Challanging Ed Miller's Criticism of Lee Jones

[Blarg]

[ QUOTE ]
For instance, say you think your opponent either has an ace or a lesser hand, and the chance of each is 50%. Also, suppose that he would check EVERY time, no matter what he has. But after you bet, he would check-raise with his good aces (say 50% with a strong kicker), and just call with is bad aces (the other 50%). He check-calls 100% of the time if he has less than an ace.

Thus, 25% of the time, he has a good ace and check-raises. The other 75% of the time, he check-calls, and you don't know what he has. But he has less than an ace 2/3 of the time (50% of the total divided by the 75% that he check-calls).

So his prior probability of having an ace was 50%, but after he checks and calls, he has an ace only 33% of the time!

You DO gain information when bad players check and call... you gain information that they didn't have a hand strong enough to raise

[/ QUOTE ]

Not strong enough to raise another paired ace.

But Leavenfish is talking about holding a pair of kings.

So he isn't getting quite as much nformation about the strength of a non-raising opponent's hand compared to his own as you suggest.

[Al Mirpuri]

Would you have believed it?

[Mike Haven]

I have calculated the following possibilities, using the actual numbers, if you have been dealt KK. For these, I have assumed that all opponents will see the flop if they are dealt Ax.

Pre-flop, the chance that one of your 9 opponents was dealt at least one Ace is 84.4%.

If the flop falls Axx, then the chance that one of your 9 opponents was dealt at least one Ace is 77.5%. You are behind nearly 4 games out of 5.

If the flop falls AAx, then the chance that one of your 9 opponents was dealt at least one Ace is 62.4%. You are behind more than 3 games out of 5.

If the flop falls AAA, then the chance that one of your 9 opponents was dealt at least one Ace is 38.3%. You are behind nearly 2 games out of 5.

(It doesn't matter if one opponent calls or nine opponents call your flop bet in the scenario where any opponent will see the flop with Ax.)

e&oe

[John Biggs]

Since the example concerns a three-way pot (only three players saw the flop), why don't you recalculate accordingly? The full table information isn't very useful here.

[Mike Haven]

it doesn't matter how many players saw the flop if there were ten players receiving cards

i have stated that in my calculations i assumed any player receiving Ax will see the flop - therefore, with this criterion, if only one player saw the flop and the flop was AAA there is a 38.3% chance that he has Ax - this seems odd at first glance, but you have to remember that the other eight players were dealt two cards pre-flop that were not Ax

incidentally, coming from the other end, an individual following the Ax rule of seeing the flop, "knowing" that your pre-flop raise means you have KK, will flop Axx almost once every five times he calls

[razor]

In a game where only 3 players see the flop there are players capable of folding weak/mediocre Aces.

[John Biggs]

I think you've put in a lot of effort to calculate on some very flawed assumptions. The results are therefore not just questionable but useless.

[Mike Haven]

the results are not questionable, and no correct results are ever useless

it may be that some players won't call with, say, A6o - that would affect real-life results to a minor extent

name the scenario and my programme should be able to give you the figures within moments

i am giving facts not recommendations - what you decide to do armed with the facts is up to you

[Ed Miller]

i have stated that in my calculations i assumed any player receiving Ax will see the flop - therefore, with this criterion, if only one player saw the flop and the flop was AAA there is a 38.3% chance that he has Ax - this seems odd at first glance, but you have to remember that the other eight players were dealt two cards pre-flop that were not Ax

This is not correct Mike. Again, Bayes' Theorem bites you in the ass. [img]/images/graemlins/tongue.gif[/img]

38.3% is merely the PRIOR probability that someone was dealt an ace. But the fact that only one player has called gives you a TON more information about the distribution of hands.

If that's not clear, then think about it this way. Assume that you know all nine of your opponents will play any ace, as well as a host of other hands like two big cards, a lot of suited hands, and some connected hands.

The flop comes AAA.

How likely is it that you are against an ace if all nine people called preflop?

How about if only one person called preflop?

What if zero people called preflop (yes, I know, there would be no flop in that case... assume you were rabbit-hunting)?

These numbers are NOT all 38.3%. [img]/images/graemlins/smile.gif[/img]

Here's a general rule for everyone. As soon as you get ANY more information about a situation, the probability CHANGES, and the prior probability is no longer correct. The number of people calling preflop is very significant information.

[John Biggs]

[ QUOTE ]
This is not correct Mike. Again, Bayes' Theorem bites you in the ass.

[/ QUOTE ]

My man!!! This is what I intuitively thought. If Mike doesn't have time (though it looks like he's pretty dedicated) I'll do the math myself.