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Position in poker is the order in which players are seated around the table, and the strategic and tactical consequences of this. On any betting round, the player who acts first (called being "under the gun") has a distinct disadvantage compared to those who act later (who are said to be in "late position"), because the later players will always have more information on which to base their decisions. You are said to "have position" on players who act before you in a betting round, and are said to be "out of position" to those players who act after you.
Because players act in clockwise order, a player seated on your left is said to "have position" on you in the game in general (not just a particular betting round), because he will act after you far more often than he will act before you (the latter will only occur rarely, such as when you have the button in a rotating-deal game). It is said that money flows clockwise at a poker table, your goal being to interrupt the flow as it passes though you. For this reason, players' seats are always drawn randomly in tournaments, and are occasionally redrawn during play. When there are only two players (called being "heads up"), neither has position in general as the players alternate who acts first on each deal.
Stud games, in which the first player to act on each betting round is determined by upcards, are called "non-positional" games, because players generally can't use knowledge of position to plan strategies for future betting rounds (though relative seating still matters). Other games like Draw are extremely positional, and in fact one's position relative to an opponent can be more important tactically than the cards you hold.
Here's an example from Texas hold'em: There are 10 players playing $4/$8 fixed limit; the player to the left of the button (let's call her Angela) pays a $2 blind, the next player (Bill) pays a $4 blind, and you (Charlie) are next to act. If you have a hand like K♣ J♠, you should probably fold. With 9 players remaining to act, the chances are reasonably high that at least one of them will have a dominating hand like K-Q or J-J that you will be unlikely to beat, and of those remaining 9 players, 7 of them (all but the two players in the blind) will have position on you in the next three betting rounds. Now let us suppose instead that you are Ian, and the button is to your immediate left in front of John. Charlie, Donna, Eve, Frank, Gina, and Harold all fold, and you now find the same K♣ J♠ in your hand. Now things are different. There are only three players left to act, so the odds that one of them has a dominating hand are considerably less. Secondly, two of those three (Angela and Bill) will be out of position to you on later betting rounds. The play here is to raise, and hope that this will convince John (the only player who has position on you) to fold. You might even steal the blinds if they don't have playable hands, but if they do play you will be in good shape to take advantage of your position.
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