Full disclosure: I don't much care for bounty tournaments. To my mind, the bounties diminish the prize pool. However, the play in them is generally weaker than in tourneys of the same buyin price, and I've recently cashed in three of the last four I played. So I thought I'd write about them and what strategy adjustments to make, and what ones not to.
What is a Bounty Tournament?
In a bounty tournament, a portion of your buyin goes to a "bounty" on your head rather than to the prize pool. This bounty goes to the player that knocks you out. If you win, you get to keep that chip. For instance, one of the tourneys I played recently was a $60 tournament with a $10 bounty. So when I bought in, I was given my seat assignment, my stack of starting chips, and a $10 chip that went into the pot when I was all in. Whoever wins that pot gets that chip and can cash it out at the end of the tournament. So in addition to whatever you might win from your finish in the tournament, you also get money for every person you knock out.
In bounty tournaments, you don't have to get "in the money" to show a profit. If you knock out enough people, you can sometimes win more than people who cash in the bottom of the money even if you don't cash. This is rare, but at the very least, you often will get one or two knockouts that will defray your tourney costs those times you don't cash.
The prize pools are proportionally smaller. And to make up for what you lose in prize pool,you need to gather a lot of bounties. In a typical bounty tournament, you would need to collect 17 bounties when you won to make up for the amount of money that was taken from first place.
Strategy adjustments in bounty tournaments depend entirely on the size of the bounty. Typical bounties are 1/8 to 1/5 of your buyin. "Big" bounties are 1/4 to 1/3. With typical bounties, you should make almost no strategy adjustments except to realize that some people will be calling all ins more often in their quest to collect bounties. Bluffing and semi-bluffing all in are therefore less desirable actions when your fold equity is less. However, the bounties aren't worth much in these tournaments, and you shouldn't really adjust your play to look for them. Keep your eye on the prize and try to cash these tourneys and let the bounties come naturally in the course of play.
In Big Bounty tournaments, strategy changes a little, as getting six bounties will often pay you the same as a minimum cash. Still, don't put your tournament life on the line for a third of your buyin. You do want to play the short stacks a little more liberally as you only need to take out three of them to be on a freeroll. Also, you can now bet into a protected pot when a short stack is all in to try to hog their bounty if they missed.
Try to remember that the profitably of bounty tournaments doesn't come from the bounties; it comes from the bad strategy adjustments poor players make in their eagerness to capture them. Stick mostly to optimum tournament play and only take very small extra chances to gather a bounty and you will do very well in these events.