CARO: How to lose $47K playing AA with 9K stack

I know this has been discussed before, but it still facinates me. Brings out my love for poker.

Caro shows when & why folding AA can make you money.
http://www.poker1.com/archives/1718

Scroll down the page about halfway for Caro's example:

OK. There are three of you left in a tournament, and $750,000 remaining to be awarded. The money will be divided as follows: $400,000 for 1st (40% of an original $1,000,000 prize pool); $250,000 for 2nd (25%); and $100,000 for 3rd (10%).

You have $9,000 in chips (plus $1,000 invested as the big blind), and
Jack has $369,500 in chips (plus $500 invested as the small blind),
and Jill has $370,000 in chips and is first to act.

Just as you look at the cards just dealt to you and see a miraculous pair of aces, Jill moves her entire $370,000 stack into the pot. You begin to say, “yum-yum” when Jack adds his $369,500 to the $500 already blinded. Both your opponents are all-in. Should you call?

Of course not! .......

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Also, like in the recent locked KK cash thread, I'm always interested in the "what if's": What if your stack is bigger? Say 50K? 100K? Where's the threshold to call this and make it worth trying to move up and win the tourney? Anyone care to try the math?

We are approx 70% favourite vs 2 opponents.

By subtracting the 100k already won from the prize pool we get 150k for 2st and and additional 150k for 1nd.

Let say we have x chips and the total amount of chips are y.

By folding we get (150+150x/y)k$
By calling we get (0.7)(150+450x/y)k$

How much of the total amount of chips (z) do we need to call?

Well, we just need to solve the equation:

150+150z=0.7(150+450z)

45=165z

z= 45/165= 3/11

This is provided the effect of blinds and antes are redundant and opponents have equal stacks.

If we continue by involving the big blind (1k) and the total # of chips mentioned in the example (750k) we get:

150+150(x-1)/750=0.7(150+450x/750) (x>1)

So in conclution:

(1) When our opponents knock each other out its always EV+ for us.
Especially if we are short stacked.

(2) There is no unbeatable hand in poker, not even AA.

I feel like this is very very different from folding KK pre-flop in a $1/$2 live cash game. Here your EV is hard to quantify - because although calling is likely +EV, it is possible that the EV we gain from having one of our opponents get knocked out is be much more than the EV of calling. In a cash game, your EV is much easier to model, since we know our pot odds and can figure our win odds based on our opponents ranges.

This is a tourney with ICM considerations. Cash games have no such considerations.

WVHillbilly said:

This is a tourney with ICM considerations. Cash games have no such considerations.

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+1000000000 this is the deciding factor

Sorry guys if my words were misleading. I understand that the only thing here that is similar to that KK thread is my desire to discuss the "what if's".

only_bridge said:

We are approx 70% favourite vs 2 opponents.

By subtracting the 100k already won from the prize pool we get 150k for 2st and and additional 150k for 1nd.

Let say we have x chips and the total amount of chips are y.

By folding we get (150+150x/y)k$
By calling we get (0.7)(150+450x/y)k$

How much of the total amount of chips (z) do we need to call?

Well, we just need to solve the equation:

150+150z=0.7(150+450z)

45=165z

z= 45/165= 3/11

This is provided the effect of blinds and antes are redundant and opponents have equal stacks.

Click to expand...

Thanks OB. So that's 3/11ths of the total chips? So if I understand correctly and apply that to Caro's example with 750K total chips, that would be 204,545 or 3 x (750,000/11)?

Wow. I wonder how many average players could figure this out in the heat of the moment if they were at say 180K or so? Also, having a micro-stack like in the example nearly always brings out a sense of desperation in most of us. Now I guess I'm gonna have to add this line of thinking to my late tourney decision making.

Stick66 said:

Sorry guys if my words were misleading. I understand that the only thing here that is similar to that KK thread is my desire to discuss the "what if's".

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Oh. Whoops, lol. My bad Sorry for taking it out of context.

WVHillbilly said:

This is a tourney with ICM considerations. Cash games have no such considerations.

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We have a winner folks!!!!

The problem, of course, is this is a very rare situation to find yourself in. As soon as your opponents have uneven stacks there's no guarantee* that someone will be knocked out and you'll be guaranteed at least second place money. Removing that guarantee changes a lot.


(* there's no guarantee in Caro's example either, FWIW, because of the chance of a chopped pot)

WVHillbilly said:

This is a tourney with ICM considerations. Cash games have no such considerations.

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Yup.

For those of you with limited knowledge of ICM/bubble factors, think of it in terms of risk vs reward. In the OP example, if we call all in there we are going broke around 30% of the time (getting 3rd place $), and tripling up 70% of the time.

But tripling up to a 27k stack when our opponents have 300k+ each is really very little value. There's far more value in just folding in hopes that one villain knocks the other out.

If you change the stack sizes, there's a point at which we have enough chips and taking the 70% chance on tripling up/30% chance of busting out is better than folding.

So, we have AA and two people just open shoved 370bb deep? lolwut?

TheDevilsLuck said:

So, we have AA and two people just open shoved 370bb deep? lolwut?

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Like I said, it's an incredibly rare and really quite sily example.

Actually, here's a slightly more interesting (and much more relevant to real life situations) question: what range should Jack be calling with? Can he call with anything other than AA? Should he even be calling with that?

Stick66 said:

Sorry guys if my words were misleading. I understand that the only thing here that is similar to that KK thread is my desire to discuss the "what if's".


Thanks OB. So that's 3/11ths of the total chips? So if I understand correctly and apply that to Caro's example with 750K total chips, that would be 204,545 or 3 x (750,000/11)?

Wow. I wonder how many average players could figure this out in the heat of the moment if they were at say 180K or so? Also, having a micro-stack like in the example nearly always brings out a sense of desperation in most of us. Now I guess I'm gonna have to add this line of thinking to my late tourney decision making.

Click to expand...

no the average player would not figure that out lol . and I'm not sure I know what you figured out unless you're saying it would be +ev to call if you had at least 204,545 .
but for me it would still be risking an almost guaranteed extra $150,000(real dollars) and not worth it , take an almost guaranteed 2nd pl then fight for first .

I think I was in a spot like this once , on a much smaller scale of course and after I folded they both had same hand and split the pot and I was out the next hand with crap .

OzExorcist said:

Like I said, it's an incredibly rare and really quite sily example.

Actually, here's a slightly more interesting (and much more relevant to real life situations) question: what range should Jack be calling with? Can he call with anything other than AA? Should he even be calling with that?

Click to expand...

Good point. It's kinda like online at the bubble and the bubble player is very short. Why would you play for stacks against the other big stack when you know you'll most likely cash if you just pressure the shorty in HU pots? Not sure why Jack would call the shove here and risk handing second prize to the shorty.

Stick66 said:

Good point. It's kinda like online at the bubble and the bubble player is very short. Why would you play for stacks against the other big stack when you know you'll most likely cash if you just pressure the shorty in HU pots? Not sure why Jack would call the shove here and risk handing second prize to the shorty.

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I suppose because this isn't a bubble for starters - Jack is guaranteed at least third place money and if he wins this hand he's all but guaranteed first place. On that basis there's definitely some good reasons to call, the question is with what?

Stick66 said:

Where's the threshold to call this and make it worth trying to move up and win the tourney? Anyone care to try the math?

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Bored and tilty from busting out of a big tourny, I'll give the math a go.

ICM equities given the current stack sizes:
http://www.holdemresources.net/hr/sngs/equitycalculator.html

# Payout %
1 400000 53.3
2 250000 33.3
3 100000 13.3

Id Chips equity
1 370000 322214
2 370000 322214
3 7000 105570


Assuming a ranges (these ranges don't matter a whole lot):

99+, AJs+,AKo for button
QQ+ for the SB
We fold AA

(Pokerstove)
equity win tie pots won pots tied
Hand 0: 31.364% 30.10% 01.26% 442214760 18573378.00 { 99+, AJs+, AKo }
Hand 1: 68.636% 67.37% 01.26% 989795316 18573378.00 { QQ+ }

98.74% of the time there's no tie (we'll assume this is 100% though for ease) and our equity changes to:

# Payout %
1 400000 53.3
2 250000 33.3

Id Chips Equity
1 741000 398795
2 6000 251204

<>

Using the same ranges if we call...

equity win tie pots won pots tied
Hand 0: 14.591% 13.36% 01.23% 500943528 46278614.00 { 99+, AJs+, AKo }
Hand 1: 18.219% 15.62% 02.60% 585708252 97582700.00 { QQ+ }
Hand 2: 67.190% 63.53% 03.66% 2382658404 137211446.00 { AA }

67.2% of the time we double up leaving the chip stacks/equities at:

1 726000 395783
2 21000 254216

The rest of the time (32.8%) we bust out in 3rd due to having less chips than the other loser of the hand.

Call and win + Call and lose (getting 3rd place $)
(.672 * 254,216) + (.328 * 100,000) = $203,633 equity

Folding vs Calling
251,204 - 203,633 = $47,571 difference in equity, favouring folding


I plugged in some data into a spreadsheet and found that we'd have to start the hand with more than 242,000 chips (with each other villain having the same 370k at the start) in order to call profitably with aces. There's just that much value in letting the other players knock each other out, given this payout structure.

only_bridge said:

So in conclution:

(1) When our opponents knock each other out its always EV+ for us.
Especially if we are short stacked.

(2) There is no unbeatable hand in poker, not even AA.

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there is 1 inbeatable hand in poker....the one that you fold....the hand you fold cant be beaten

bigpick76 said:

there is 1 inbeatable hand in poker....the one that you fold....the hand you fold cant be beaten

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unless you're in the blinds or there's an ante

bigpick76 said:

there is 1 inbeatable hand in poker....the one that you fold....the hand you fold cant be beaten

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...except that by folding it you're saying that you are beat.