How to improve replayability in a game
Most of this amounts to "vary the experience", which of course is what provides replayabilty--varied experience.
Variable rather than set starting positions (players choose their starting positions)[drawback:lengthens the game]
More than two players (each player provides variability of himself)[drawback:lengthens the game]
Asymmetric game (starting position is not the same for all players)[drawback: makes it much harder to balance the game (give each player an equal chance of winning)]
Use of event cards (especially in symmetric games or games without other chance factors)[drawback--can be seen to increase chance]
Multiple ways to win/multiple winning strategies[drawback: makes it much harder to balance the game]
Scenarios (which amount to differences in positions or victory conditions (or both)). Used primarily in historical games. [drawback: more time-consuming to design]
Optional rules. Again seems most common in historical games. Alternative ways to play the game. At some point, many rule choices in a game design are largely arbitrary, that is, one choice leads to just as interesting a game as the other choice, but the designer must choose one. The other can become an optional rule. [drawback: virtually none, if the optional was tried sufficiently in playtesting]
Thanks for the comments so far.
Variable board is a version of variable setup, but should be explicitly mentioned. Ditto player-constructible characters.
Metagaming is another I should have thought of, but I tend to think in terms of boardgames these days, not CCG where metagaming is common.
Luck inevitably the variation of experience, but is not suitable for all games.
"Increase player interaction" (whether it's trading of auctions or something else) should be added.
Freedom of choice, at least as I first interpreted it, increases variabiilty, and at the same time is likely to lengthen the game. In fact, as I read the suggestions, I realize that most (if not all) methods of increasing replayability tend to lengthen a game at the same time, because they are increasing the number of choices available.
I'm afraid I don't see how restricting choice can improve "what if" or replayability.
"Enjoyable experience" is of course important, but depends almost entirely on the player. Some people want lots of plausible choices, some people want a few. Some people want as few restrictions as possible (which leads to longer games), some refuse to play a game longer than an hour regardless. Some enjoy "deep thought" (classical play), others enjoy "take that" (romantic play). Presumably if players enjoy a game they're more likely to replay it, but I don't see how we can alter a design on the basis of enjoyability because it varies so much by person. (Or to put it another way, if we could be sure what "enjoyability" was, we wouldn't have to worry about anything else in design.)
Lew Pulsipher