Challanging Ed Miller's Criticism of Lee Jones

[Ed Miller]

There is another reason (using Bayes Theorem) to discount the likelihood that your calling opponents have an ace. That is that your opponent MIGHT have raised if he had an ace.

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 (of course, he could be slowplaying... but that doesn't matter... all that matters is that he might SOMETIMES find a hand worth raising).

This idea is also explained beginning on p.308 of SSH... River Hand Example #9.

[Al Mirpuri]

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Certainly all sorts of factors come into play here. tolbiny mentioned an important one. With only 3 seeing the flop it is much more likely that there are players in the game willing to fold weak Aces... Even a 10% drop in the number of players would play any A would mean you may be leaving a TON of chips on the table, if you fold KK before showdown.


One thing that I'm not sure is clear from you posts is what you would do in the case that you get called on the flop. Obviously, all sorts of factors come into play but in general are you looking to go into check/call mode and get to showdown as cheaply as possible or check/fold mode?



I hope you don't mind the play on words with your typo...

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I’ve done quiet well there so far

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I did QUIET well too until I realized I wasn't nearly agressive enough and my game needed work. My results aren't quite so QUIET...

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There is little value in pointing out poor diction. It certainly does not invalidate the argument.

[Al Mirpuri]

Would you have believed it?

[razor]

[img]/images/graemlins/confused.gif[/img]

[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

[Blarg]

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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

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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.

[jedi]

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Consider these factors when looking at your profit/loss analysis:

1. The Mystery Hand—if he does NOT have the Ace, may see his opponent betting into him religiously and not see his hand thru to the end—he may well fold on the turn or not call the river.

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Well, this HAS already been taken into account. You're playing against a player that will take his losing hand too far.

[Leavenfish]

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Consider these factors when looking at your profit/loss analysis:

1. The Mystery Hand—if he does NOT have the Ace, may see his opponent betting into him religiously and not see his hand thru to the end—he may well fold on the turn or not call the river.

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Well, this HAS already been taken into account. You're playing against a player that will take his losing hand too far.

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Just time for a quick note.
Too far can simply mean a desire to see the flop with Ace/Little...or even to see the turn, or thru the river...to automatically assume that the Mystery Hand--be it Ace/Little (with a likely win) or 5,6 off--will always go thru the river is what the calculation is based on. That's simply not realistic.
If you are going to realistically try to figure your win rate in the equation (for those occassions when Mystery Hand does not have an Ace), you have to place your profit from...well,lets say on a continum of 1 (dropping after the flop) to 5 (always calling/betting thru the river)...at about a 3.5 or 4 or whatever it may be and try to factor that into the equation. It's unrealistic to assume maximum profit 100% of the time.

[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