Still, this got me thinking about whether any playable game could be created using ambigrams. That second issue is the pitfall—it's hard to think of a way to make ambigrams an integral part of the game rather than just an irrelevant gimmick like they are in the card game linked above. In fact, the only workable way I could come up with offhand is to make the players create the ambigrams.
So, basically it would be sort of like Pictionary, except that instead of drawing pictures, the players would draw ambigrams. Which means there'd need to be at least four players, so you could have at least two teams and at least two players per team, one to guess the word while the other's drawing. Having the players try to draw symmetric ambigrams that read the same word when rotated or reflected wouldn't be feasible for practical reasons; without some sort of odd mirror arrangement, there would be no way to enforce the symmetry. So it would have to involve drawing an ambigram that read different words. Also, it would be more practical to have the words changed by rotating rather than reflecting, because it's easier to turn the paper over than to show it in a mirror. (Though reflective ambigrams could be an optional advanced rule.)
My first thought was to have cards with two related words on them for the player to draw ambigrams for. But then I thought it might be more interesting to have cards with only one word each, and have the player draw two cards—he probably wouldn't end up with related words that way, but the number of possible combinations would be much higher.
So, basically, one player would draw two cards and then try to draw an ambigram for the two words; the other player(s) on his team would then try to figure out the words. Once the words were guessed, he'd draw another two cards, and so on, trying to get his team to guess as many words as possible within the time limit. If there were two words he just couldn't do, he'd be able to pass on them, but at the cost of a fifteen-second penalty (or perhaps some other time; this could be refined in playtest, maybe—or maybe the penalty wouldn't be necessary, since the time just to draw the words and consider ambigraming them would already be enough).
Initially, I'd figured that if the other players were having trouble guessing a word, the drawing player could try redrawing or refining the ambigram in play. But then I realized this led to a major loophole. Suppose the words were, for example, SQUAT and OLIVE. Now, suppose the other players got OLIVE, then were stuck on SQUAT. Technically, if the drawing player is allowed to revise his ambigram however he wants during play, he could now "revise" it by just writing the word "SQUAT"—since his team had already guessed "OLIVE", the fact that the word looked absolutely nothing like OLIVE when inverted wouldn't matter. For that matter, he could just write "OLIVE" to begin with, without bothering to make it look like anything when inverted, and then after his team had "guessed" that word he could "revise" it by just writing "SQUAT". Obviously, this would defeat the entire purpose of the game.
So arbitrary revisions are out. I considered ruling that the ambigram couldn't be revised in play, but that just guessing one word was sufficient, and that the team didn't have to guess both—but, again, then the drawing player could just write one word without bothering to make it look like anything when inverted, so that doesn't work either. To avoid these fatal loopholes, I think it's necessary to disallow the revision of an ambigram in play, and to require them to be guessed in both orientations to be scored.
But then that might make the game too hard—most people are going to have a very hard time, given two arbitrary words, to get something that looks halfway recognizable. So to make things a little easier, maybe after the players guess a word, if it's wrong, but some of the letters are right, the drawing player can write down the correct letters. For instance, if instead of SQUAT they guess SAVOT, the drawing player can write S____T, and the rest of the team can keep guessing from there. That might make it easier... but then, does the team have to eventually guess the whole word, or can they get "partial credit"? Maybe give them credit for whichever fraction of the word is smaller; if they guess "OLIVE" but can only get the first and last letters of SQUAT, they get 2/5 of a point? But then, aside from the inconvenience of adding fractional points (and I can think of a simple way around that), this leads to yet another loophole; what if the player writes, say, the first half of each word right-side up followed by the first half of the other word upside-down, so he quickly gets half credit for each word, and then can rush through them that way, getting only half-credit for each word but doing it so quickly that he gets more than twice as many words as the person who tries to play it as it's meant to be played?
For that matter, another fatal loophole still occurs to me, even without the partial credit rule. What if the player just writes one word right-side-up, next to the other word upside-down, and claims it as a single ambigram? Obviously, this goes totally against the spirit of the game and makes it way too easy, but it's hard to think of a rule that would disallow this (or similar workarounds) without also disallowing some legitimate attempts at making a good ambigram. (I mean, yeah, I could make a rule explicitly about not doing that, but the player could claim that he's trying to make a genuine ambigram but it's just accidentally looking like the two words combined with one upside-down.) Hm. I have to think further about this. There may be a way to tighten up the rules to avoid any such loopholes, but it's going to take some work to figure it out. Any suggestions?
Actually, maybe I'm worrying too much about this; I mean, these "loopholes" are pretty far-fetched. Really, along the same lines, one could argue that a player in Pictionary could just write a word and claim he's drawing a picture and it just accidentally looked like the word. Sure, he could claim that, but the other players aren't going to let him get away with it. So... yeah. I'm probably overthinking this.
Of course, even if I do manage to tighten up the rules, there's still one major flaw in the game: it would probably have a very tiny target audience. I mean, I enjoy creating ambigrams (and I think I'm pretty good at it, though I certainly don't have ceruleanst's experience and skill), but I don't know how many other people do; there are probably a lot of people who enjoy seeing ambigrams but have never tried creating one on their own, and don't have that much interest in doing so. Then again, the rules about "partial credit" and so on may make the game somewhat accessible to ambigramming neophytes... (Plus, really, if most of the players are more interested in seeing ambigrams than making them, you really only need two players who are interested in trying to create ambigrams; you can have the same players drawing the ambigrams throughout the game, if you want to.)
You know, I'd initially thought of this as just kind of an intellectual exercise, but if I can come up with a sufficiently rigorous set of rules I'm actually tempted to publish this game now, through the print-on-demand press ceruleanst linked to earlier. Maybe I will, at some point, though with all I have on my plate it probably won't be for a while.
I will call it "Ambit".