[Catt]

Nice value bet explanation, though I'd add that a value bet also needs the condition that you'll likely win money by betting. Even with the best hand, if you know your opponent will fold to the value bet, then there is no value in betting -- you win nothing additional by betting or raising.

Pot equity is a little different from your explanation, though. Your "pot equity" is the amount of the pot that is "yours" by virtue of the strength of your hand.

A few pot equity examples. HU you have a flush draw and Villain has a strong made hand on the flop. Assume you will win if you hit your flush and Villain will win if you don't. Your pot equity is ~35% since you will win on the river about that often. If the pot is 10 SBs, your pot equity is about 3.5 SBs and Villain's is about 6.5 SBs. Every bet that goes into the pot before you hit a flush costs you 0.65 BBs since Villain is "entitled" to 65% of the pot and all bets going into the pot. If there are three others in the hand (and your flush will still beat everyone else), you still have pot equity of about 3.5 SBs; but Villain's pot equity will go down depending on the strength of the other player's hands. You might have 35% equity, Villain might have 40% equity with a strong hand, and the three remaining players might be sharing the remaining 25% of the available equity because they are behind and drawing pretty thin. You "own" 0.35 of your bet and evryone else's bets that go into the pot; Villain "owns" 0.40 of your bet and all other bets. With four callers, your bet or raise costs you 0.65 bets but "earns" 0.35 bets X 4 players or 1.4 bets, for a net gain of ~1 bet for every bet or raise you make. Your share of pot equity determines whether or not betting or raising is appropriate (disregarding for a moment non-equity reasons to bet/raise such as bluffing, semi-bluffing, attempting to buy a free card, etc.).

If your own pot equity is greater than your "fair share" (the total pot divided by the number of players without regard to the relative strength of hands), then a bet or raise is generally called for. Going back to the flush draw example, HU your equity is only 35% whereas your fair share is 50% -- you don't want to be betting or raising because you don't have an equity advantage. With four opponents, your equity is 35% versus a fair share of 20% -- you generally want to get as much money as possible into the pot without losing more than two players (and reducing your fair share below 35%), even if you currently do not have the best hand (provided you think a flush wins the hand -- if you knew your opponent flopped a full house, your equity sucks because hitting the flush still doesn't win the hand for you).

Hope that helps.