[jai]

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Thus it seems to me as though the total amount in the pot multiplied by the probability you'll win the pot is your "pot equity."

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Yes. But this includes all bets put in the pot, including the ones from the current betting round (this means your bet as well), which is where the confusion is arising. In a traditional EV calc, you don't include your bet in what you can "win", and this creates a lot of headaches for figuring equity in split pot games by the normal means. Which is why percent equity is much easier to work with.

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I figure "expected value" (also known as "E.V.") to be the net you expect to win (if positive) or lose (if negative). In Texas hold 'em, that's based on the probability you'll win the hand, how much will be in the pot when you win, and what it will cost you to see the showdown.

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Just to make sure we're on the same page, let's see if we agree on the following analysis for HE (or any non-split pot game). On the turn, I have 20% equity (roughly equivalent to having 9 outs). You bet $25 into a $100 pot. Should I call or fold? Assume implied odds don't matter. Well, if I call there will be $150 in the pot (which is what I stand to win). My cost for playing is $25. 20% of $150 is $30, so I profit $5 by making the call. Note that we could have come up with the same answer by a tradtional EV calc (assume 45 unseen cards to make the math nice): EV= (9/45)$125-36/45($25)=$5.

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In Omaha-8 (or any split pot game) the issue is complicated by the split pot nature of the game. The plain truth, and you seem to clearly recognize it, is that <font color="red">when you scoop a pot, you actually win more than twice as much as when you win half a pot</font>. And because of this you CAN NOT simply multiply your half pot wins by two and add them to your scoop wins and use the combined total to correctly get your E.V.

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EV and pot equity are different things in this context. When we say you have pot equity of x%, we do not mean this number alone will give you EV. This depends on other things, like size of the pot, humber of players in, and the amount you have call.

Let's see if this example can show you what I mean. Your are playing PLO8. On the turn, you have nut flush and nut low draw. You know your opponent has top set with no other redraws and no blockers. He bets pot all-in for $50. Can you call profitably? Well, you have 7 non-pairing flush cards to give you a scoop. 16 low cards give you nut low, but 4 of them are already counted as flush outs. So that is 12 outs for half the pot. Let's assume 40 unseen cards. So 7/40 times you win 100 (+$17.50). 12/42 times you win 1/2. Now this is the tricky part. You will win only 1/2 of $50, the times you win low, not 1/2 of $100. So your net win in that case is 12/42*25=$7.50. 21/40 times you lose your whole $50 bet and get nothing back, for a net loss of $26.25. So that means we lose about $1.25 on average in this case. So how can we use pot equity to get the same answer? Well, we 7 outs to the whole pot, 12 outs to half, so we'll count that as 6. Thus out pot equity is 7/40+6/40=13/40, which is a little bet less than 1/3. Since at exactly 1/3 we would be getting exactly right odds to call a pot sized bet (1/3 equity*$150=$50, which is the cost of playing), the simple pot equity analysis shows us that we are making a slightly losing play by calling, just like the more thorough EV calc did above.


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Think of it this way, when you're playing heads-up and you split evenly for high and low, you win nothing. Two times nothing is nothing.

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Not exactly correct. You "win" 2x half the dead money in the pot (your net is zero in the heads up case, but that is not what is important for EV calcs). You win nothing on future and current bets.

Also, Buzz, I think you are generally a good poster, so I hope you don't feel offended by me challenging you on this point.