Equity

The share of the pot a hand is worth by its chance to win: its average value, not the actual result.

Equity is the share of the pot your hand owns by its odds. The cards are not turned over yet, but the money on the table is already divided: a hand that wins 80 times out of 100 owns 80% of the pot. Not because that is how this hand will end, but because that is how it ends on average if the same cards are dealt a thousand times.

It is counted by enumeration. Take two hands and every card that can still come, and see who wins in each case. On the turn there are 44 cases, on the flop about a thousand, before the flop 1.7 million. No one does it by hand; a program does it in a second. When the opponent's cards are hidden, the count runs against every hand he could have arrived with, and equity becomes the average over that set.

An example from session 3

A♠A♦ against K♥K♦, both stacks in before the flop, $121.46 from each side. Enumerating all 1,712,304 run-outs: aces win 81.71% of the time and split another 0.46%. By equity the hand was worth $75. The deck fell my way and I took +$118. The 43-dollar difference is a gift from the deck, not a merit of the decision. On another day the same aces lose, and the decision is exactly as right.

What it is for

Equity is the only way to judge a decision apart from its result. The result of one hand says something about the deck; equity says something about you. Everything else grows out of it: compared with the price of a call it answers whether to pay or fold; summed over every hand of a session it gives EV, what the session was really worth.

A common mistake is to count equity against a single opponent hand, the most convenient one. The opponent rarely shows his cards, and the real share is counted against the whole set he could have arrived with. Against one pair of kings the aces have 82%; against a set of «any pair and ace-face» it is less, and it is the second number that costs money.

The same in business

A deal that closed was not necessarily good, and one that fell through was not necessarily bad. Equity is the habit of judging a decision by the share it had at the moment of deciding, not by what came out later. An investor whose one deal in ten pays for the fund looks at the portfolio as a pot: every position has its share, and it is the sum of the shares that counts, not the fate of one.

The whole hand is in session 3: “Results and decision quality are kept in different books”.

The other terms are in the glossary.