out
An out is a card which, if drawn, would improve your chances of winning. Exactly which cards are outs depends very much on the situation and your estimation of other players. Counting outs is a speculative activity.
Hand Betterment
You can practice counting outs with this game.
The easiest case to understand is to simply consider an out to be any card which improves your hand; a card which gives you a hand better than what you have now. Usually you'd consider only significant changes, and not those which simply improve your kickers.
Outs can be used as a way to estimate your chances of winning via calculating your pot odds. This is referred to as counting outs.
Myrion is holding 6♣ 3♠ 6♦ K♣ in a game of five card stud. He has 8 cards which would improve his hand, that is, 8 outs. One of 3♣ 3♦ 3♥ K♦ K♥ K♠ would give him two pair. One of 6♥ 6♠ would give him three of a kind.
Comparative Betterment
Knowing which cards improve your hand is a good thing, but it doesn't necessarily help you in a real situation. Simply improving your hand may not be enough to win. What you'd really like to know is which cards will improve your hand enough to beat the other players.
This is wrought with pitfalls as it requires knowing what the other players have. As you will never know for sure, reasonable guesses will have to suffice.
We are dealing with three classes of outs: the guaranteed outs, the possible outs, and the potential outs.
Guaranteed Outs
Guaranteed outs will, with a reasonable certainty, give you the winning hand. These are outs which upgrade a hand from a mediocre to strong. Typically these outs will complete a straight, flush, full house or four of a kind.
Mack is holding Q♠ T♠ with on a flop and turn of 2♣ 5♠ 4♠ 9♥. He feels rather certain that a queen high flush would win and thus counts 9 guaranteed outs: the 9 remaining spades.
Possible / Potential Outs
Possible outs only exist in games with community cards.
A good draw for you could also be a good draw for an opponent. That is, although you think it would improve your hand, you have a suspicion that it would also improve the other player's hand. Such outs are called possible outs.
Similarly, there are always several outs that while technically improving your hand, don't assure victory. Your opponent may already be holding a stronger hand, discounting your interest in the card. These are known as potential outs.
Loreen is holding T♠ 9♠ and the flop shows Q♦ K♣ 5♠. A jack would certainly be good, but it'd open a straight for several other players as well. She'll consider that she has 4 possible outs. Though unlikely, she also considers that a pair of tens might just win. She'll consider them as 3 potential outs.
Generally both possible and potential outs can be considered equivalently when estimating your pot odds. You will to some degree discount their value.

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