Alright Buzz, we are on the same page with regards to fresh money equity (which as I stated before is the same as pot equity, except you multiply it by the bets going in instead of dead money in the pot to get the absolute number). Given that we know we have a "fresh money" equity edge with top set (you may not believe this yet, but hopefully you will), I will argue until my lips bleed that you can't be making a losing play by raising. Raising may not always be the
best play, and you provide several important reasons for that throughout this thread. However, when you contend that it is a losing play because your hand is "drawing", you imply that it does not have "fresh money" equity, which I think is wrong.
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You can absolutely come up with a mathemetical realtionship between the two: EV=pot equity x total amount in pot (including your calls)-amount to call.
[/ QUOTE ]I'd like your mathematical expression better if you put “total amount in pot” minus the “amount to call” in parentheses. In other words I'd like it better if you subtracted the amount to call from the total amount in the pot before multiplying by pot equity. See the difference?
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I see the difference. But the correct way to calculate EV using a percent equity is to include all of the bets that will go into a particular betting round, and then multiply that by your equity. The thing that you are getting hung up on is that your net "win" in a split pot case is less than when you scoop when looked at from the perspective of the middle of the hand—you can only "win" half of the dead money in the pot. However, when you include
everything in the pot, including your calls, then the amount you "win" in a split pot case is exactly half of when you scoop. And it is the total size of the pot that is important in an equity calculation since you will get back, on average, your equity share of bets being put in
currently as well as the dead money.
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But although computing pot equity seems relatively simple without a split pot, arriving at pot equity in a split pot seems more complicated to me.
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It is more complicated when you try to use the traditional "I have x outs and my pot odds are y to 1; do i have a call?" since, as you alluded to, the amount you can win in a split pot is less than half of y. By using percent equity and including all bets put into the pot by the end of the betting round, you can avoid cumbersome calculations. To see how this is case re-read the example I provided
here
Once you have convinced yourself that percent equity works and can be used to calculate EV and "fresh money" equity, try out the following calculators:
ProPoker Tools Simulator Twodimes Calculator
Try to come up with as many possible scenarios as you can to have top set on the flop texture we've been talking about. I think you'll find that top set will have better than fair share on "fresh money" equity.
But in case you still don't believe me, chew on this for a bit. You stated earlier that 2/3 of the time with top set you'll be drawn out on and won't win anything. Of the 1/3 that you win, 6/11 times you'll have to split with the low. Well let's use these numbes to figure fresh money equity. Given n players in the pot, two out of three times we will lose a bet. 6/33 times we'll win n/2-1 bets and 5/33 times we'll win n-1 bets. When n=4, we are losing 1/33 of a bet with each bet that is going in. With n=5, we are clearly
winning with each bet put in. I believe your numbers are less accurate for the cases when there are fewer players (n=4 or less) because you overestimate the number of times all the draws are out against you, and you underestimate how often your opponents may have the same draws, thus eating up outs. With 3 or fewer opponents, not all low cards will fill a straight. You may even occasionally win half on a flushed board. Given these possibiliities, I think even your calculations will allow that putting extra money in with top set can be a winning play.
Hopefully that clears up the argument I've been trying to make. I hope I've at least been able to help you think about how to use equity at the tables, if not convince you that raising top set is not a losing play!