A3 versus A2

[DoubleDuke]

If I hold an A3 hand in a ten handed game what is the chance one or more pleasers will be holding an A2?
And what is the chance that one or more pleasers will be holding A3 or A2? (I mean at least A3 which will quarter me)
Does anybody know these figures?

[Buzz]

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If I hold an A3 hand in a ten handed game what is the chance one or more pleasers will be holding an A2?

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Double Duke - I'm assuming by A3, you mean A3XY, where X or Y is neither ace, deuce, nor trey.

If so, it's about a toss up.

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And what is the chance that one or more pleasers will be holding A3 or A2?

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The first time I read the word "pleasers," I thought it was a typo. But since you wrote the word twice, maybe not. What are "pleasers"?

Assuming "pleasers" is equivalent to "opponents," and again assuming by "A3" you mean A3XY where neither X nor Y is ace, deuce, or trey - and assuming by "A2" you mean A2XY where this time either X or Y could be another ace or deuce (but I'm wondering if it could be a trey - let's say it could be), better than even, something of the order of seven to three.

That is roughly seven for AA22, A222, AA2X, A22X, A2XY, AA33, AA3X, A33X, A3XY, AA23, A223, A233, or A23X (where X or Y is neither ace, deuce, nor trey) to roughly three for none of these. Something like that. Depends a bit on what hands your opponents will play.

Ace-trey by itself would not a good Omaha-8 hand.

But of course you never actually have ace-trey by itself. You always have two other cards to go with it.

There are hands with an ace and a trey that are poor starting hands. A378n ("n" means non-suited), and A377n, for example, are poor starting hands, probably not worth seeing the flop - probably not for even a half small bet from the small blind. And there are many various other poor starting hands with an ace and a trey.

But if the ace is suited to another card in the hand - or even when it isn't but the other two cards in the hand are not middle cards (sixes, sevens, eights, and nines) - or when only one of the other two cards in the hand is a middle card and the fourth card is a wheel card or queen or king (eg. A358n, or A38Kn), the hand is at least sometimes playable, though not great.

I remember Ray Zee (properly) took issue with me for suggesting that I'd usually play a hand with ace-trey. At that time I was sorry I'd answered a question about ace-trey, because there never is an ace-trey. There always are two other cards.

When you take A[img]/images/graemlins/diamond.gif[/img] and 3[img]/images/graemlins/club.gif[/img] out of the deck, there are 50*49/2 = 1225 two-card combinations left, and most of them are, for experienced and savvy Omaha-8 players, playable, even if not great.

Of course you need sense. When you hold A-3-6-9-double-suited, you have a generally playable, but not really very strong, starting hand. Then if the flop is 5-7-K with two cards in the same suit as your suited nine, you probably will want to have read Ray Zee's book to know what to do next.

But if I pull A[img]/images/graemlins/diamond.gif[/img] and 3[img]/images/graemlins/club.gif[/img] out of the deck, I can immediately pull another 21 other cards out of the stub that I'm going to play regardless of the fourth card (all the rest of the diamonds, the aces, the deuces, the fours, and the fives).
21+20/2 + 21*29 = 819, and that's over half the missing two-card combinations. And then you're surely going to play A3KK or A3QQ, suited or not, and that's another six. So almost immediately we have 825/1225 A3XY hands we're going to usually play for a single bet - and that's most hands with an ace and a trey. That's assuming you play well after the flop.

(And for most of the A3XY hands I think are playable, I hope the flop is not something like 5-7-K-suited-but-not-to-my-ace).

But ace-trey by itself? No. It's not very good.

Ace-deuce by itself is not very good either, in my humble opinion, although you maybe could usually get by playing it for itself alone.

But not ace-trey. You need something more to go with ace-trey. And then you have to play well after the flop.

Just my opinion.

Buzz

[DoubleDuke]

Buzz,
Thanks for your very comprehensive answer!
By A3 I mean A3 and two other cards not being an A or a 3 or a 2.
Pleasers are players and it was definetely a double typo.
(Maybe a Freudian typo, although in Omaha/8 my opponents don't please me much so far)
Do you happen to know where I can look up those kind of statistics?

[Buzz]

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Do you happen to know where I can look up those kind of statistics?

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Double Duke - No. I calculated them - and then ran various simulations as a check on my calculations.

There's some stuff posted in old r.g.p. threads that might be helpful to you, but finding what you want is tedious - and then weeding out the truth from mis-information is not always easy.

There are some excellent posters on the 2+2 probability forum. I imagine there are threads derived from them that might be helpful to you.

Buzz