Can someone show me the math for this..

I want to understand why value betting in a situation where your against one or more opponents is correct - even though they have odds to call you.

For example, On page 30-31 of SSHE:

"Say you are playing $2-$4, and the pot is $44 on the turn. You have top pair, and your lone, loose opponent has four outs to beat you. If you bet $4, then the pot will eb $48 (the original size plus your bet), and your opponent will have pot odds of 48 to 4 or 12 to 1. Since that is more than the break even point for his draw (10.5 to 1 for four outs), he can call profitably."

What I want to know is that since he is making a positive expectation play by calling your bet, you must be making a negative expectation play by betting into him. I understand in poker that with every decision you want to MAXIMIZE your expectation. I think I'm missing a basic concept, and if anyone could show me why value betting here is right along with the math I would greatly appreitate it.

if u dont bet then you are giving him INFINITE ODDS to draw to.. so whats worse giving him odds at which he must call (giving you more money when he dont hit) or giving him INFINITE Odds..hmm thats not a hard question... so think about this.. when playing limit poker it is sometimes imposibble to control what pot odds u are giving ur opponent. so u must value bet and not worry about this in times like this..

Ok that makes sense, so basically if I check I'm losing even more expectation then when I bet right?

[Xhad]

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What I want to know is that since he is making a positive expectation play by calling your bet, you must be making a negative expectation play by betting into him.

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This is a fallacy. Your opponent can only profitably call because of the dead money already in the pot. He still loses money due to your betting (as opposed to checking), even though he gets to call your bet.

Look at it this way:

For the favorite: a bet your opponent can't correctly call > a bet that your opponent can call > no bet at all.

For the underdog: no bet at all > a bet you can call > a bet you can't call.

Since this is limit, as the favorite you can't give yourself the best-case scenario because you can't bet enough, but you can get your opponent out of HIS best-case scenario by betting.

Here's another way of looking at it:

Coming into the turn, the money already in the pot is up for grabs. The amount of dead money in there, as Zhad pointed out, makes it a favorable situation for both remaining players.

Now, you have to say to yourself, Do I want to give my opponent another even money bet on this hand?

Since his odds of winning are 10.5 to 1, of course you do.

[pudley4]

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What I want to know is that since he is making a positive expectation play by calling your bet, you must be making a negative expectation play by betting into him

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No, this is wrong.

You are correct in betting because you are the favorite to win the hand. Therefore you're making money on every single bet that goes in.

He is therefore losing money on every bet that goes in; however, the money that's already in the pot more than makes up for what he's losing by calling your bet. (And this explanation is another way to describe pot odds.)

[TiltSeeker]

Yes, the math here - we must consider this like we consider a sword to have two edges - as you said, because this dumb animal has retardly chased down, he should still chase down by what you say. Vote yes on legalized marijuana. Neways - the point of betting here is as follows. Forget the pot when you're playing limit - use the pot size to read your opponents, (how stoned are they?!). Now stop thinking about pot size and hear this. Each time you place a bet, think about your bet as under a bell curve with your greatest expected value of play highlighting only the furthest region from the origin. The greatest expected value of betting are the bets placed furthest obscured from the origin as possible (hopefully to the right). Every time you place a bet later in the hand(with your opponent still drawing to the same outs as he was) your string of bets is becoming further obscured from the origin; you are doing your string of bets a great service. All the bets leading to this last bet you speak of tend closer to the origin of the bell curve than the bets placed later in this hand, hence a more positive value created to place bets later because his odds of winning at that point are DRAMATICALLY decreased and therefor your point of betting is dramatically increased as you approach the end of the hand. If your opponents are chasing heavily, jam that bitch.

[TiltSeeker]

Is this my signature?

[OrangeKing]

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Ok that makes sense, so basically if I check I'm losing even more expectation then when I bet right?

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Actually, you're still gaining expectation with every bet that goes in, and he's losing expectation - just not enough to make it unprofitable to call (as long as he still has the odds). If you are 90% to win, 90% of every bet that goes into the pot belongs to you, regardless of whether or not your opponent has the odds to call. So by firing out that $4 bet, and him calling you've made about $3.20 (you "win" $3.60 of his bet, but 10% of your bet - or .40 - is his share).