Challanging Ed Miller's Criticism of Lee Jones

[Leavenfish]

I understand that Bayes Theorem deals with discerning the probability of one event happening given that another does. But instead of shouting the magic words "Bayes Theorem", could someone actually use some math to explain how it applies to the actual situation in question? We have a low limit game like occurs on Party Poker where most everyone tends to stay in to see the flop with an Ace/Any (I believe the odds are somewhere near 80% that someone in a 10 handed game was dealt an Ace); two people then call when an Ace appears on the flop and the guy with KK has bet...seems perfectly logical given the kind of game you are playing in and the calling of the bet when an Ace has flopped and given that there is such a good chance of someone playing an Ace/whatever...why would you think it only that "sometimes" you are up against AA as opposed to "probably"?

[Al Mirpuri]

[ QUOTE ]
If you've got your pocket Kings, it's a family pot, and an Ace falls, you have some reason to be cautious. But three-way is totally different.

It would be the same with any big pocket pair vs. a single overcard on the flop - say you've got JJ, raise preflop and get two callers, and the board comes with a Queen. Obviously you bet. If no one plays back at you, you bet the turn too assuming it's not scary.

[/ QUOTE ]

Wrong! Players are more likely to play naked Aces (as well as those with good kickers) than they are to play naked Queens.

[Al Mirpuri]

Well challenged, Leavenfish.

[Blarg]

Interesting point. My KK and QQ are getting slaughtered after moving from 1/2 on Party to 2/4, which is much looser and where a huge percentage of people play any Ace from any position, sometimes even for a raise and even cold-calling a raise to do it.

Obviously this kind of thing depends on the texture of the game you are in and is not a matter of a reliable, hard and fast rule. But generally, in my experience anyway in the 2/4 at Party, at least for the about 14,000 hands I've played it, you're right on the money -- if the flop has an ace in it, it's very likely that someone has just made a pair of aces.

[Phil Van Sexton]

As pointed out already, your numbers/assumptions are wrong. I'm afraid that your logic is so flawed that nobody of significance will spend time replying to this thread. I don't fall into that category, so here goes...

Here is some math....
After the flop, there are 47 unknown cards and 3 remaining Aces. The probability the no one was dealt an ace can be found as follows (I think). 44 non-aces, so 44/47 or 93.6% chance of not being dealt an ace for each card. The chances of the 18 dealt cards not being an ace is 93.6% ^ 18=30.5%. So 30.5% that nobody was dealt an Ace, or 70% that someone was dealt one. Not 80%.

Furthermore, not everyone plays every Ace. I know the players are bad on party, but there are still plenty of people who will fold A2o for 2 bets. I can't put a hard number of this, but it certainly changes things.

After your flop bet is called in the example, there are 4 big bets in the pot. To call down your opponent, you will need to put in 2 more bets on the turn and river. Therefore, you are betting 2 to win 6 BB (the 4 already in the pot, plus the 2 more that he puts in). You are getting 6:2 or 3:1 on your money. At 3:1, you need to win only 25% of the time to break even.

Ed's 2 points here are...
-When a fish simply calls, this tells you almost nothing about their hand.
-You must always factor in the size of the pot. Because of the size of this pot, it is profitable to show down your KK even if you lose 70% of the time.

[Randy Burgess]

-- by picking on a detail that I don't disagree with, but that doesn't affect my argument in the slightest.

[Leavenfish]

[ QUOTE ]
Bayes

[/ QUOTE ]

From what (perhaps little) I understand of Bayes Theorem in relation to poker, you have to be able to reasonably put your opponent on a particular hand—like the chances that a tight player will be raising or re-raising into you only with hands like AK, AA, KK—seems like I saw that in TOP or something. That is TERRIBLY hard to do at the low limits we are talking about. One thing you DO know, however, is that most people play Ace/Any to the flop and often deep into the hand. For them it is a ‘magical card’—pair it and you all of a sudden have top pair and hope your kicker holds up or maybe you can even pair it. It’s their mindset which is why it is so annoying and at times difficult to play against the throngs of them you encounter on Party when their collective stupidity reaches a critical mass when your good hand gets sucked out on.

Heck, come to think of it, maybe THEY are subconsciously looking to bring Bayes Theorem into play in the future in their decision to play A/Any….if one comes out on the board—knowing they already have an ace, they can then reasonably put you (the correct playing KK guy or whatever who raised) on something other than an Ace and feel confident that they at least stand to have what you started out with beaten. [img]/images/graemlins/blush.gif[/img]

Anyway, if someone can show me how Bayes Theorem applies here rather than simply waving it about magically as proof you should only sometimes think that your opponent has lucked upon the one thing that beats your pkt K’s in this situation…making “sometimes” more probably than “probable” that is, please do. The pot is pretty small, I can’t see the long term expected wins exceeding the losses in this situation when you reasonably only stand to improve most of the time with another King.

[Blarg]

[ QUOTE ]
One thing you DO know, however, is that most people play Ace/Any to the flop and often deep into the hand. For them it is a ‘magical card’

[/ QUOTE ]

I have been called to the river many times by people with Ace-rag who hit nothing on the flop or turn, but just hoped to spike an ace on the river. Sometimes they had to eat some raises to do it, too. And sometimes they then called me down with an ace-high only!

For people who don't regularly play these levels, at least at this site, it can be hard to believe this kind of thing happens very often at all. But...it actually does, in 2/4 at least. Not quite so much in 1/2 and 3/6, but more in 3/6 than 1/2.

However, people will sometimes think YOU are the one who paired the Ace if you keep betting when an ace hits the flop, so betting out can induce some folds you want to see happen. If you do have the best hand, it gets more money in the pot for you in case you actually wind up winning. And, finally, if someone has spiked an ace, with pocket kings you're pretty much screwed and with Kx, you generally need to spike your kicker without him having or spiking his second pair. Both not good long-shots. But I still bet out into an ace just in case. You may still have the best hand, and if you can get calls from many people, that helps balance out the extra bets you lose getting raised by and maybe calling down a better hand.

I think if you fold every time someone raises you when an ace hits the board, people will really start to walk all over you, too. Considering how crazy the games can get in the first place, I feel the last thing I need is people lining up to see who's going to pull a move on me first every time an ace or any overcard hits the board. People need to respect and even fear you a little bit at the table, I think, and that's worth eating a bet or two for sometimes.

Just my thoughts anyway. I could be a bigger winner than I am, so it's just throwing some thoughts out there.

[razor]

[ QUOTE ]
It’s their mindset which is why it is so annoying and at times difficult to play against the throngs of them you encounter on Party when their collective stupidity reaches a critical mass when your good hand gets sucked out on.

[/ QUOTE ]

Their collective stupidity also results in a some pretty nice, LARGE pots heading your way that more than make up for their suckouts...

[AKQJ10]

Bayes theorem is basically about figuring out the probability of the cause given the effect. This is a reversal of most "standard" probablility calculation (Given that 2 Aces are left in the deck -- cause, so to speak -- what's the probability of seeing one on the river -- effect).

To effectively use Bayes here, you'd have to have an estimate of the probability a certain opponent will act a certain way given a certain hand, the probability he'll act in a different way given the same hand, etc.. -- and then you need the raw probability of that hand, which is pretty easy.

Example: I estimate that Charlie will limp in with pocket 6's 30% of the time. I estimate that he'll raise 10% of the time and fold 60% of the time.

Furthermore suppose we also know that in general Charlie raises 5% of the time preflop, independent of his hand (or technically 5% WITHOUT 66). And of course we know the probability that he was dealt pocket sixes independent of his actions: 1/220, but for simplicity let's call that 0.5%. .

So if he raises preflop, what's the probability he holds pocket sixes?

Using the methodology on the Web site, let's envision 10K hands:

Group 1: Charlie holds 66 -- 50 hands
Group 2: Charlie holds something else -- 9950 hands

Group A: Charlie raises with 66 -- 10% of 50 hands, or 5 hands
Group B: Charlie doesn't raise with 66 -- 45 hands
Group C: Charlie raises with something else -- 497.5 hands
Group D: Charlie doesn't raise with something else -- 9452.5 hands, but I'm doing the math in my head so I may have made an error.

So if Charlie raises preflop, chances are 5 / (5 + 497.5) that he in fact holds pocket sixes.

OK, back to the issue at hand....

If you tried to answer the KK with A flop question by setting up multiple Bayesian formulations (preflop, postflop, check/bet or fold/call/raise on each decision, AA vs. Ax vs. xx, etc., each of 9 opponents) you'd soon have a problem too complicated to solve. But with simplifying estimates perhaps we can cut through the thicket:

<ul type="square">[*]Probability that three others limp in, irrespective of their hand [*]Probability that one of the three is dealt an A.[*]Probability that at least one of the is dealt a "good Ace" (which I'll define as a hand with an Ace that WLLH, SSH, or your favorite book would advocate entering with) [*]Probability that at least one of the three would limp in WITH any A. [*]Probability that at least one of the three would enter with a GOOD A (this should be 100% but might not be) .[*]Probability that all three would limp in without an A.[/list]
So yeah, even that's a lot of data to process, but perhaps we could do so.

I think you're better off knowing the probabilities but using well-informed intuition, and my partially informed guess is that the chances of someone playing A2o in any seat at microlimits is 80%. [img]/images/graemlins/smile.gif[/img]