[Poker Clif]

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Two thngs.

First, 6 of your outs aren't outs to someone holding a J. So you might want to make the flop JsTs2h or something. Also, with the board paired, there will be as many as ten cards that make a full house by the river, so 7 of your flush outs and all of your straight outs will dry up as well. All I'm saying is that if your goal is to think of the combination of a hand and flop with the most possible outs that is not yet a made hand, don't pair the board. It discounts too many of your outs because of all of the redraws and the possibility a K or Q won't win.

Second thing is that your hand is a favorite here to win by the river even if you're not a favorite on each street. You get 21 outs twice, so on the turn you're (21/47) to improve and (21/46) on the river. There will be a million people here who understand this better than I do, but I think you end up being better than a 2 to 1 favorite against, say, a lower pocket pair like 88 or something.

And I realize my post isn't too precise, but the moral of mine is that a made hand on the flop isn't always better than a drawing hand.

Oh, one other thing--this is even more true when the pot is multiway. I'm assuming for the sake of simplicity that this is heads up. And by "better," I think you mean which hand will win the most pots when you might want to consider which hand will win the most bets.

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Thanks for the comments, they were just what I was looking for. As an intellectual and math exercise, I thought it was better for me to try to figure this out by myself, then have someone explain to me where I went wrong.

I understand the dangers of a paired board, and I'm surprised that in this context I didn't think about that.

I know you're right that I'm a favorite here. I have read that that's true. If anyone can help me with this, go for it, because I can't figure out why it's true.

If I have a whole bunch of outs, it's true that I have them twice, both on the turn and the river.

However one I thing I learned in my statistics classes is that "numbers don't have a memory".

There is no law of averges, that is, if my numerous outs give me a 48% chance of hitting, and I miss, that doesn't make it any more or less likely that I will hit on the river, which will be a 49% chance with one more "bad" card out of the way.

So, statistically speaking, we have fourth and fifth streets, two almost independent events (the extra known card on the river will make about a one percent difference in the likelihood of hitting one of my outs).

With each event, I have a less then 50% chance of hitting one of my outs. So how am I the favorite? What am I missing here?

Can any mathematicians out there help me with this?