Fold Equity

I've found both "Kill Phil" and "Kill Everyone" very interesting, and well-written. However, I am confused by the description of "fold equity" found on page 22 of the revised and expanded edition of "Kill Everyone." The authors describe it thus: "Pot equity is the expected value of the pot when dealt to showdown, with no more betting. Fold equity is the forfeited pot equity." However, in most other contexts, the term "fold equity" is used to describe the likelihood that the opponent will fold to a bet or raise, which has a lot to do with table image, position, and stack size and may not have a whole lot to do with the opponent's pot equity, which usually can't be known with any precision anyway in the course of playing a hand. So it seems to me that the authors' definition may not be "correct," and that when they and others use the term "fold equity" they actually mean something like: "the likelihood that an opponent will fold to a bet or raise." Any thoughts about this will be welcome!

"is used to describe the likelihood that the opponent will fold to a bet or raise"

It's not a likelihood, it's an equity. Thus, it's the probability your opponent will fold times what you gain when they fold.

Thanks for your reply wagon30. Your view is closer to the way I use the term, and I think to the way the book's authors use the term (which is not consistent with the formal definition that they give). So, yes, you can say that if I have a 20% chance of raising my opponent out of the $1,000 pot, my fold equity in the pot is 20% (which is a probability (a/k/a "likelihood")) or $200. Of course, those numbers could be vastly different from my opponent's actual pot equity, which we could only know if we could see all the cards at that point in the hand. That is, the opponent might well have a hand that is more likely than mine to win if dealt to showdown. If so, the opponent's pot equity is >50% and that is the sum that becomes the opponent's "fold equity" under the author's confusing definition when the opponent gives up. So you see that the bettor's fold equity in this example is 20% of the pot, while the opponent's fold equity as defined by the authors is >50%, and therein is the source of my initial confusion. I feel pretty confident that the way you and I actually use the term is what the authors really intended, and it makes a lot more sense than the formal definition that they put in the book.

No, because what I gain is not the pot. It is my opponent's equity in the pot. Your example is fine for the river, but in many situations I will have equity if my bluff fails. Thus, I'm not gaining the entire pot, just the amount of the pot my opponent had claim to.

(also, 20% is a probability/likelihood, $200 is not)

As for "seeing the opponent's cards," that's just how we do theory, we put our opponents on ranges of hands. By your logic, pot equity is a meaningless concept, because it too requires seeing the opponent's cards.

I guess you have misunderstood what I was trying to say - It seems I was not as clear as I had hoped, so I guess I can't bash the authors too much! To sum up, I think the author's definition of pot equity is meaningless (as a practical matter) because, as you say, it requires knowing the opponent's cards. In contrast, the practical definition of pot equity that you and I and most others use is meaningful - being the equity the bettor has in the pot due to the probability that the opponent will fold to the bet - I don't think we differ about this but somehow the words got in the way. Thanks for your thoughts.

Pot equity depends on your opponent's cards.

If I have AhAd and my opponent has KcKd, I have 82.637% pot equity. On a Qc Jc Tc board, I have 49.798% pot equity.

You are right that we don't know the opponents cards, so we usually put our opponent on a range of hands and figure out our equity against that range.

Exactly. And unlike pot equity, fold equity depends on the opponent's cards in an indirect and subjective way depending on how the opponent reacts to all those parameters I mentioned in my first post, and some I did not (position, stack size, table image, size of the bet, stage and form of the particular competition, what the opponent ate for breakfast, whether he or she is tilted, etc.). As you described the notion of fold equity (correctly, I think): ". . . it's the probability your opponent will fold times what you gain when they fold."