These two terms are sometimes used as if they are synonymous. They’re not.

Every starting hand sorted by position and opposition, comes with a price tag. Some of them cost money (-EV) and some win money (+EV). These price tags do not show how much money you will win or lose this particular hand, but how much money you can expect to win. Expected value. It’s that easy.

For instance, pocket aces figure to be worth about 3 big bets to me when they’re dealt to me on the button in limit hold ‘em. I win the most with pocket kings, overall. I’ve won more in total with AKo than with AKs, but that’s not because AKo is a better hand, it’s just that I get it a lot more often so the cumulative total is greater even if the price tag of the hand itself is smaller.

There’s another value that can be associated with each hand… if all other hands around the table are known. Equity, or “chance to win.” For instance, if three people see the flop, each of the three hands will have some chance of winning. The sum of their chances to win is of course 100%.

If we always knew everyone else’s hand, we could easily (well, maybe not so easily, but there are computer programs to help us) calculate our exact chances of winning, and therefore make what Sklansky calls “the perfect play.” But we don’t know our opponents’ exact cards so instead, we have to rely on ranges to help us. For instance, an extremely tight player might raise only with the big pocket pairs and AK/AQ. So when he raises, we have a fairly narrow range of hands to look at, and we need to try to guesstimate our chance of winning against that range.

This is pretty basic stuff.

Here’s where I’m going with this, though: Using a program like PokerTracker and looking at a large sample of limit hold ‘em hands, I believe you will find that the “equity” of the hands (i.e. how often they win) correlates fairly well with their EV price tag. A hand that figures to win often, will usually also average a larger amount of money won. Hopefully that makes sense to you.

But: If you do a similar search on a large sample of no-limit hands, you will likely find much less of a correlation. Certain hands with mediocre equity suddenly show huge profits. Some hands that have good equity, may be over-all losers. Like ace-ten offsuit.

Does that make as much sense to you as the statement about limit hold ‘em above?

When playing no-limit, we should not focus on hands that win pots but on hands that win money. When playing limit, especially short-handed, the two are much more correlated and we can make plays based on equity because that’s easier. Not so with no-limit, where we should look at expected value rather than equity.

Equity: Wins pots.

Expected value: Wins money.

It’s difficult for a hand to win money if it can’t win pots, but it’s not difficult for a hand that wins pots to lose money.

Edit: I feel I phrased the sentence with “you can expect to win” clumsily. I did not mean to imply that you’ve earned the right to a certain amount of money. I was merely trying to paraphrase what “expected value” means; it’s the average of all possible outcomes.