A buy-in is the initial amount of money a player exchanges for chips when they sit down at a poker table to start their session. In a tournament, this money is exchanged for some amount of tournament chips which are not redeemable for cash; in a ring game, the money is exchanged for chips with the same cash value as the player exchanged.
In ring games chips can often be purchased directly from the dealer. He is usually required to verify each transaction with the floor manager before handing the chips to the player and depositing the cash in a secured drop box underneath the table. To save the dealer time, some casinos require players to purchase their initial stacks from the cashier, however the player can still rebuy from the dealer in smaller cardrooms, often larger rooms employ chip runners to relieve the dealers of this duty. Always ask the casino staff about their specific rules before playing.
All modern poker games have a minimum buy-in. In games with blinds, the buy-in is usually ten times the big blind, and in games without blinds it is usually ten times a small bet, but it may vary: ask the casino about the rules for the game you wish to play.
Some variants may also impose a maximum buy-in. In particular, no-limit games often do this at their lower limits to prevent excessive bullying by the big stack at the table. For example, imagine a player sitting down with $10,000 at a no-limit table where all other players have $100. The player with $10K could simply move all-in preflop on every hand, forcing the other players to play for their entire stake in any hand. Almost regardless of his cards, eventually the big stack will win and win all the other players' money.
At higher limits there is often no maximum buy-in, even at no-limit tables.
If the game being played imposes a maximum buy-in, a player may never purchase chips in a quantity which would bring their total chipstack above that maximum buy-in. They may win more chips than the maximum buy-in, but if they wish to buy chips, they may only buy enough to bring them up to but not over the maximum buy-in for the table.
Exceptions to the minimum buy-in
In general, any new player at a table must buy at least the minimum buy-in of chips in order to join the game. However, if a player is joining a game because they are from a broken game of similar stakes, they may enter their new game only by carrying over the amount of chips they had at their previous table, even if that amount is less than the minimum buy-in or over the maximum buy-in. If a player changes tables due to voluntary table change, they must follow standard buy-in rules and buy-in at their new table for some amount between the minimum and maximum buy-ins.
A player may also rebuy additional chips while they are within a single session, though not while they are within a single hand (see table stakes). In most cases, casinos allow a player to rebuy additional chips in a quantity less than the minimum buy-in, though casinos generally have rules (sometimes complex rules) limiting the number of times a player may do this. A rebuy for fewer chips than the table's minimum buy-in is called short buy.