How low would you go...

[Saborion]

... in your calling standards when you are in a situation similiar to this one.

Big live MTT. 3 players left. Blinds at 80k/160k, antes at 15k. Prize structure is like 1M, 500k, 250k.

Button has ~T150k.
SB has ~T5M.
You have about T1M in the BB.

Button folds. SB pushes. He's capable of doing this with any hand that has some value if called, so remove 73o from his range, but include Kx and 78s etc. What's the lowest hand you'd call with, if any?

[ansky451]

Pairs, QJ+ KT+ A2+.


EDIT: Just saw the button. Make that 99+ AJs+

[Bill Smith]

AA. Maybe KK. That's about it.

[KneeCo]

When you say he's capable of doing this with a wide range do you mean under regular circumstances, or even given the current situation with the shorty button?

If it's the former, I think you still have to give him so credit in this particular case.

[ansky451]

Well for what its worth, if im the SB and I know the BB is a thinking player, I'm pretty sure its cEV+ to push any 2 here... and I'd say that equals EV+

When reading this situation I like to remember the post Sirio made on his log some time ago about folding AA preflop.

Button is going to be BB next hand and is auto-allin with any two cards. Given this information I would fold any two cards, even AA. Since a suckout is lurking around every corner.

[Bill Smith]

Hmm... time for a little math.

Against a random hand, or even slightly better than random hand, you're about 85% to double up with AA.

15% of the time, you take 3rd and get $250k.
85% of the time, you lock up 2nd and take 1st ~40% of the time. ($500k * .60 + $1M * .4) = $700k.

EV = $250k * .15 + $700k * .85 = $632.5k

If you fold AA, let's assume SB drops. You take 2nd 85% of the time and 1st about 15% of the time.

EV = $500k * .85 + $1M * .15 = $575k

Call with the AA.

[Exitonly]

no no, this is different han the sirio hand.

he had everything to lose, and nothing to gain, becacuse it was a satelite 12th paid as much as 1st, so theres no reason to go from say 10th chip stack to the leading chip stack when theres 13 left.

In this situation though where 1st is substantially more than 2nd, it helps us a lot to double up here. Still we're not going to want to get knocked out right now a big % of the time. So i'll be conservative still, and say he's only pushing the top 50% of hands. ANd i'll arbitrarily decide that i want to still be around 70% of the time, so that would be JJ+ .. and that's it.

if he's pushing more than 50%, or if you dont need quite 70% equity for it to be good, then add in 99+ AJs+ AQo+

If he has any skill at all to situations like this and knows about the pressure he's gonna move with almost any hand in my opinion since he knows the button will be AI. He is guarenteed 2nd place no matter what happens. I'd make his range really loose and would play it as if I wanted to win the tournament. A8+,88+. I think common hands for him to push are suited connectors, any ace, any pair, and if he knows this kinda situation basically any two. With that calling range my ace will be dominating him over half the time if he has an ace any my pairs will be overpairs to him over half the time or a 55/45 favorite most of the time. Hands like KQ and KJ are probably appropriate against a large range, however, I don't want to get my money in as a dog to any ace.

I like your first range here, probably even better than my own because I still have the fear of busting out. If you want to win the tournament, I like Ansky's original calling range.

[Lloyd]

x=% of time you call and win

Total chips = 6,150,000
Total prize money playing for = $1M ($250k already wrapped up for each)

Fold = 825k
825k/6150k = 13.4% * $1M = $134,146

Call and win = 2,015,000
2015000/6150000 = 32.8% * $1M = $327,642

Call and lose = OUT

Value of calling = x($327,642)

$327,642x = 134,146
x=134,146/327,642
x= 40.9%

So theoretically, if you win 40.9% of the time the value of calling equals the value of folding. We obviously need to win more than that for it to be profitable. 50%? 60%? I'd probably lean toward the 50% number.

Put him on a range of 22+,A2s+,KTs+,QTs+,J9s+,T8s+,98s,87s,76s,A8o+,KTo+ ,QTo+,JTo. That sounds about right based on what you've said. Therefore, you could call with 66+, A9s+, KQs+, ATo+ and have greater than 50% equity. If you wanted to be very (perhaps too) conservative and require 60% equity you would need TT+, AQs+, AK. Obviously there's a middle ground there as well. I do think he could be pushing with a huge range of hands here and doubling up gives you a legitimate shot at 1st.

[Lloyd]

That was referring to a satellite tournament where he could fold into the money. Very different here. And very dangerous to apply the same principles.

[KneeCo]

[ QUOTE ]
Well for what its worth, if im the SB and I know the BB is a thinking player, I'm pretty sure its cEV+ to push any 2 here... and I'd say that equals EV+

[/ QUOTE ]

I don't think that 'thinking player' is right here.
Rather, if he has a read that the 1M stack wats to move up and will accordingly fold anythng but KK+, pushing with any 2 is good.
However, the 5M stack is primed to enter HU with a 5:1 chip lead, why automatically risk making it 2:1 just to pick up the blinds?

[Exitonly]

That equation is flawed, theres no way that if he folds worth he's that substantially less than 3rd place (250k).

[Saborion]

I don't know how to make the math, but the SB is an aggressive player, capable of raising with a lot of hands. The reason I asked this is because when I played some SnGs I remember that when it's 4 people left and you have a big stack, you can bully them quite a lot. This seems to apply here as well since the short stack is likely to bust soon, especially if they gang up on him on the next hand. The difference of $250k prize money between third and second place is quite a lot, but it's all relative and you've got to draw the line somewhere.

I don't know at which level they were thinking and all that, but I'd like to believe that AA and KK may be slightly less likely due to the push, which makes calling with lesser hand a bit more attractive. Can't be certain though, have to have been there I guess. I just think that I would've been quite tight there, but I wonder how tight "correctly" tight is. If he push with A5o and we call we'll still lose 30 % of the time. Very nice sitaution to get all in, being that big of a favorite. Is it good enough given the situation?

I know it isn't the same situation. And normally I wouldn't apply this principle, but the Button is being swallowed by the blinds in the next 2 rounds. If his stack was 2BB then I would definately not fold AA, but now he has to push in the SB otherwise a double up in the BB won't matter that much to his stack.

Ofcourse it's +EV to call with AA, but I rather play HU with a 5-to-1 chipdeficit then finish 3rd and donate an extra 250k to the shortstack. I know Christmas is coming, but this is insane!

Shorty is all-in next hand. Biggy is correct to push any two here, and you are correct to fold any unpaired hand even knowing this information.

As for pairs, if he's indeed pushing any two, I think you'll find TT+ as +EV. If he's pushing only 75%, then call QQ+. If you think his range is less than that, then stick with just Kings and Aces.

My ICM calculations puts the value of your stack at ~550K if you fold and ~650K if you call and win. Obviously you win 250K if you call and lose.

So if we want to find out the chance you need to win (we'll call that P) to break even, we get 0 = P * 100K - (1 - P) * 300K. That translates into P = 75%.

So calling with a dominating hand is wrong, since you're usually only about 70% to win those. You basically need an overpair to his two cards. And without running stuff in Pokerstove, I'd say only AA and KK gives you good enough odds against his range.

[Lloyd]

Not flawed. Third place money is already locked up and not included. That's why there's only $1M of prize money being played for and not $1.75M. Everyone has locked up $250k.

[Dave D]

[ QUOTE ]
no no, this is different han the sirio hand.

he had everything to lose, and nothing to gain, becacuse it was a satelite 12th paid as much as 1st, so theres no reason to go from say 10th chip stack to the leading chip stack when theres 13 left.

In this situation though where 1st is substantially more than 2nd, it helps us a lot to double up here. Still we're not going to want to get knocked out right now a big % of the time. So i'll be conservative still, and say he's only pushing the top 50% of hands. ANd i'll arbitrarily decide that i want to still be around 70% of the time, so that would be JJ+ .. and that's it.

if he's pushing more than 50%, or if you dont need quite 70% equity for it to be good, then add in 99+ AJs+ AQo+

[/ QUOTE ]

I agree with Ansky's range pretty much. Maybe even ATs b/c I'm a sucker for that hand.

This isn't like the sirio situation for the reasons given, but also no one's really explicitly considered the fact that you need a stack to take on the big stack with. Everyone's implying that more chips=good, but what this really means is you have to put yourself in a position to WIN. Namely, imagine if the situation were that you had 500k and the shorty had 150k and the biggie had 10M. You can't pass up a chance to make yourself a stack to take on the big stack, otherwise you're basically conceeding winning an extra $250k for having no chance at first. You might go totally card dead the rest of the tourney. Take your shot now when you get it.

In my opinion, chips have increasing value here, as it gives you more than just a proportionate chance at taking a shot at the leader for every chip you get. You need wiggle room. Shorty could also magically suck out with 72o against Aces when he's forced to go all in, and you get fuzunked.

Always remember you're playing for first.

[Lloyd]

[ QUOTE ]
My ICM calculations puts the value of your stack at ~550K if you fold and ~650K if you call and win. Obviously you win 250K if you call and lose.

[/ QUOTE ]
There's no way your value goes up by only 18% if you double up. That just intuitively doesn't make sense.

[locutus2002]

I got about the same numbers.

Hero risks 250K to win 100K in EV or 2.5:1 and has to be 72% in the hand.

Somewhere around JJ is EV+ considering villain is tossing out the bottom range of his hands.

[ QUOTE ]
What's the lowest hand you'd call with, if any?

[/ QUOTE ]

Haven't read the other posts, so apologies if this is a re-run.

Call me crazy but why would anyone call with anything less than KK or AA? Maybe the player even has to consider folding QQ and JJ here.

The button is going all in on the BB next hand with the average hand being T-8 offsuit, I have to like that chances that he is going down, as it is 2-1 that someone gets dealt a better hand.

If button gets lucky and doubles or triples, then I'll cross that bridge when I come to it. Last thing I want to do is tangle with the chip leader when the only remaining player is on life support, especially for that prize differential.

[adanthar]

Lloyd,

Your equation *is* flawed, because the assumption is that the short stack will bust first. While you can't really count on it, it will happen ~90% of the time (as he'll be forced into at least 3 all ins by pot odds as a random hand) and therefore the hero has 500K locked up, not 250. You can consider it 450K if you'd like, but you still need waaaaay more than 40.9% to call.

BTW, this is from one of the, like, two WPT events I've ever seen on TV and the guy's call was *horrible*.

[Saborion]

[ QUOTE ]
Lloyd,

Your equation *is* flawed, because the assumption is that the short stack will bust first. While you can't really count on it, it will happen ~90% of the time (as he'll be forced into at least 3 all ins by pot odds as a random hand) and therefore the hero has 500K locked up, not 250. You can consider it 450K if you'd like, but you still need waaaaay more than 40.9% to call.

BTW, this is from one of the, like, two WPT events I've ever seen on TV and the guy's call was *horrible*.

[/ QUOTE ]

Yes, this was from a WPT event that I re-watched the other day. Personally I think the guys call was very interesting, not something I would do. Hence this post. The numbers may not be 100 % accurate, but they are close enough. If the BB would've had a little smaller stack I think the call would've been a must, but with 1M I think I'd want a bit better hand than the one he had. With more than 1M I'd want an even better hand since we're so much more likely to survive the short stack. But 1M is starting to get borderline with those blinds, since it's not impossible that the short stack will double/tripple up on the next hand, although unlikely, it will still suck big time.

Anyway, thought it would be interesting to know what the "math" says that we should do. For those interested it was from the Doyle Brunson blah blah, I think it was season 3? The BB called the SB (Carlos Mortensen) A5o push with TT without too much hesitation, if any at all, and doubled up.

[Dan Mezick]

The #3 to #2 diff is 250K.

The Button has 150K left and he's allin on the Big next hand.

If you assign a probability of 90% that the T150 goes away on the next 6 hands, why call with ANY hand here? If SB is that wild right now, he will take care of the T150K Button.

And you'll be 250K richer.

The fact that SB has you outchipped 5:1 has everything to do with this decision to fold just about everything until Button is eliminated.

[Lloyd]

Okay,

So let's say the value of folding equals $250,000 (the difference between the guaranteed 3rd place money and 2nd place). And what we are really playing for is the $500k difference between 1st and 2nd.

If we call and win we'll have 2,015,000 chips out of 6,150,000 total. That's 32.8%, multiplied by 500,000 equals 164,000. That makes sense. Essentially if we call and win we'll have 1/3 of the total chips and use that as an approximation of equity.

If we call and lose, we're LOSING $250,000 (what we have essentially locked up).

So the value of calling where "x" equals the percentage of the time we call and win:

x($164,000)+(1-x)(-$250,000) = 164000x -250000 +250000x
414000x = 250000
x=250000/414000
x=60%.

So we need to win 60% of the time for it to be a neutral decision. Let's say we need to win 70% of the time for it to be profitable enough.

We're then calling (versus my previous range) with AA-QQ. JJ would be slightly +$EV and TT would be neutral (and thus increasing variance with no reward).

I do agree that without taking into consideration the blinds my previous calc was flawed.

Edit: If we change his range of hands to any 2 cards (which I think is certainly reasonable) then a +$EV range would be 99+ so in that sense it could have been correct to call with TT.

[Piers]

Playing with http://sharnett.bol.ucla.edu/ICM/ICM.html assuming the stack sizes are after posting blinds (not clear form post). Prize fund is (.57,.286,.144)

If you fold stack sizes are (524,100,15) giving a EV of 312.5.
If you call and win stack sizes are now (400,224,15) giving an EV of 377.8.

You should call if you chance of winning is grater than p against his range where

p = .3125/.3778=.82715. or nearly 83%

Aces will always be worth a call.
If you reckon he is rasing more than two thirds of the time, which he probably is, then you can call with kings. Also calling with queens would only be a small mistake. Calling with anything else would be a big mistake.

[Lloyd]

Usually when people post stack sizes they are before blinds/antes. While I'm not sure that's the case here (and the stack sizes are approximate in any case) that's what I based my numbers on. So folding actually leaves him with 835k, not 1M.

[locutus2002]

the ICM model does not account for position, blind or stack size. All very important in this situation.

Short stacks equity in the pot is irrelevant.
Hero has about EV 550K if he folds, $ 250K if he loses and EV 650K if he wins. (according to ICM).

Betting 300K to win 100K is a terrible bet. Short stack is all in next hand, hero should probably fold everything other than AA. The chips won are worth much less than chips lost because of the preponderance of chips held by the big stack. If you make the stacks more similar, the EV goes up substantially. In other words the match is already over (in the most likely case).

[Piers]

[ QUOTE ]
the ICM model does not account for position, blind or stack size. All very important in this situation.


[/ QUOTE ]

Obviously my ICM calcualtions are an approximation. To improve you could do a look ahead approach; include all possible results for the next hand in the mode. Certainly this would help to quantify the error in the first order ICM approach. Have you done this? My guess would be that the error is small, and the first order ICM approach is accurate enough for practical purposes.

[ QUOTE ]
Short stacks equity in the pot is irrelevant.


[/ QUOTE ]

/images/graemlins/confused.gif /images/graemlins/confused.gif

Just because the short stack is all in on the next hand, does not mean the short stack will automatically loose the hand.

[Piers]

Using stack sizes (519,83.5,13.5) I get a TEV of 3055
Using stack sizes (398.5,203,13.5) I get TEV of 3724

p = 3055/32724 = .821

Need to take a little more care with kings, but should still be OK if oppo is raising with well over half his hands.

The only contentious point appears to be, how loose the small blind needs to be before it is correct to defend with kings.

[Dan Mezick]

The short stack has about a 90% of being eliminated in the next two orbits; especially since the big stack will attack with almost any reasonable hand.

[Piers]

My guess would be closer to 85%, but you could be right.

Is your 90% estimate based on anything other than a blind guess?

[M.B.E.]

[ QUOTE ]
x=% of time you call and win

Total chips = 6,150,000
Total prize money playing for = $1M ($250k already wrapped up for each)

Fold = 825k
825k/6150k = 13.4% * $1M = $134,146

[/ QUOTE ]
I don't quite understand this -- aren't you overlooking second place money?

With a stack of 825k, we'd have a 13.4% chance at first plus an 82% chance (approx.) at second, with let's say a 4.6% chance at third. So our equity on folding is not $134,146 but $555,500.

(13.4% x $1M) + (82% x $500K) + (4.6% x 250K) = $555,500.

[ QUOTE ]
Call and win = 2,015,000
2015000/6150000 = 32.8% * $1M = $327,642

[/ QUOTE ]
Should be more like $658,500.

(32.8% x $1M) + (65% x $500K) + (2.2% x 250K) = $658,500.

So that agrees with Fiskebent's post: because of the prize-payout schedule and the very short third stack, the value of your stack increases by only 18% if you double up.

Here are my complete ICM calculations:

You fold (Stacks are 5M, 1M, 150K)
$EV = 1000000/6150000 * $1000000 + ( you take 1st )
5000000/6150000 * 1000000/1150000 * $500000 + ( BigStack takes 1st, you 2nd )
150000/6150000 * 1000000/6000000 * $500000 + (ShortStack takes 1st, you 2nd )
5000000/6150000 * 150000/1150000 * $250000 + (BS 1st, SS 2nd)
150000/6150000 * 5000000/6000000 * $250000 (SS 1st, BS 2nd)

$EV = $162611 + $353482 + $2033 + $26511 + $5081

$EV = $549718

If you double up (Stacks are 4M, 2M, 150K):
$EV = 2000000/6150000 * $1000000 + ( you take 1st )
4000000/6150000 * 2000000/2150000 * $500000 + ( BigStack takes 1st, you 2nd )
150000/6150000 * 2000000/6000000 * $500000 + (ShortStack takes 1st, you 2nd )
4000000/6150000 * 150000/2150000 * $250000 + (BS 1st, SS 2nd)
150000/6150000 * 4000000/6000000 * $250000 (SS 1st, BS 2nd)

$EV = $325203 + $302515 + $4065 + $11344 + $4065

$EV = $647192

[Saborion]

[ QUOTE ]
Always remember you're playing for first.

[/ QUOTE ]
First, sure. But you can avoid some situations on your way there. I would've called with TT in an instant if I had just a slightly lower stack myself. I would've folded a lot of hands if my stack would've been a bit bigger. I think 1M in this specific situation made things a bit tougher. If the shorty doubles or tripples up on the next hand, things aren't too cool anymore.

at this point i wouldnt be playing for first.. there is a huge dioff from 3rd to 2nd in pay. i owuld fold anything short of QQ b/c variance is a b**ch and u are in great shape for 2nd