Cribbage is a card game that lends itself to a solitaire of strategy, perhaps better than any other. You can win at cribbage more often than at most card game solitaires; but solitaire cribbage invokes more skill than other solitaires.
Deal six cards to your hand and two to a blind crib (most players do this in a 3-2-3 sequence. Whatever the sequence, however, you must deal to yourself first, because of what you do with the turn card later, which will be shown). Throw two cards from your hand to the crib, on top. Then turn the card on top of the deck (and peg two points if it is a jack).
You get to count both your hand and the crib, but the play is against the crib. Play one card from your hand; then play the bottom card (one of the two you have not seen) from the crib; then, another from your hand; then, the other card in the crib that you have not seen, and so on. The rules and scoring of play are the same as in regular cribbage, but you score only your own points in the play, not the crib's.
Count both your hand and the crib, and peg the points from both. Then turn the turn card over, face down, on the deck again (it becomes part of the next hand), and place the used cards face up on the bottom of the deck. The first card face up at the bottom becomes the turn card in a free crib at the end of the game; so it is important which discard is on top (a jack is usually best, as you get to score two points for it when you reach the free crib; a five is usually the second best choice).
Deal again, throw, turn, play, count, return and discard as before, and again, and again, and again, and again - you will find that there are six hands and cribs to play and count in the deck. After the sixth hand, you will find four cards left face down on the top of the deck. This is the "free crib," and the first card beneath them, face up, is its "turn" card (for which you get to score two points if it is a jack). Count these five cards, and the game is over. If you have scored more than 120 points (i.e., passed the end of Fourth Street on the board, as in regular cribbage), you have won.
Here's a variation you can use to enhance your chance of winning. Before stacking the first hand face up at the bottom of the deck, peek at the four bottom cards in the deck. That way you will know which is the best discard to place on top for the "turn card" of the "free crib" at the end of the game. (Some might call this cheating; but, if it's part of your rules, who's to call it?)
Throwing to the crib in solitaire cribbage is a little different from throwing in a two-handed game, because it is always offensive, never defensive; the other two cards in the crib are never the product of an opponent's defensive throw, but always random. Thus you can expect more of the crib than you can playing two-handed; you will find fives, sevens, eights and jacks as often as other cards.
In this alternative version of solitaire cribbage, you play not only against the board but also against the deck. You win either by passing Fourth Street or by beating the deck (and you can count two games won if you do both).
Peg your own points as in the first version above. For the deck, peg the points the crib wins in the play; in the count, peg for the deck the total of points you would have scored had you thrown to the crib for a maximum count. Thus you will never beat the deck in the count, but you often will in the play (since you are playing with eyes wide open and the crib is playing blind).
You may wish to keep track of the points you lose to the deck by not maximizing your throw. You can do this with poker chips, matches, toothpicks or similar dilcods, or with cribbage pegs if you have a three- or four-track board. If at the end of the game there are no such points lost to the deck, you have scored a "perfect game" (which you still may have lost, if the crib has tied or beaten you in the play, or if you count only passing Fourth Street as a victory). Counting these points and adding them to your final score will tell you also when you "coulda shoulda woulda" won a game had you maximized the throw.
I kept statistics on a series of 100 games of this alternative. I found that my average deficit in not maximizing throws to the crib was 10 points a game (9.98, to be exact); so you could call a 10-point-deficit game "par" (5, a "birdie"; 0, or "perfect," an "eagle"; 15, a "bogey").
I counted as games won both those in which I beat the deck and in which I passed Fourth Street (scoring two games won if I did both). By this reckoning I won 27 of the 100 games. I "coulda shoulda woulda" won 51 more had I maximized my throws to the crib, indicating a 78 per cent winning potential. But I scored only three "perfect" games.
Also, I was skunked (did not reach Fourth Street) 23 times, but the deck itself was skunked 10 times; so net skunks totaled 13 (blame the others on the cards). I was never double-skunked, and neither was the deck.
If you like solitaire but get tired of winning and losing merely on dumb luck, you'll like this game. And then I'll teach you how to play solitaire euchre [see Natty Bumppo's Columbus Book of Euchre for details].