[Buzz]

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Mathmatically the analysis that the case Ace may be one of the cards NOT held I think fails to take into account the fact that if the Ace was one of the 36 other cards dealt to one of your opponents,....

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Mendacious - Good point.

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....chances are it is still in play.

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Well... sort of. I'll fold lots of hands with poorly connected aces, and I think I'm not alone. A78Kn, for example is a horrid starting hand in a limit game, and not even the worst example I could come up with. Hard to estimate the percentages, but I'll maybe fold a third of the hands with aces I'm dealt.

Thus a truer breakdown in a ten handed game would be somewhere in between 20/45 and 36/45 - maybe closer to 30/45 than either of the extremes in a ten handed game. I play mostly nine handed, so that I'm thinking 28/45 is a better estimate than 20/45 for my usual games.

At any rate, I'll call it 30/45 instead of 20/45 for a ten handed game. On reflection, I agree 30/45 is better than 20/45. (Maybe 31/45 is even better for some very loose ten handed games).

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Which means that in reality you are probably a little better than 65% likely to win the hi.

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No.

Hero is slightly better than 65% to encounter an opponent with an ace - but that opponent still has to have a card the same rank as one of his other cards appear on the turn or river - and without also a deuce or a jack on the river or turn. For that there are several cases, the most common of which is the case where the opponent with the ace has no other cards matching Hero's cards and also has no pair. And that figures to about 288/820.

(2/3)*(288/820) = 0.234.

That makes Hero slightly better than a three to one favorite to win for high.

Hero should bet to charge the lows to draw and also to charge any other possible opponent with an ace to draw.

36/45 is not correct for the probability of facing an opponent with an ace - but even using 36/45 makes Villain's chances to win <font color="white">_</font>for high only 28% or so.

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AGAINST ANY HAND WITH AN ACE and two low cards you are a 60-40 DOG!!!

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I don't think that's true. If you give Villain a hand with an ace plus two low cards, Hero is a dog, because Hero can rarely, if ever, make a winning low while Villain is a big favorite to make a winning low when it is possible, which is more often than not thus forcing Hero to split most of the time. But it's more like 55 to 45.

And, considering that this is a limit game and Hero has multiple opponents, that is not the situation anyhow. Hero is not one-on-one with an opponent who has the case ace plus two low cards.

It's possible Hero could end up that way, and it's possible Hero could lose this hand - but there are also various other possibilities that I think are much more likely.

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Therefore, in PL, I check this hand and the ONLY cards I even consider calling on the turn are high cards.

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You'd be making a huge mistake playing that way, even in a pot limit game.

You're still at least a 72 to 28 favorite to win for high, even in pot limit, when you hold A22J and the flop is AA2. Even if nobody ever folds a hand with an ace and you're playing in a ten handed game.

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Plug in some other Ace hands in two dimes and see how bad off you really are.

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Now you're giving your one opponent an ace plus a probable cinch for low. Without bothering to run it, I'll grant that Hero is a dog.

But let's make Hero's hand and the flop what they are (A22J and AA2), and let's give Villain a hand that simply contains an ace plus three random cards.

Isn't that more reasonable?

And if you do that, it's about 51 to 49 in favor of Hero. (I just did the sim, using Wilson's simulator which, unlike twodimes.net, allows such a distribution of known cards plus random cards).

Hey, I'm surprised it was so close. I thought Hero would be way out ahead. And Hero is way ahead for the high end. But the lack of a decent low after being double counterfeited hurts Hero more than one opponent with an ace plus random cards. Neither Hero nor Villain with one ace plus three random cards makes low 5774 times in 10000, but when somebody does make a winning low, 4226 times in 10000, it's almost always Villain with the winning low.

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...but I am thinking about this in Pot Limit terms which makes it much worse of a hand.

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O.K. I see that. Interesting.

It was very clear to me way before this thread that limit and pot limit are very different games. I try to stay out of pot limit posts for that reason.

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I suppose in limit you probably do bet it and hope your hi holds up, and a couple lows come along for the ride.

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No doubt about it in my own mind. You bet it and expect your high to hold up, and you also expect some lows to chase along, and maybe some poor high draws as well.

You seem to think Hero's high is not favored to hold up. But in truth, Hero's high is favored to hold up. I'll grant that Hero, having been already double counterfeited by the flop, has crap for low. But sometimes nobody will make a low and Hero will scoop. Most other times several opponents will make low and Hero will make high and get half the pot, after having contributed less than half the pot.

Sure, Hero can lose for high. <font color="white">_</font>But that's not very likely.

You made a good point about opponents tending to play starting hands with aces and got me to recognize 20/45 was not the correct probability of encountering an ace. I don't think 36/45 is right either, at least for a typical limit game. But 30/45 is probably closer to the truth.

Thanks for that correction. Very good correction.

Bottom line: In a limit game Hero should definitely bet that hand/flop! Hero is about a three to one favorite to come away with the high half of the pot (even in a pot limit game) - and with vigorous betting might end up scooping and at least figures to end up with more than he contributes to the pot.

Just my opinion.

Buzz