First came Cribbage, in which the first player to complete two laps of the board (121 points) wins the game. The card-counting rules for Cribbage are quite standard and are widely available.
Next came the slightly more devious Anti-cribbage, played only once around the board (61 points) to save time, in which all card-counting rules are the same,* except that one wins in Anti-cribbage by not going out first and must strategize accordingly. (*Muggins is usually not claimed, for obvious reasons.)
The general strategy in Anti-cribbage is to minimize your own chances for card-counting and pegging points while maximizing those of your opponent. At times this can be quite challenging, especially if you are stuck with the crib.
Now, for the truly twisted, there is Quantum Cribbage!!!
Quantum Cribbage, so named because of an indeterminate strategic wrinkle, follows the same card-counting rules as the other two games, despite lasting for only half a lap of the board (31 points). The wrinkle is that going out first either wins or loses the game, depending on which player has dealt the final hand.
This is because the end-of-game rules are designed to vary from hand to hand, alternating between Cribbage and Anti-cribbage.
Each game of Quantum Cribbage opens by cutting for the deal, but with a twist. Low card earns the deal and the first crib, as in the other variants, but in Quantum Cribbage the cut also specifies an alternation order: if the two cards in the cut are the same color (both red, or both black), then all odd-numbered hands are played under Cribbage end-of-game rules (first to go out wins) and all even-numbered hands are played under end-of-game rules for Anti-cribbage (first to go out loses). The order is reversed for a non-matching cut (one red, one black).
For example, if your Quantum Cribbage game starts with an Anti-Cribbage cut (red, black), then going out will win you the game during the second or fourth hand but lose it during the third!
Fortunately, Quantum Cribbage games are fast, as well as frequently hilarious, so the inevitable miscalculations don't leave much of a mark. Individual games run on the order of five minutes and average about two or three hands apiece, so they are admirably well suited to being played in sets. An unusual combination of alternation and uncertainty gives Quantum Cribbage gameplay a surprising degree of strategic sophistication. Cribbage and Anti-Cribbage fans alike can expect hours of entertainment from this variant on an old classic.