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Message: [QUOTE="zachvac, post: 646618, member: 26306"] I wrote my response before I saw this, and he basically said some of what I said, but I have a question about whether the end of this is right. If we are beating every opponent head on (including draws and such, not just at this moment), are we guaranteed to be +ev? In fact, this is definitely false, as we'll see in a second with my example (AA having A9 instead). Mostly right, but it doesn't matter if we're ahead of each of them, it matters if overall we are 10% to win each hand or better. That's all that matters. Getting 2nd place every hand doesn't win any money, and if we can beat all but one in most situations (which I believe will be the case in my example), we still beat everyone the majority of the time, but the small majority of the time they beat us, they beat everyone. As I mentioned, there is. Nice analysis, and correct about the suited not mattering. Trips cannot win the hand, any hand we have that will win the hand will also beat a flush, thus we can ignore the flush (which further emphasizes the fact that comparing against single opponents, where the flush WILL impact our head-to-head percentage, it does NOT impact our overall percentage thus we can ignore it). So about that example, where AA has A9 instead. Let's look at each head to head. A9 vs. 99, flop=963, he only wins with running aces, we win every other time, we have him dominated. KK, QQ, and JJ vs. 99, He has 2 draws to 2 outs, we're the clear favorite 66, 33 vs. 99, he has 2 draws to 1 out, we're the clear favorite again 87 vs. 99, this is the best hand against ours, as he is drawing to 8 outs, has 2 shots to do it, plus if the suited cards match one of the board's suits he also has runner-runner flush draw. But we have re-draws of 6 outs if he hits the straight (another of whichever card completes the straight, or a 6 or 3). But although he has a good draw, and he may have odds to call in a hand against us if we don't bet big enough compared to the pot, he is still obviously the underdog here, as simply drawing to 8 outs even with 2 cards to come is not greater than 50% (1-(37/45)(36/44)) = 32.7%. Runner-runner draws (also some re-draws for us) are not enough to make up the difference and make them a favorite 45 vs. 99, pretty much identical to the above with different numbers to straight, same concepts though, and should be identical percentage. 75 vs. 99, again, pretty much the same percentages, this time it's not a straightforward open-ended draw, but there are still 2 cards to fill the straight, thus a very similar percentage. We are again the favorite. But because we have such a strong hand, we end up in 2nd place a lot. So although we're ahead of every hand and the majority of the time we beat each individual hand, we end up in 2nd place a lot, thus counting for us beating 8 of our 9 opponents yet winning 0% of the pot. So we come away with 4.926% to win (according to pokerstove) and we would NOT call if we saw A9 flipped over rather than AA. [/QUOTE]

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