The number underneath everything
Equity is the share of the pot your hand is worth right now, if the rest of the cards were dealt out and the hand went to showdown. Not how strong it feels, not how often it is ahead. The share.
On the turn, with one card to come, there are 44 cards you cannot see. Every one of them is equally likely. So the calculation is not an estimate at all — it is a count:
That is the whole thing. Everything difficult about equity is working out which cards win, and the shortcut everybody learns is a way of avoiding exactly that work.
Where the rule of two comes from
One card out of 44 is 2.27%, so each out is worth a shade over two per cent. Round it down and you get the rule people quote:
Nine outs gives 18%, and the real number is 20.5%. The shortcut is a little pessimistic, which is the right direction for a shortcut to err — you will occasionally fold something marginal, and you will never call something you should not have.
It is a good rule. It is also doing something very specific, and it stops working the moment you use it for something else.
The first lie: times four
The rule has two versions and they are not interchangeable. On the flop, two cards are still to come, so it is outs times four. On the turn, one card is coming, so it is outs times two.
Reaching for the wrong one does not make you slightly wrong. It doubles your answer, and it doubles it in the direction that makes every call look profitable. Nine outs on the turn is 20%, not 36%, and there is a very large difference between those two numbers when somebody has just bet the pot at you.
The second lie: not every out is an out
This is the one that costs real money, because it survives knowing the first one.
An out is a card that wins. Not a card that improves you. Those are different sets, and the difference is invisible if you only look at your own two cards.
You hold two spades and there are two more on the board. Nine spades left, so nine outs, so 18%. Except the board is paired. Two of those nine spades pair it again, and the flush you just made loses to the full house they already had. You do not have nine outs. You have seven, and you were about to call a bet priced for nine.
The same thing happens with straights. The card that completes yours can complete a better one, or put a third suit out and hand them a flush. Count what beats them, not what helps you.
The two ways to get it wrong
The wrong answers in the game are these two errors and nothing else, so a miss tells you which one you made.
Counting as if two cards were still to come
Times four is the flop rule. On the turn there is one card left, so it is times two, and using the wrong multiplier doubles your answer.
Counting outs that improve your hand but still lose
Look at what the card does for them as well as for you. A flush card that pairs the board, a straight card that makes them a better straight — these look like outs from your side of the table and are not.
How the answers here are worked out
Every equity in this game is exact. Not simulated, not looked up, not estimated — the game deals all 44 remaining cards one at a time, plays each hand out, and counts who wins. Ties count as half to each side, which is what a split pot is.
That matters because you can check it. Every other equity trainer shows you a number from a simulator and asks you to trust it. If you disagree with a number here, you can deal the 44 cards yourself and find out which of us is wrong.
What equity does not tell you
Equity is how often you win. Whether to call is a different question, and it needs a price — which is what pot odds are for. Equity above the break-even price is a call; below it is a fold. The three games are one calculation split into its parts: count the cards, turn the count into a percentage, compare it to the price.
It also assumes the hand goes to showdown with no more betting, which real hands do not. Money still to go on the river cuts both ways: it can make a draw worth more than its equity when you get paid, and worth less when you are bet off it.