One of the beauties of match play is that a player can tell their opponent that they don't have to play their next shot; it's good.
Sometimes, giving putts or other shots -- a concession or a gimme -- is a courtesy. You know your opponent will make that 2-footer for par. You know you're going to make your birdie putt, so you don't need to see your opponent hit their putt. Your opponent is struggling and you know you'll win the hole, so there's no need to put them through the paces.
However, sometimes, giving putts or other shots is a strategy. Sometimes, golfers will give their opponents lots of putts early in the round, preventing them from hitting the knee-knocking 3- and 4-footers that will save holes. They do that so when the match gets tight later, they can for their opponent to make those putts without having faced that pressure throughout the match. It can be unnerving.
Then there's the idea of trying to use concessions as a way of getting a player out of rhythm. If a player likes to take a lot of time over each putt, then conceding a putt to them to get to the next hole sooner could flummox them -- particularly if you wait for them to largely get through their pre-putt routine before giving the putt.
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In team match play -- foursomes -- then there's the added dynamic of teammates having putts on similar lines but for different scores. If one partner has a longer putt for par while the other partner has a shorter one on the same line for birdie, then it makes sense to concede that par putt in hopes that the lack of a free read might make the player putting for birdie miss.
But that's all on the greens. There are sometimes when it's just the right thing to do to concede the hole.
When you're in a position on a hole where you find there's basically no way to win the hole barring some kind of meltdown, it's a wise idea to concede the hole. There are several reasons why.
The obvious one is pace of play. You can move on to the next hole and not play extraneous shots.
It's also good for your psychology. You may have just put two in a row in the water, and there's no need to potentially keep hitting poor shots. Stop the cycle, give up the hole and spend a minute instead thinking about what went wrong, clearing out the bad thoughts and hitting the reset button.
It also may have an impact -- to your benefit -- on your opponent's psychology. If you give up the hole when you're clearly not going to win, then your opponent doesn't get the emotional benefit of potentially making that birdie or par putt that will get the adrenaline pumping more than simply winning the hole without having to finish. The opponent might then be on a more even keel after you take a short break following the concession.
Psychology is an important part of all competitive golf, but it's particularly relevant in match play situations. If you know how your mind works and how you can use the rules to control the psychology of your opponent, you have a better chance of winning.