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Interesting Stats on Pocket Aces   

Phil Gorden started a column over at ESPN. He included in his latest entry, a table detailing the chances of Pocket Aces against Pocket Kings in subsequent hands. This'll be old hat to some of you, but I found it interesting so I'm posting.

Quick note: This is when you are holding pocket aces and you're opponent has pocket kings. It basically details the cumulative chance (like in a tournament) that you will survive an all-in holding pocket aces.

Mr. Gordon says this, "Over the course of 7 days of play, 10 hours of play a day, you face this situation 14 times. 14 times you'll have to "not get unlucky" in order to win the tournament. What are the chances?"


AA vs. KK
Chance of All In Survival

1 81.26%

2 66.02%

3 53.65%

4 43.59%

5 35.42%

6 28.78%

7 23.39%

8 19.00%

9 15.44%

10 12.55%

11 10.19%

12 8.28%

13 6.73%

14 5.47%


He goes on to say, "From this little table, you can see that you only have slightly better than a 50% chance to survive the first three of these confrontations! 46.35% of the time, you will have taken a bad beat and be joining me and the rest of the poor saps at the Palms Hotel's Ghost Bar, where we will seriously consider throwing ourselves off the 55th floor."



Here's the link in case anyone wants to read the entire article. Not the greatest poker article, but interesting.

http://sports.espn.go.com/espn/poker/columns/story?columnist=gordon_phil&id=2015263

  [ Views: 3258 ]  


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Interesting Stats on Pocket Aces
Authored by: DevilFlush on Friday, March 18 2005 @ 09:43 AM EST
Of course, this assumes that we are the shorter stack every time.

If we've doubled through twice with pocket Aces, chances are we're a decent stack--the one time in 5 that we get beat, the pocket kings guy would have to have us outchipped or be able to cripple us--otherwise on average we'd have another 4 double-throughs with the Aces before we lose another hand

...so basically what I'm saying is that if the bad beat comes early, we're out, but if it is delayed by 1 or 2 from the average, then it doesn't affect us nearly the same as it ordinarily would, since we'd have doubled through 5 or 6 times already before the beat.

The point is that AA vs KK will hold up 4 out of 5 times, and the 1 time it doesn't, we'd only be in big trouble if the KK happened to come from a large stack relative to ours, which becomes increasingly less likely with each successive double-though.

---
2nd Place at the 2009 WSOP

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Interesting Stats on Pocket Aces
Authored by: DevilFlush on Friday, March 18 2005 @ 10:00 AM EST
Also, run the same test on any hand vs any other hand--this is likely the best odds situation you can have.

---
2nd Place at the 2009 WSOP

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Interesting Stats on Pocket Aces
Authored by: dletter on Friday, March 18 2005 @ 09:51 AM EST
This "statistic" seems to be a little bit like thinking you can predict that black is "due" to come up in roulette because red has hit 10 straight times.

Yes, the "odds" of you winning all 3 AA vs. KK matchups is 53%. But, if you won the first two, what are the odds you'll win this third matchup?

Yes, its still 81.26%. It's an INDEPENDENT trial folks. The cards on that 3rd hand don't care what the first two did.

And really, its not AA vs. KK, its AA vs. ANY pair, because they just need to hit the trip to beat you, even if its 2's.

So, don't psych yourself out that you should fold your AA's because you won the first 2-3 times, and now your odds are 40%. Your odds are still, and always will be, 81.26%.

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Interesting Stats on Pocket Aces
Authored by: messiahmoose on Friday, March 18 2005 @ 09:58 AM EST
I don't think he's telling anyone to fold pocket aces because you're right, your chances are still 81% that particular hand.

What he's saying is that bad beats are a part of poker. In a tournament if you're pocket aces are busted you shouldn't fly off the handle because that's poker, and chances are they WILL get busted at some point during the tournament.

Additionally, more often than not, the winners of the tournaments are the folks that either, a) Didn't get unlucky and won when they were supposed to, b) Got lucky and won when they weren't supposed to, c) [and most common] a little bit of both.


---
Part of the "24hrStr8" Club

[A♦][5♦]

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Interesting Stats on Pocket Aces
Authored by: Tokenizer on Friday, March 18 2005 @ 10:11 AM EST
Just a note...

you took the only three possible outcomes of that situation to make a statement which says anyone who wins a tourney *has* to fall into one of those categories. Are you a lawyer or something?

---
Life would be so much easier if I had the source code.

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Interesting Stats on Pocket Aces
Authored by: jcbloch on Friday, March 18 2005 @ 11:02 AM EST
IMHO, Phil is being a bit reckless with statistics. Though I do agree with the original poster ("I don't think he's telling anyone to fold pocket aces because you're right, your chances are still 81% that particular hand."), I think I will be contacting Phil to give him a piece of my mind.

Phil is ignoring "Bayes". Sure, he is right with his math ( if the odds of AA beating KK is 81%, the probability of AA beating KK n times is 0.81^n.) But, what he is calculating is the a priori conditional probability of a certain isolated event, and quite frankly that don't matter much in a poker tournament. Said another way, the only way I get to come up against an KK with my AA requires that I am still in the game. In real-life the actual conditional probability of winning that n-th AA-KK battle depends heaviliy on what happened before that battle. For example, assume that I somehow manage to play only hands where I am a huge favorite (don't ask how) and assume that I play 1/10 of all hands dealt. Mathematically, assume that the probability of me winning each hand is p = 0.90. Now, assume that I see a KK against my AA every 221 hands. When I see my first AA/KK battle, i've played about 21 or 22 hands (1 out of every ten). So, the probability of reaching this moment in time is the product of all the probalities of all those 21 hands. For this thought experiment, assume I was always a 9:1 favorite. This yeilds 0.9^21 = 0.10 or 10%. Wow, I only have a 10% chance of seeing that first AA/KK battle. If somehow I win that one, I have another 10% chance of seeing that second AA/KK battle-- or 1% from the beginning. That is, one might extrapolate, and say, on average (I am assuming "ergodicity" here), only 1% or 50 of the 5000 players might ever play long enough to see 2 AA hands.

ok, calm down. I admit there are problems with my "thought experiment". In real games, one doesn't win on the strength of his/her cards alone (a priori probability) but rather, if things go well, on one's betting skill also. That is, my thought experiment shows how important it is to win pots independantly of one's a priori probilities (based on delt cards). Basically, if you play only 9:1 favorites, you won't likely live to see AA even once, so why worry about seeing it 4 times? Instead, one needs to (1) concentrate on winning pots without showing cards and (2) realize that when one does need to win by having the better hand, prior hands have no roll whatsoever in the outcome, ever. That is, the probability of AA beating KK is, as Phil puts it, still 80% or so.

-jcbloch

(yup, Andy's big brother)

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Interesting Stats on Pocket Aces
Authored by: Tokenizer on Friday, March 18 2005 @ 10:07 AM EST
I think in general people know the odds and know that they are the same vs any pair.

The point he's trying to make, and it's not done in a very good way, is that you have to get lucky every now and then to win a big tourney. There is plenty of skill used to build stacks but it can all change if you are against someone equally skilled to build a large stack and get unlucky with a hand that you may get in with preflop like AA vs KK. A pro can fold pocket QQ and below here against a large stack.

This is more or less an article to online monkeys that think AA is unbeatable and you can win tourneys by waiting for only the premium hands and just jamming the pot at that point. He's trying to say that what seems unlikely will happen if the chances of it happening are better than zero. He would have been better off explaining in more detail how "violent" a game like holdem is. Holding two cards and getting five shared cards makes preflop odds a much different animal than say 5 card draw. It's this "violent" aspect that makes it fun and challenging.

Phil obviously forgets to mention the fact that pros won't just go allin before the flop with a drastic overbet and they know when they are beat so it's not like AA is make or break hand. I'm sure every pro on the tour has a hand they like to "play" much better than AA.

---
Life would be so much easier if I had the source code.

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Interesting Stats on Pocket Aces
Authored by: EmmSee on Friday, March 18 2005 @ 10:49 AM EST
Well yeah Phil@!# With Aces.... I think we all know that since you're only a 80% fav, you're going to lose 1 out of every 5 AA vs. KK ... That's all it comes down to.

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Interesting Stats on Pocket Aces
Authored by: badtony on Friday, March 18 2005 @ 11:35 AM EST
I especially thought about this line: "Bottom line is this: being all-in gives you an opportunity to be all-out."

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