesting work regarding ranges of all-in's pushes and calls was done by several posters in the STT forum, specifically by eastbay. Some of it is relevant only to SNG enviroment, but I assume that at least part of it can be adapted into CEV=$EV spots. I'm also certain you are aware of what is known as the "Sklansky-Karlson chart" and it's variations. I believe that curtains dealt with multiple players adaptations of the SK chart, which are very relevant for what you are doing here.

[SoBeDude]

I'm also certain you are aware of what is known as the "Sklansky-Karlson chart" and it's variations.

Not sure I am. where is it printed? any chance u have a link?

-Scott

[PrayingMantis]

Here's the chart:

SK chart (http://www.decf.berkeley.edu/~chubukov/rankings.html)

There were many discussions about this, you can search the theory forum, STT forum and here too, and also look through the archives because there is some good older stuff too.

[SoBeDude]

[ QUOTE ]
If my math is right, it really drives home the importance of position. Check out the swings in stack sizes (in BB) as you move closer to the button.

Players left/ Max BB
9/ 7.4
8/ 8.3
7/ 9.6
6/ 11.2
5/ 13.6
4/ 17.1
3/ 23.0
2/ 34.9

[/ QUOTE ]

This thread has really got my mind going. for that I thank you.

if I read all this correctly, this chart is specifically for the hand AT right?

If so, couldn't we then calculate a matrix to determine a minimum hand per position (based on chip stack) to push that is +EV?

now THAT would be useful!

-Scott

[SoBeDude]

can u give me the quick rundown on how u use it?

[PrayingMantis]

Birth of SK chart and background (http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&Number=382772&page=&view=&sb =5&o=&vc=1)

Basically it's what A PLUS has done here with ATs, only much more fundamental: it's HU, and your cards are face-up. For each hand, how many SBs should your stack be in order for a push to be +EV.

[Alex/Mugaaz]

What blind sizes is this chart based on, and what position are you supposed to be in?

[PrayingMantis]

[ QUOTE ]
What blind sizes is this chart based on, and what position are you supposed to be in?

[/ QUOTE ]

I really suggest you'll do a search on "karlson" or some variations here, because there were many discussions about this and it doesn't make much sense to start an explanatory thread here. To your questions, as I said it's HU, and the blind sizes don't matter obviously, only the ratio stack (your stack, of course) to blind (SB as presented).

[A_PLUS]

First, thank you Mantis. I respect your game, and appreciate your advice. I am aware of the HU work that sklansky has done, as well as some of the work of the STT forum. That forum is amazing with regards to mathematical poker.

I have really been trying to stay away from other work on this stuff. FOr myself working through the logic of these problems, crunching the numbers, and discussing it is a lot more useful. I realy needed to get my hands dirty with the numbers for it to add anything to my live game, when I have a few seconds to act.

OK, let me try to explain what I am trying to do next. I will continue with the ATs example, but want to do it for many hands.

I assume a 'worst case scenario'. That my opponent, would call with any hand that I would have < 50% chance of winning the hand. So hands like AK-AJ, 66+ (I dont know which exact PP I would use). So knowing this I would have an idea of wether this play is definitely +EV. Any hand that my opponent could call with (not in the above mentioned range) would be +EV (for me), so they can be disregarded.

The purpose of this is to recognize plays when I am getting short stacked where I must push at a certain point. You can also get an idea of how often you will need your opponents to fold a hand that you are behind, for a particular play to be +EV.

Now, this isnt to create some sort of mechanical pushing scheme, but doing the work hopefully will make my short stack play closer to optimal.

I'd really appreciate any comments you have on the strengths and weaknesses of this plan.

[PrayingMantis]

OK, I think I see what you're trying to do. I have 2 things to say. First, giving your opponents a "worst case scenarion" range, which will obviously included many more PPs, BUT without giving them any hands like at least a few dominated aces (maybe A9) and surely some kings, is not being very consistent with the range, IMO. Particularly when you're talking about a short-stack push. The beauty about calling ranges of hands, when your hand is not face up, is that in most normal circumstances people will tend to fold some hands that are ahead and call with some that are behind, because they put *you* on a range. This is rather simple. By that I'm saying that making a calculation for an artificial "worst case scenario" might be a bit unrealistic, although interesting.

An interesting thing you might want to check, that I haven't seen anybody really doing consistently, is seeing (for fixed or non fixed stack sizes) how much all kinds of pushing hands are doing against different kinds of fields, from very loose to very tight, in terms of calling standards. Obviously there are hands that need a very tight field to be +EV for certain stack sizes to push with, and OTOH, hands that really want loose fields (very strong hands). For all the hands in the middle, you'll get the most EV out of specific levels of tightness along the range. The results might be interesting, I think.