A metaphor from American and Canadian Football.  A punt is a long kick downfield, after which the opposing team gains possession of the ball and attempts to advance it from the end point of the kick.

In these games, you have a certain number of plays 'N' to advance the football a specified amount of yardage 'Y'.  After N-1 plays, your team may realize it's statistically unlikely that you will get to Y in one more play.  You use your last play to punt, willingly giving the ball up to the other team, but (hopefully) in worse field position than they would have had had your team tried to advance the ball with their last play.

Subtly different from simply giving up, but sometimes used interchangeably.

''Not to belabor the point (or the metaphor), but there is another kick (in AmericanFootball anyway) that ''can'' yield scoring results, the FieldGoal kick.  The constraints on this kick are that you have to get the ball over the bar between the goal posts, and to do this reliably, you have to be within the distance the kicker can reliably achieve that result.  This is more of a "SettleForLess" solution where you don't come away empty-handed, but get half the points.''

''The punt, on the other hand, is the choice used when scoring is unlikely, or it is strategically better to have the ball deeper in opposition territory.  The election to punt has, therefore, a number of subtleties beyond "this is the only choice left."''

See also http://www.catb.org/~esr/jargon/html/P/punt.html