Would you fold AA in this senario?

[FirstClash]

I recently discussed this with a friend.

Suppose you are at a single table tournament. There are 5 people left. 2 more people need eliminated before you get in the money. 3rd=$20 2nd=$30 and 1st=$50.

Every one has even chip stacks of 3000 chips.

3 people go all in ahead of you.

Do you call with AA and take the risk or fold and practically guarantee yourself to be in the money?

What is the mathematically correct decision?

Seems to me that your actually chances of winning the hand is between 50-60% with all 4 people in the hand--risking knocking you out of the tournament.

If you don't fold and win, you end up with 12,000 chips against 3000 chips.

If you fold, you end up with 3,000 chips against 9000 chips and 3000 chips. Or the unlikly senario where the pot is split, your 3000 chips against 4500, 4500 and 3000.

I say fold, my friend says call.

[SpeakEasy]

Assuming that the all-in players ahead of you are sane, logical players, you probably dominate their hands by 4:1 or better -- AK, AQ, KK or QQ. Easy call.

[Tom Bayes]

No.

[valenzuela]

I say fold because i have a very small bankroll( 10 bux)

[1C5]

[ QUOTE ]
I say fold because i have a very small bankroll( 10 bux)

[/ QUOTE ]
hahahahahaha

[FirstClash]

Considering what you said... I'm going to have to change my stance that the mathematically correct/most profitable choice in the long run is to call... You won me over.

But I see a lot of players who go all in with TT, JJ, KQ, and such... those hands have more outs and lower your chances of winning that hand down between 50-60%. The hands you suggested brings your chances of winning between 60-75% because you dominate them.

I guess if you are playing really tight players you are definitly better off calling... If you are playing semi-loose players, it could go either way.

[Mr_J]

Like someone said, it depends on the range of hands.

You'd need to win 72% for it to be even (calling vs folding). This is assuming that with 12k vs 3k you have a 75% chance of winning and 25% chance of coming 2nd. This also assumes of you fold you have a 25% chance of winning, and 37.5% chance each of 2nd and 3rd.

Those winrates will be different for everyone though, so this is really just a guess.

Confronted with the situation in real I'd call, but after looking at it like this I really don't know. Maybe someone can come up with more accurate figures.

[microbet]

Calling is probably worth around $25 with a bit better than 50% to win the hand and then a good chance to go on to win.

Folding is worth at least $25 as you will be tied second in chips.

So folding is probably better. But, in real life I would probably call. Maybe not, now that you made me think about it.

[RobGW]

If you fold you automatically make the money(in most cases). If you go on to win 20% and are 40% to place 2nd or 3rd your EV is (.2*50+.4*30+.4*20)= $30. If you call, you'll win 55-65% of the time. If you win the hand you'll have about a 80% chance to win and 20% chance to take 2nd. Your Ev is (.6*.8*50+.6*.2*30+.4*0)= $27.6. Now there are other considerations. How do you rate against the others players? Considering three people are going all in which is almost certainly a mistake, I would just muck here and try to outplay whoever is left. Would your decision change if this was the final table at the WSOP where the difference between 5th place and 3rd is life changing $$?

[Pokerscott]

your absolute best outcome is something like

initial better: A8o
1st caller: AKo
2nd Caller: KK

Here you are a 78% favorite and it is a good call.

I guess at worst you could have something like:

initial better: JTs stealing
1st caller: QQ
2nd Caller: AA

The second caller is in a very similar position to you. They have to be VERY sure of a win to justify getting in the middle of all this. This makes AA here not really impossible...(I have seen AA vs AA but never your scenario btw /images/graemlins/wink.gif )

Now you win 2%, lose 39% and tie 59%...not so great /images/graemlins/smile.gif

Pokerscott

[jedi]

In a satellite where top 3 are paid the same thing (a seat to another event), I fold.

In a normal SnG with increasing payouts, I call.

[Gramps]

Easy call, do you see why? (I just wanted to say that once).

First of all, you'll probably be about 50% or so to win the hand and have a 4:1 chip lead HU.

But, the reason why it becomes an easy call is that even if you call and lose, you need two players to beat you to finish out of the money. If your Aces are second-best after 5 cards are flipped, you're eliminated but in 3rd place. At worst you'll get 3rd the vast majority of the time.

I'm too lazy to do the math, but I assume if you plugged it into ICM or something it wouldn't even be close (between call and fold) given the payout structure and stack sizes (all equal).

[valenzuela]

im a math genius: ehem...
fold= $30( u win 20% of the time, 40% second, 40% third)
call= $30 IF u have a 66% of chance of winning the all-in.($46 avg. profit if u win the all-in). Aces dont win 66% of the time against 3 other cards whihc means the fold is correct.

[Adjective]

I would say that this is an easy fold, unless you want to feel extreme heartbreak and sadness when your aces get busted by a lower ranking hand that outdraws you. There is a pretty good chance one of the other players has an aces even further lowering your chances, but *three* people all in infront of you? I'd say just fold and save yourself the heartbreak of getting your aces outdrawn by a lower hand. Also looking at the payout of the tourny I would rather fold and get in the money then play and get diddly.

Mathematically speaking however this is probably an easy call, but then again you're not going to win every tournament doing what math tells you to do

[david050173]

I the best for you would be something like
AKo
AKo
KK

At that point you just have to dodge have the 2 of the 4 flushes and the QJT straight (ok there are a few split pots)
you win 93% of the time with 5% split pots

In the worst case, 67s is worse for you than JT(it doesn't depend on having queens, or aces as outs).

You will win 2% of the time and losing 43%. You can mess around increase your loss percentage put in turn you win % would go up.

I assume (in the no split pot case) if you get 4th you get 1/3 of a buyin (chip stacks equal, 3 people eliminated on the same hand) back which wasn't accounted for in the EV calculations done earlier. That money changes the call from EV- to EV+ according to the prior calcs.



In the WSOP final table which is a once in a lifetime thing for most people this is fold. In a 10 dollar sng where you can play 50 a day if wanted, I am calling all day long. I don't want to develop bad habits like thinking about folding AA.

[Evolution Crisis]

I can't understand why you'd want to fold here... you're dominating most hands, and you're ahead of any hands you're not dominating. There's no guarentee that you're winding up in the money even if you fold anyways, there's always split pots with 2 of them having the same hand, or a straight hitting the board or something; and then you're playing to avoid 4th place as the short stack anyways. You have the same odds of hitting a 3rd A for your set as anyone else does of hitting their set (before seeing the opponents cards obviously, even if you do think one may have AK or AQ), and even though you might be up against AK or AQ you having AA just lowers their chances of catching anything.

[valenzuela]

eek....i forgot one tiny detail..theres third place money in case u bust which should be $6,7 since everyone had the same strating chips.
fold:$30
call:$30 with a 60% of chance of winning the all-in.

[valenzuela]

btw my exact number was $30,28 but with third place at $6,7...

[Mr_J]

I think you forgot to deduct the buyin /images/graemlins/wink.gif

I'll just add something, if EV was even then folding is the better move since there's less variance.

Best scenario is you are up against KK and 2 AK. That way everyone is almost drawing dead (ruling out str8s).

"Would your decision change if this was the final table at the WSOP where the difference between 5th place and 3rd is life changing $$?"

I'm not sure on the difference in prizemoney but I think that it probally favours a 'gamble for 1st' approach. You won't get paid 5th anyway. I'm not sure how they do it for WSOP (if stacks are same, do they tie or judge by hand?).

[Mr_J]

"I can't understand why you'd want to fold here"

Look at the maths examples. It's not about being ahead, with AA you are easily ahead (unless someone else has AA). It's whether it is more profitable to fold and slide into the money, and it looks like it is.

I think one thing needs to be made clear here:

If you lose, do you share equal third, or do they decide place by hand strength?

[valenzuela]

[ QUOTE ]
"I can't understand why you'd want to fold here"

Look at the maths examples. It's not about being ahead, with AA you are easily ahead (unless someone else has AA). It's whether it is more profitable to fold and slide into the money, and it looks like it is.

I think one thing needs to be made clear here:

If you lose, do you share equal third, or do they decide place by hand strength?

[/ QUOTE ]

If u have the same skill as the other players 60% is the magical number. I read party rules and they said nothing about it..the most logical thing would be split third place money. Anyway I just realized that if this ever happens to you , you must call because:
u are defending a blind and the blinds are now huge.

[bugstud]

[quote
Best scenario is you are up against KK and 2 AK. That way everyone is almost drawing dead (ruling out str8s).



[/ QUOTE ]

2 QQ's and AK

87%

[Mr_J]

"and the blinds are now huge."

This is a $10 sng, so we might not even be at level 4 /images/graemlins/wink.gif

You are missing the cost of buyin.

If 3rd place prizemoney is split, that obviously gives a pretty good boost to the EV for calling. Surely the worst party can do here is split it. Maybe you're lucky enough that placing is judged by hand strength? Doubt it.

But yeh 60% is close to the mark when you count the split 3rd prize. Win% should be higher for both since you can outplay opponents, and 2nd% should be a bit higher than 3rd for folding.

Now it really depends on the range of hands you put the opponent on. You could have as much as a 93% shot, and as low as 30% (that I bothered to look at anyway).

It'd help if we knew blind sizes. 1st guy could be stealing w/ Ax, 2nd guy might have a good PP or high Ax, say TT or AQ. 3rd guy might have KK/QQ and you with AA. I wouldn't worry about being up against AA.

[Mr_J]

"2 QQ's and AK

87%"

If both AK for AA-KK-AK-AK are unsuited, that gives >93%.

[BigDave]

If my goal is to make it in the money, I fold.
If my goal is to win this thing, I call.

In the case that this is a $10 SNG, I will call every single time.

[Gramps]

There's no "splitting of 3rd place prize money," that's not how it works in NL tournies (absent some odd made up rule). Whoever gets 2nd out of the 4 players in the all-in (if you call) gets 3rd.

Your Aces will win close to 60% of the time against your opponents' likely range of hands (and I'm really giving them the benefit of the doubt - like AK/AQ and 88-AA - in a $10 SNG you'll probably see a wider range of A-x's which favors your AA even more). Of the (slightly more) than 40% of the time that they don't, they'll get 2nd about 2/3 of the time (against your opponents' likely range of hands). Thus, by calling this all-in, you will finish out of the money approx. 15% of the time.

So, 85% (approx.) of the time you finish in the money. That breaks down (roughly) to about 1/3 (28%) 3rd places. Of the times you win the 4-way all-in (assuming about 57% of the time about), you'll get first the vast majority of the rest of the time with your 4:1 chip lead HU. Say you win 3/4 of those (I don't have a formula for %s there) that means 43% 1st, and 14% of the time 2nd.

.43 (50) = 21.50
.14 (30) = 4.20
.28 (20) = 5.60

$31.30 on average by calling (roughly). Even if you have a skill edge on the other players, I highly doubt that your expectation would be close to $31.30 if you were 100% guaranteed (assuming no ties in the 3-player all-in if you fold your Aces) to be in a 3-player 9k:3k:3k chip situation (with you having 3k).

[Nottom]

[ QUOTE ]
There's no "splitting of 3rd place prize money," that's not how it works in NL tournies (absent some odd made up rule). Whoever gets 2nd out of the 4 players in the all-in (if you call) gets 3rd.

[/ QUOTE ]

Every tourney I have ever played in places people according to how many chips they had before the hand started.

[Gramps]

[ QUOTE ]
Every tourney I have ever played in places people according to how many chips they had before the hand started.

[/ QUOTE ]

Same here. And my understanding is in the Party SNG structure (or any other tournament) when the players have the same # of chips (which is rare), the tiebreaker is who beat whom on the last hand. Hence, it would be very difficult to finish out of the money by calling with Aces.

[niin]

[ QUOTE ]
But I see a lot of players who go all in with TT, JJ, KQ, and such... those hands have more outs and lower your chances of winning that hand down between 50-60%

[/ QUOTE ]

Er. Huh? How does JJ and TT have more 'outs' to beat AA? They have 2. Just as many as AA, and if AA hits one of their outs it virtually doesn't matter what the others do.

KQ can hit one of it's 6 'outs' to make a pair. And lose. It has to hit 2 of its outs to win.

In your example of AA vs TT vs JJ vs KQ, AA indeed does only have a 56% chance to win. Against 3 other opponents. The others have about a 15% chance to win.

http://twodimes.net/h/?z=732700

[bigredlemon]

I went all in as the chipleader with KK once, trying to induce a call by faking a steal. Got called by TT, QQ, and AJ!!?? The Q flopped a set and became the new leader. I lost half my stack. Not sure what it has to do with this thread, I just like telling the story.

[Mr_J]

Well if 2nd best hand gets the full 3rd amount then that's the what makes the difference (that's why I asked for what the rule actually was).

Calling would be more fun than folding, but going up with 3k vs another 3k and 9k would be even more fun /images/graemlins/smirk.gif

[Mr_J]

"If my goal is to make it in the money, I fold.
If my goal is to win this thing, I call."

I'd think your goal should be to maximise your EV?!?

[SNOWBALL138]

Lets say that u win 50 percent of the time against the three hands, and that you can beat the remaining shortstack 80 percent of the time. that means that in 100 identical scenarios, the breakdown is this:

50 times, u bust out.
50 times, u come out with a huge stack and go heads up with a 4-1 chip lead.
Of those 50 times, u place 1st 40 times.
10 times, u place 2nd. 10x 30= $300
40 x 50 = $2000

so, your total prize money is %2300

Compare this to the probable outcome if you fold. If you fold, u end up guaranteed 3rd place all 100 times. This means that you win 20 dollars at least all 100 times, which gives you $2000 dollars. Additionally, u have a marginal chance to take 1st place, and a decent chance to take third by outmaneuvering your fellow shortstack.
lets say that if you can outmaneuver your fellow short stack even 20/100 times, u still come out with $600 those times. BTW, u can outmaneuver your fellow shortstack A LOT more often then that.

You get paid more for folding. Folding is the best play.

[Mr_J]

Not if they give 3rd place to the 2nd best hand. If 4/5 all-in, and the 3 loser get nothing, folding is clearly the best play. If the losers get a 3way split for 3rd prize, then it's close. If 3rd prize goes to 2nd best hand, then calling is better.

Anyway, you'll win more than 50% on average.

[ColdestCall]

AA is a call here for many reasons, one of which is the opposite of what you suggest. The "extreme heartbreak and sadness when your aces get busted by a lower ranking hand that outdraws you" is absolutely nothing compared to the heartbreak of watching the cards come out, seeing your AA hold up, and contemplating what a gigantic (expletive) you are for folding AA.

The day I fold AA preflop is the same day I stop playing no limit hold em.

[FirstClash]

The basic idea I wanted to portray is if you lose, your out... So maybe I should have Made it like this:

The 3 people in front of you have 1 more chip than you... 3001, 3001, 3001, then 3000 for the other guy who's not all in and 2997 for you. For me I think it's an easy fold here being the short stack, but your close to even. If I have just 1 chip more than the other 3 All-in's--so I'm pretty much guaranteed 3rd or better--it becomes an easy call for me.

For me it's like this, if I call, there is a 30-50% chance I'm going to be out of the tournament and out of the money. That's a chance I don't want to be subject to. By folding I protect myself from the effects of variance of the outcome for this particular play. I'm still in the tournament and can play the hands with less risk; and if I play correctly, I still have a chance for 2nd and 1st. I'd rather have a guaranteed chance to win rather than a chance for a great chance to win.

My friend does not believe this is the correct mindset to have if you want to be a champion. Any opinions on this?

[Mr_J]

That removes chance of picking up at least a piece of 3rd if you call, so yeh with the new stack sizes it's a fold.

"My friend does not believe this is the correct mindset to have if you want to be a champion."

This is an sng, and not a WSOP final table /images/graemlins/wink.gif Your mindset seems fine for your example. It looks like you are looking to maximise EV.

"and if I play correctly, I still have a chance for 2nd and 1st."

I think this is the wrong mindset. Here I'm thinking 2nd place is probally mine. If I'm unlucky I'll come 3rd, and if I get a break 1st is a great chance.

[SpeakEasy]

[ QUOTE ]
The day I fold AA preflop is the same day I stop playing no limit hold em.

[/ QUOTE ]

Yeah, what he said!

[SpeakEasy]

For those that say fold, try this as an experiment.

Get a deck of cards. Pull out AA, and any other 3 hands that will go up against your AA in this all-in example. Use some reasonable hands, yet not out of the realm of possibilities, like AKs, KK and QQ. Or maybe AQs, JJ and TT (loose table).

Lay these four starting hands face up on the table. Shuffle the rest of the cards. Deal the five community cards ("burn" and turn, if you like, to keep this scientifically accurate...). Record the result.

Leaving the 4 starting hands on the table, collect the community cards, shuffle and repeat 99 more times. Keep track of the results.

See what I mean?

[Frogistador]

For those that say fold, try this as an experiment.

Get a deck of cards and a cast iron frying pan. Pull out AA, and any other 3 hands that will go up against your AA in this all-in example. Fold your AA. Hit yourself upside the head with the frying pan. Repeat 99 times.

[ColdestCall]

"For those that say fold, try this as an experiment.

Get a deck of cards and a cast iron frying pan. Pull out AA, and any other 3 hands that will go up against your AA in this all-in example. Fold your AA. Hit yourself upside the head with the frying pan. Repeat 99 times."


Post of the Day! LMFAO.

[se2schul]

I got into a similar situation lastnight.
Party, 10+1.
Bubble with blinds 100/200
I have average stack in the BB.
UTG folds.
Button goes all-in for ~800
SB goes all-in with ~1500
I am dealt AA and after thinking for a while I call.

We all show.
Me AA
Button TT
SB 55

The only reason I'm posting this is because of the CRAZY flop. It came down
AT5

All three of us had trips.

I'd tell you how it finished, but then it would just sound like a bad beat post /images/graemlins/wink.gif

I'm convinced that calling in this situation is the only play to make for low-limit SNGs. If you lose, no big deal, just buy into another. If it were bubble time on a STEP 5 or something like that (which would be a huge for a low buy-in player like me), I'd probably be weak and just try to coast into the money, even though I admit it is likely the wrong play.

ss

[MrMon]

If anyone would bother to look up the rules of ties, they would see that (at Paradise at least) when two or more players go out at the same time with the same chip stack, any money is split evenly, regardless of what your hands were. (If that's the rule at Paradise, it's likely the rule everywhere.)

That said, I like that you move the chip stacks by one. Makes for a much more straighforward problem.

Odds of AA winning in this situation +- 55%
If AA wins and has a 4:1 chip lead, I'd say the odds of winning overall are 90%.
If AA folds, 3rd place is a 100% guarantee, you would be even money to beat the other short stack to second, and given the ~ 3:1:1 chip ratio, I'll say you and the other short stack will each win overall 15% of the time, meaning bigstack wins 70% of the time.

Case 1 (You Have 1 less chip)

All-In:
45% you lose so that's 0$
55% you win, finishing 1st 90% of the time, 2nd 10% so .55 * (.9 * $100 + .1 * $60) = $52.80

Fold:
100% you win $40
50% you win an additional $20
15% you win an additional $40 or
1.0 * $40 + .5 * $20 + .15 * $40 = $56

Fold is the play if you have less chips. In order to justify the all-in, you need to win 58% of the time.

Case 2 (Equal # of chips)
Same as above, except if you lose, you are in a 3 way tie for 3rd, worth $13.33, so add .45 * $13.33 to $52.80 = $58.60, or a slight edge to the all-in. But so close that it really is a coin-flip.

Case 3 (You have 1 more chip)
Folding is still the same payoff of $56

All-in:
45% you come in 3rd, which is added to $52.80 or
.45 * $40 + $52.80 = $70.80

All-in is a clear cut winner.

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

Some of the answers here tell me why I see the plays I do. But if you are short stacked, getting in the middle of a multi-way is often a bad idea, even with AA. The math doesn't lie. Try running the same situations with less than AA and you'll really see what I mean. Short stacks need to play heads-up, period. Remember this on your next bubble. No scrums when you're the little guy.

[slydeni]

LOL- now that is a funny post!

BUT-- I think its wrong -- DEPENDING ON YOUR MOTIVATIONS.

If you wanna make money over the long haul--- you FOLD!
if you wanna gamble and play poker for fun -- you gamble and love the action!!!

wait wait! before you call me names. This is definitely str8 out of a Sklansky book - TPFAP maybe? Here are two arguements for the FOLD!

1. The sklansky one: FACT #1: you are a champion backgammon player; FACT#2: you have $500 in yer pocket and can get no more. SCENE: A guy wants to flip you coins right now and is gonna give you 2-1 on the flip...but he's only gonna flip you for $500 (everything you have in yer pocket). BUT tomorrow you are gonna get some Backgammon action that you are a sure favorite to win money at, and not for your entire bakroll. whatta you do?

answer::>> you take the backgammon action. Why gamble with yer case $500 on a situation (even if yer a slight favorite) when it may break you??? Get the money in the long haul!!

2. The math answer::: Lets say you are 50% to win with the aces. AND YOU CALL. So 50% of the time yer gonna have 12000 chips. This will give you a 80% chance to win tourney (of course these are approximations not taking into account skill, and such). The other 50% of the time you have 0 chips and 0% chance to win the tourney, or make money.

so EV is:: .8 x 50 + .2 x 30 = $46. -- won with aces
50% of the time--->> so its $23 EV.

--- now... if we dont call we lets assume we make the money 100% of the time to keep it simple. so we'll have 3000 chips, one dude will have 9000 and another 3000. we have 20% chance to win.

--->> so when we fold the aces:: .2 x 50 + .4 x 30 + .4 x 20 = 45 (if we do take ties into account it will be a bit lower...but not lower than $40).

--->> so... when we fold the aces our EV is +40 ish (taking the ties into account).

---->>> when we call...our EV+ is +23.

I think I'll hold off on the frying PAN!

sly

[slydeni]

DONT GET caught up in the ties... it may lower the EV a bit...but certainly not from 45 to 23.

FOLD them bad boys!

sly

[Frogistador]

[ QUOTE ]
wait wait! before you call me names.

[/ QUOTE ]

Not to worry. I have to admit that I didn't read this thread very carefully at all. Sarcasm is my Pavlovian response to the "Should I fold AA" threads.

/images/graemlins/grin.gif

[FoldingAAPolice]

SIR, I'M GOING TO HAVE TO ASK YOU TO STEP OUT OF THE CAR, DROP THE CARDS, AND PLACE YOUR HAND BEHIND YOUR BACK.

YOU ARE UNDER ARREST FOR THE CRIME OF POSTING ANOTHER 'SHOULD I FOLD MY AA PREFLOP' THREAD, THE MOST USELESS THREAD POSSIBLE ON THIS FORUM. YOU HAVE THE RIGHT TO REMAIN SILENT AND ANYTHING YOU SAY CAN AND WILL BE USED AGAINST YOU IN A COURT OF LAW. PLEASE GET INTO THE POLICE VEHICLE AND COME WITH ME TO THE STATION WHERE YOU WILL BE STOPPED FROM EVER POSTING THIS THREAD AGAIN.

THANK YOU FOR YOUR COOPERATION.

[sofere]

Wow...someone went through the trouble of creating a new handle for the express purpose of that post. Thats gotta tell you somethin.

[FirstClash]

But people seemed to like to analyze it and it's helped me understand similar senarios and what's important when deciding whether to hold or fold.

For example. If it's correct to fold AA's in this senario, then there's no question about KK, QQ, JJ, TT, AK, AQ, KQ, etc. Now I may be simplifying it and might get some responses about how it's not so strait forward with some of the non-paired cards. But in any case, knowing how close of a call it is here makes it easier to fold the others in similar senarios.

This also gives me a reference point that I can start adjusting variables... like now it's only 2 people all in before you with only 4 people left... Seems clearer to call with AA now. But what about KK? Another variable for me to look at later. By taking an extreme example you won't see very often, then applying the same math in more common examples, patterns form and with that I learn the principles I need to play better.

In any case, I found people's responses humerous at times, very insightful at other times, and really got me thinking about different angles I hadn't considered.

Thanks for all your responses.

[Roland Deschain]

[ QUOTE ]

--->> so when we fold the aces:: .2 x 50 + .4 x 30 + .4 x 20 = 45 (if we do take ties into account it will be a bit lower...but not lower than $40).

--->> so... when we fold the aces our EV is +40 ish (taking the ties into account).

---->>> when we call...our EV+ is +23.


[/ QUOTE ]

I realize this thread is basically over...but, I couldn't understand the discrepancy between this statement and earlier scenarios using similar assumptions that indicated it was a much closer decision.

So I looked at this math...and as far as I can tell:

.2 x 50 + .4 x 30 + .4 x 20 = 30, not 45.
(0.2 * 50 = 10; 0.4 * 30 = 12; 0.4 * 20 = 8)

So now it's $30 for the fold vs. $23 for the call. And I suspect the difference is a little conservative based somewhat on not factoring in ties, and somewhat on what seems to me a slightly low estimate of how often the AA holds up.

Not saying that it turns it into a clear call. Just saying this argument actually lines up pretty well with the earlier posts showing it as close. Can't access twodimes from work to check the odds of AA against various hands, or (more interestingly) to see how other hands like KK, AKs, etc would hold up.