A raise, and especially a check-raise, as a bluff is more psychologically intimidating than just opening. Of course it also risks more of your money and makes the pot bigger (and therefore more likely to be called), so it must be used with care.
Sandbagging
Sandbagging (also called "slow play") is deceptive play in poker that is roughly the opposite of bluffing: betting weakly with a strong holding rather than betting strongly with a weak one. The Check-raise is one such play.
This might involve a check or call with a hand that you might otherwise raise with, to lure other players into the pot who might fold to a raise, or to lure them into betting more strongly than they would if you had bet or raised. This is often dangerous because it sacrifices the Protection that a bet or raise would give you, and it also risks losing the pot-building value of a bet if your opponents also check.
It can nonetheless be profitable to do this under circumstances that include the following:
• Your hand is so strong that protection isn't needed.
• An opponent is likely to bet when you don't.
• Opponents are likely to fold or just call if you bet.
Even in games (such as California lowball) where the check-raise is not allowed, one can make other sandbagging plays such as just calling ("flat calling") instead of raising with a very strong hand and then later raising.
In games with many betting rounds, such as stud poker and community card poker games, one can make multiple-round sandbagging plays. Let's say, for example, you are playing Seven-card stud and your first three cards are all fours. An opponent with a king showing bets first, and you raise, getting two callers. On the next round, the first bettor catches another king, and you miraculously catch the last four. You suspect he has two pair or three kings, and he suspects that you have two pair or three fours (four of a kind is so unlikely that he will probably ignore the possibility, just as you can probably ignore the possibility that he has four kings). He bets again, and you just call. You should probably just call for next round or two, and maybe even check if no one bets, rather than raising, for several reasons. Your hand is so strong that the chance of getting beaten is negligible, so you don't need protection. If the bettor just has two pair and you act strongly, he may think you have three fours and fold if he doesn't improve. Allowing other players to continue for smaller stakes might allow one of them to catch a hand such as a straight, flush, or full house that will call your final bets or possibly even raise you back, building a very big pot. Finally, keeping as many players in the game as possible will make a bigger pot. At some point, though, you will have to "come out of the woodwork" and bet strongly; after all, the point of the exercise is to get more money in the pot, and you can't do that by continuing to check on every round.
Another common sandbagging play that occurs only on the last betting round is called "fishing for the overcall". This occurs when the last card you are dealt makes you a very strong hand, a player in front of you bets, and there are more players to act behind you. While you might normally raise with your hand, just calling may encourage the players behind you to overcall when they would have folded to a raise. This play is best when there are several players behind you, and they are the kind of player likely to call one bet but not a raise. If there is only one player behind you, for example, then getting the overcall gains no more money than raising and having the initial bettor call (at least in a fixed limit game). This play also sacrifices the profit you might have made from players who would have overcalled even the raise.
Game theory
Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics,
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