in the money decision

[sluttysteve]

Relatively new to SNGs, so bear with me... this is on Party 10+1.

Three players left, my stack is around 2500, big stack has 4800 and little stack has 700 left. I'm in BB, big stack raises all in, little stack in SB folds, I hold AQo.

Fold/Call?

[Phill S]

its a toughy to do, but id fold.

your basicly garanteed 2nd. if the stacks were reversed id call for sure. and im sure he has nothing, but its too likely to make you a loser for my liking.

if your say 75% fave, its still a 1 in 4 chance your walking in 3rd.

dont do shortstack a favor here, fold it up. heads up is where you need to take this guy on. no reason to run for it at the moment.

Phill

[krille]

[ QUOTE ]
Relatively new to SNGs, so bear with me... this is on Party 10+1.

Three players left, my stack is around 2500, big stack has 4800 and little stack has 700 left. I'm in BB, big stack raises all in, little stack in SB folds, I hold AQo.

Fold/Call?

[/ QUOTE ]

Since he moves in he has almost definately got a low/medium pocket pair. An instant fold for ýou.

[chill888]

Easy fold... if he flashes 72o i'd still probably fold as you are only a 70% favourite. No biggie. NEXT HAND

gl

[poboy]

I'm going to take the opposite stance, just for arguments sake. Though I myself would rarely make this call, here are some reasons why I think it's not a terrible thing to do so:

1> Chances are good that he is just stealing and has a mediocre hand. Even if he's not there aren't many hands that AQ is a huge dog against.
2> If you win you will have the large stack and will have an easier time heads-up and certainly have 2cd locked up.
3> If you lose there really isn't that big of a difference between 2cd and 3rd payouts
4> The short stack could double or triple up at any time, making your guaranteed 2cd not so guaranteed.
5> If you do win, the other players will be less likely to bluff at you, because you've already shown a willingness to bust em.

With all that said I'd probably still fold.

[willperkins]

I fold. I do not want to do battle with the big stack unless I have to. If I have to do battle with him, I want to be the aggressor. I would fold and fight another day.

[ilya]

What are the blinds? If they are somehow still level 1-5, it's an easy fold.

Otherwise, I think it's pretty damn close, tilting slightly towards fold if the blinds are 150/300 and towards call as the blinds rise further to 300/600.
Let's imagine you have 2200 left after posting the big blind and you fold. Then, let's pretend that you magically have 0% chance of finishing 3rd, and that you thus have a 70% chance of finishing 2nd and a 30% chance of finishing 1st.
Your EV then would be 100*0.275 + 60*0.725 = 71

Now let's imagine that you call and win 50% of the time. Now you're out in 3rd 50% of the time and the other half the time you have 5150. Again, let's assume that if you call and win your chances of finishing 3rd are 0% (this would now be much closer to being accurate). Your 1st/2nd breakdown would be 64%/36%. So your EV for those times you win against the big stack is 85.75
Thus, if you call and win half the time (and magically can't finish 3rd) your EV is 40*0.5 + 85.75*0.5 = 62.875

71 is a lot more than 62.875 so it looks like an easy fold. But remember, we assumed that you had 0% chance of placing 3rd in both cases. This is very close to being correct in the 2nd case (you call and win), but appreciably off in the 1st case (you fold and now have 2350 to the small stack's 550). Also remember that we assumed you were only 50/50 to win the hand if you called. In reality, I suspect you're no worse than a 55/45 favorite against the big stack's probable range of hands. So in reality, I think it's quite close. You might even want to consider that calling is likely to speed the game up.

Now let's imagine the blinds are 300/600. At first glance, it looks like an easier fold because it's so extremely unlikely that you will get 3rd if you fold. But...the blinds have made the pot much sweeter. Let's repeat the calculations with the same assumptions (0% chance of placing 3rd if you fold/call&win, linear EV for heads-up, 50% win chance if you call).

Case 1, you fold --
(1900/8000)*100 + (6100/8000)*60 = 23.75 + 45.75 = 69.5.
A touch worse than the first case since the big blind has taken a bigger chunk out of your stack.

Case 2, you call --
50% 40
50% (5300/8000)100 + (3700/8000)60 = 66.25 + 27.75 = 94

0.5*40 + 0.5*94 = 67!


69.5 vs. 67...it still looks like you should fold, especially since in this scenario the chance of finishing 3rd in case 1 is much closer to the 0% assumption than when the blinds are 150/300...
but...with the blinds this high, you're even more likely to have the best hand when you call (since even the big stack is <10xbb). You're probably better than 55/45 against his range of hands here.

Let's say you are exactly 55/45

Then, the 2nd case calculation becomes

40*0.45 + 94*0.55 = 69.7. That means you should call!


To sum up, with blinds at 150/300 and higher this seems to be an extremely close decision. Personally, I would call at 150/300 and above.

[SmileyEH]

call and its not even close.

-SmileyEH

[eastbay]

[ QUOTE ]
Relatively new to SNGs, so bear with me... this is on Party 10+1.

Three players left, my stack is around 2500, big stack has 4800 and little stack has 700 left. I'm in BB, big stack raises all in, little stack in SB folds, I hold AQo.

Fold/Call?

[/ QUOTE ]

You left out a critical piece of information. What's the blinds?

eastbay

[eastbay]

[ QUOTE ]
Relatively new to SNGs, so bear with me... this is on Party 10+1.

Three players left, my stack is around 2500, big stack has 4800 and little stack has 700 left. I'm in BB, big stack raises all in, little stack in SB folds, I hold AQo.

Fold/Call?

[/ QUOTE ]

Let's say you fold. I'll assume for the sake of argument that big stack picks up 300 in blinds to make it:

2500
5100
700

in which case your equity is about 34% of the prize pool by the independent chip model.

Let's say you call, and for the sake of argument let's say he's on one of: any pair, any ace, KQs-KTs. You're about 58% to win the hand. If you win, you double through and have 41% equity (by ICM), if you lose, you go out in 3rd with 20% equity.

(.58)(.41) +(1-.58)(.20) = .238 +.084 = .322

With these assumptions, you lose equity by calling.

If you can put him on any two cards, your edge is .64, in which case you get:

(.64)(.41) +(.36)(.2) = .262 +.072 = .334

Wow. You still lose equity by calling. Can someone check my math here? It's late, and this latter result surprises me.

In the absolute best case scenario, if he's on any ace, your edge is 67%:

(.67)(.41) +(.33)(.2) = .34

In which case you break even by calling! Ok, I admit I am very surprised by this result, and would appreciate a critical eye on it.

eastbay

[dethgrind]

I checked your numbers and they look good. That is an odd result.

In TPFAP, there is a chapter called "Prize Structure Implications." Sklansky explains how you can be a significant favorite in an all-in situation and still lose $EV. The key is to be the raiser and not the caller.

[Gramps]

How big is the big blind? How often has the big stack been doing this? Is the SB playing to "hang on as long as possible," obviously foldilng in spots where a rational player would take a stand?

What I don't want to have happen if I fold is for this pattern to continue (big stack pushes, I fold, SB folds, big stack picks up blinds, my 2500 gets whittled down, SB finally makes a stand, wins and stays alive to fold another round of blinds....now even if I end up in 2nd place, I'm down to only 1,000 - 1,500 in chips - or - I get whittled down, SB wins an all-in or two getting his remaining chips in with a decent hand against the big stack's crap, now I'm the low stack).

In the above described scenario (particularly if the blinds are around 150/300 - big enough for my stack to get whittled down pretty quick, but small enough for SB to hang on without having to go all-in every other hand), I don't think drawing the line in the sand is bad. In most spots, though, I think a fold is a better play. Since the big stack may be pushing just about any two cards, you're going to have to get lucky (dominate the big stack's hand) to be a big favorite with a non-pair hand (even a good one like AQo). AA/KK/QQ (and maybe other pairs depending on the circumstances) I think you make the call - there's a lot of hands you're a huge favorite against with those.

[ilya]

What is the independent chip model?

It seems to me it underestimates your equity if you call and double through. 41% seems too low for 5000 chips when the other stacks are 700 and 2300. You've got to be averaging better than almost-exactly-2nd-place from that spot! Heck, even if you figure you're equally likely to get 1st, 2nd, or 3rd, your equity there is 48%.

p.s. what are you doing with the 2500/8000 (i.e., 0.3125) fraction to get 34%? I guess this is another way of asking, "What is the independent cihp model?"

[eastbay]

[ QUOTE ]
What is the independent chip model?


[/ QUOTE ]

Search for it. There is a post by pzhon which explains it well enough to write a computer program to calculate it.

[ QUOTE ]

It seems to me it underestimates your equity if you call and double through. 41% seems too low for 5000 chips when the other stacks are 700 and 2300. You've got to be averaging better than almost-exactly-2nd-place from that spot!


[/ QUOTE ]

2nd place is .30, not .40.

[ QUOTE ]

Heck, even if you figure you're equally likely to get 1st, 2nd, or 3rd, your equity there is 48%.


[/ QUOTE ]

Huh? Your equity is 1/3*(.5+.3+.2) = 1/3 = 33% for equal probabilities of 1st, 2nd, 3rd.

eastbay

[hansarnic]

[ QUOTE ]
[ QUOTE ]
Relatively new to SNGs, so bear with me... this is on Party 10+1.

Three players left, my stack is around 2500, big stack has 4800 and little stack has 700 left. I'm in BB, big stack raises all in, little stack in SB folds, I hold AQo.

Fold/Call?

[/ QUOTE ]

Let's say you fold. I'll assume for the sake of argument that big stack picks up 300 in blinds to make it:

2500
5100
700

in which case your equity is about 34% of the prize pool by the independent chip model.

Let's say you call, and for the sake of argument let's say he's on one of: any pair, any ace, KQs-KTs. You're about 58% to win the hand. If you win, you double through and have 41% equity (by ICM), if you lose, you go out in 3rd with 20% equity.

(.58)(.41) +(1-.58)(.20) = .238 +.084 = .322

With these assumptions, you lose equity by calling.

If you can put him on any two cards, your edge is .64, in which case you get:

(.64)(.41) +(.36)(.2) = .262 +.072 = .334

Wow. You still lose equity by calling. Can someone check my math here? It's late, and this latter result surprises me.

In the absolute best case scenario, if he's on any ace, your edge is 67%:

(.67)(.41) +(.33)(.2) = .34

In which case you break even by calling! Ok, I admit I am very surprised by this result, and would appreciate a critical eye on it.

eastbay

[/ QUOTE ]

Your calculations are fine.

As an aside, these types of sims illustrate an interesting conundrum that I have been puzzling over for a while - seems like a good time to bring it up.

They show that the big stack has extra EV beyond a mere chip count calculation because stacks that he can bust need such a big edge to call (You can demonstrate this mathematically by running the same calculation with the medium stack all-in and the edge the big stack needs to call is only about 55% vs. the 67% of the med stack).

That's all well and good until you consider a situation like the one we're discussing. In this situation, by calling and winning the medium stack becomes the big stack.

So clearly he gains some additional value from a call and a win that is not factored in by a simple chip count calculation of his EV (as he now needs less of an edge and the smaller stacks need more of an edge).

In which case the big stack doesn't actually have as big an edge over the smaller stacks after all as they gain extra value by calling an winning. And if the big stack doesn't have this extra edge then the small stack doesn't gain it by calling and winning. So we're back to a chip count calculation for EV.

Where we can demonstrate that the big stack has an edge. And so it goes on...

Anyway, all very theoretical, but I've never worked out a solution to this.

Anyone put me straight?

Thx

[willie]

[ QUOTE ]
call and its not even close.

-SmileyEH

[/ QUOTE ]

i got through 6 responses before i saw one that i basically agreed with.

the payout is different between second and third, but you have a real solid hand here 3 handed, and i'd definitely take a stab at choppin into the big stack and making the play for first place a bit easier with more bullets for war.

i guess i'd be going out of my way to do the small stack a favor here, but i'm going for first since that is where the money is.

[ilya]

[ QUOTE ]
[ QUOTE ]
What is the independent chip model?


[/ QUOTE ]

Search for it. There is a post by pzhon which explains it well enough to write a computer program to calculate it.

[ QUOTE ]

It seems to me it underestimates your equity if you call and double through. 41% seems too low for 5000 chips when the other stacks are 700 and 2300. You've got to be averaging better than almost-exactly-2nd-place from that spot!


[/ QUOTE ]

2nd place is .30, not .40.

[ QUOTE ]

Heck, even if you figure you're equally likely to get 1st, 2nd, or 3rd, your equity there is 48%.


[/ QUOTE ]

Huh? Your equity is 1/3*(.5+.3+.2) = 1/3 = 33% for equal probabilities of 1st, 2nd, 3rd.

eastbay

[/ QUOTE ]

Multiple brain farts. Sorry.

[Marcotte]

I'd have to say I'd probably call too, but I definately see the reasons to fold. It's a very close decision for me. If the big stack had been playing very aggressively in the last few orbits, I would be even more inclined to call.

This brings up another question. If AQ is a fold, what is a call? AK off? AKs? TT? 99? Or to put it another way, what % edge do you need to make the call +EV?

[rachelwxm]

I agree with eastBay's result even though i don't see how it add up to 800. /images/graemlins/wink.gif But the idea is there.

One interesting extension is the following:
Assuming hero acted properly, (never call all in without 67% edge), and small stack always fold since he is timid player if you push, what would you do if you are big stack?

If you check the odd table, the only two cards that are 2:1 favorable against any two random cards are
77-AA and AK AQ, there is less than 5% chance anyone will catch them.

Before post blinds,
hero 2500
big stack 4800
small blind 700

From big stack point of view,
before posting, his equity is 41.3(2500,4800,700). Assuming big stack go all in with any two.
if big stack lost all in , he still has 33.9 equity (5100,2300,600), if hero fold big stack has 42.2 (2300,5100,600).

So if hero act correctly, he will call all in 5% of the time and assuming whenever hero will allin everytime,
the big stack has equity
.05*33.9+.95*42.2 = 41.8

So it's +EV for big stack to go all in with anytwo!

If this is correct,
is it because it pays to be aggressive or is it a result of game theory? your optimal strategy leads to negative EV no matter what?

I am really confused.
/images/graemlins/confused.gif

[patrick dicaprio]

i am surprised at how many players would fold this. i would almost always call here if the blinds were high, over 100/200. thebig stack will make this play with lost of hands you beat since he cant be knocked out and can steal the blinds fairly often once the SB is out because he figures you will fold because you dont want to finish third. at least thats what i would do and that is what i normally will do.

Pat

[ilya]

[ QUOTE ]

Let's say you fold. I'll assume for the sake of argument that big stack picks up 300 in blinds to make it:

2500
5100
700

in which case your equity is about 34% of the prize pool by the independent chip model.


[/ QUOTE ]

Shouldn't those chips counts be

2300
5100
600
?

How would that change your equity according to the independent chip model?

[RobGW]

I agree with you Patrick. And now that I know that so many people will fold in this spot you can be sure that when I am the big stack in this scenario I will be pushing with any 2 everytime.

[chill888]

As you should be pushing hard as the big stack.
But that certainly doesn't make the fold wrong, We just hadn't covered how the big stack should play. he should be AGGRESSIVE

[Irieguy]

Well, if I'm the big stack, I'm pushing with any two here and hoping the middle stack doesn't wake up with a big ace or pair. Since I don't want a call with AQ if I'm the big stack, I'd call with AQ as the mid stack.

Totally different story if this was a bubble hand, but you need to be winning these things often to make money. This is a clear call. (for me)

Irieguy

[serling]

Three people left and already in the money, I'm calling. We're playing for 1st, not just to cash.

Besides, there are no guarantees you're a lock for 2nd place.

serling

[hhboy77]

needless to say, i'm also surprised by eastbay's numbers though i've looked at enough of his calculations to believe the numbers are right.

i will say this however. eastbay's number for the blinds after folding are slightly off. they should be 5250, 2200, 550. also, in a higher buy-in tournament, one is likely for the blinds to be at least 250/500 when this situation occurs, at least at party poker.

irieguy makes a point that if he were a big stack, he wouldn't want a call from aq, thus a call must be correct. and though this seems logical it can't be right, because the numbers say so. my suspicion is that what is happening is that both players may be losing equity through calling and it's all going to the short stack.

after all the third player's chances of getting second go up to about 40% if bb calls.

whoever mentions the advantage gained by becoming the big stack is quite astute, however, i think that advantage can only be wielded against players who have read this thread. while i bully a ton on the bubble, i barely at all once i get three handed. this doesn't mean i don't raise a lot, but it's now for different reasons.

[eastbay]

[ QUOTE ]
needless to say, i'm also surprised by eastbay's numbers though i've looked at enough of his calculations to believe the numbers are right.

i will say this however. eastbay's number for the blinds after folding are slightly off. they should be 5250, 2200, 550. also, in a higher buy-in tournament, one is likely for the blinds to be at least 250/500 when this situation occurs, at least at party poker.

irieguy makes a point that if he were a big stack, he wouldn't want a call from aq, thus a call must be correct.


[/ QUOTE ]

I believe that logic is wrong. In a tournament, a player's mistake doesn't necessarily help you, FTOP-style. A player's mistake can definitely hurt you, by helping those not in the hand.

[ QUOTE ]

and though this seems logical it can't be right, because the numbers say so. my suspicion is that what is happening is that both players may be losing equity through calling and it's all going to the short stack.


[/ QUOTE ]

Yep.

[ QUOTE ]

after all the third player's chances of getting second go up to about 40% if bb calls.

whoever mentions the advantage gained by becoming the big stack is quite astute, however, i think that advantage can only be wielded against players who have read this thread.


[/ QUOTE ]

Yep. Basing tournament strategy on players making correct decisions for themselves is a bad idea, because they very often won't, especially in situations like this.

If players were to only call all-in when it raised their equity, you'd be pushing many more hands than is optimal in a real game, IMO. The problem with a real game is that you're likely to be called by a player who is hurting both himself and you by calling, and you can't afford him to make those mistakes, when he inevitably will.

eastbay

[eastbay]

[ QUOTE ]
Well, if I'm the big stack, I'm pushing with any two here and hoping the middle stack doesn't wake up with a big ace or pair. Since I don't want a call with AQ if I'm the big stack, I'd call with AQ as the mid stack.


[/ QUOTE ]

Flawed logic, I think. While you may not want the call from the other side of this, that doesn't mean it helps you to make it, FTOP-style.

It hurts both players in the hand to make the call. It helps the player not in the hand.

eastbay

[eastbay]

[ QUOTE ]
I agree with eastBay's result even though i don't see how it add up to 800. /images/graemlins/wink.gif But the idea is there.

One interesting extension is the following:
Assuming hero acted properly, (never call all in without 67% edge), and small stack always fold since he is timid player if you push, what would you do if you are big stack?

If you check the odd table, the only two cards that are 2:1 favorable against any two random cards are
77-AA and AK AQ, there is less than 5% chance anyone will catch them.

Before post blinds,
hero 2500
big stack 4800
small blind 700

From big stack point of view,
before posting, his equity is 41.3(2500,4800,700). Assuming big stack go all in with any two.
if big stack lost all in , he still has 33.9 equity (5100,2300,600), if hero fold big stack has 42.2 (2300,5100,600).

So if hero act correctly, he will call all in 5% of the time and assuming whenever hero will allin everytime,
the big stack has equity
.05*33.9+.95*42.2 = 41.8

So it's +EV for big stack to go all in with anytwo!

If this is correct,
is it because it pays to be aggressive or is it a result of game theory? your optimal strategy leads to negative EV no matter what?

I am really confused.
/images/graemlins/confused.gif

[/ QUOTE ]

The problem with this is that you can't assume your opponents play correctly. They will call when it hurts both them AND you - and helps the short stack.

eastbay

[NegativeEV]

[ QUOTE ]
Quote:
--------------------------------------------------------------------------------

Relatively new to SNGs, so bear with me... this is on Party 10+1.

Three players left, my stack is around 2500, big stack has 4800 and little stack has 700 left. I'm in BB, big stack raises all in, little stack in SB folds, I hold AQo.

Fold/Call?


--------------------------------------------------------------------------------



Let's say you fold. I'll assume for the sake of argument that big stack picks up 300 in blinds to make it:

2500
5100
700

in which case your equity is about 34% of the prize pool by the independent chip model.

Let's say you call, and for the sake of argument let's say he's on one of: any pair, any ace, KQs-KTs. You're about 58% to win the hand. If you win, you double through and have 41% equity (by ICM), if you lose, you go out in 3rd with 20% equity.

(.58)(.41) +(1-.58)(.20) = .238 +.084 = .322

With these assumptions, you lose equity by calling.

If you can put him on any two cards, your edge is .64, in which case you get:

(.64)(.41) +(.36)(.2) = .262 +.072 = .334

Wow. You still lose equity by calling. Can someone check my math here? It's late, and this latter result surprises me.

In the absolute best case scenario, if he's on any ace, your edge is 67%:

(.67)(.41) +(.33)(.2) = .34

In which case you break even by calling! Ok, I admit I am very surprised by this result, and would appreciate a critical eye on it.


[/ QUOTE ]

This seems counter to advice that is frequently given on this forum in regards to making calls when facing blind steal attempts. I think I recall many threads that discuss why/how it is correct to make calls with this type of hand (AQ) when the would be blind stealer likely has a marginal/sub-par holding. These previous threads generally deal with bubble situations, but I don't see a meaningful difference in this case. Here is an example of the type of thread I'm referring to: Making Calls on the Bubble (http://forumserver.twoplustwo.com/printthread.php?Cat=&Board=singletable&main=920814 &type=thread)

The calculations using the ICM indicate that these calls are likely not correct. What am I missing here? Also, assume that the small stack is making the decision to call or fold here (assume that the BB will fold and small stack is SB), what would the ICM say is the right decision for the small stack? How about if the 2nd stack is making the push and the big stack is on the decision, what would the ICM say? Do the numbers tell us that a fold is right for each of these scenerios? If so, it seems that the "correct" decision mathematically is always to fold here? Please clarify as I'm working myself in circles.

[AA suited]

[ QUOTE ]
[ QUOTE ]

Let's say you fold. I'll assume for the sake of argument that big stack picks up 300 in blinds to make it:

2500
5100
700

in which case your equity is about 34% of the prize pool by the independent chip model.


[/ QUOTE ]

Shouldn't those chips counts be

2300
5100
600
?

How would that change your equity according to the independent chip model?

[/ QUOTE ]

if 2300,5100,600 then my #'s are:
fold = .339 equity
call + lose = .2 (3rd place)
call + win = .442

Thus you need 1.7:1 odds to call.

If you estimate him to be pushing with:
top 67% hands, then you need at least ATs, AJo, or 88 (AQo is good)
top 40%: AQo is 1.6:1 here thus you shouldn;t call

Are my #'s correct?