I'm not a big fan of Chess - it has too much memorisation and menial computation for my taste - but I do partake on occasion. Sometimes my wife challenges me, and she almost always wins. But there was one game I like to mention from time to time which went differently. We opened with a few turns of reasonable seeming moves - I brought out my queen, she responded with her horses. Then I noticed an opportunity for check and just went for it, even though I expected I'd probably lose my queen in the process. She reached to respond and then paused, looked closer, furrowed her brow, and laughed. I looked back at the board to see what the fuss was about, tried to work out which move she was considering and.. couldn't find any. I'd somehow stumbled into a scholar's mate and she - not expecting any such trickery - had fallen for it. Cue obnoxious gloating.
Another time my friend Martin challenged me to play without a board. We exchanged a few moves, it began as an interesting intellectual exercise, but before very long at all - just as it was reaching the limits of our ability to track it - he announced checkmate. Incredulous I thought through the board state, eventually admitting that yes, he'd pulled off a scholar's mate. He'd read of this opening and deliberately set out to attempt it.
Two games which were mathematically isomorphic, having the exact same moves and outcome, but with completely different meanings. One accidental, the other intentional.
How we read a game depends on who is playing. Each move has a process of thought behind it; identical moves can be interpreted differently if they differ in intent. How you understand Deep Blue vs. Kasparov depends on whether you view it as a conflict between Man and Machine, or between individual and collective human effort. A beginner taking a risky opening simply does not realise what they're doing; an intermediate player may be hoping to get lucky, or perhaps to throw their opponent off-guard; while an expert has calculated the outcome and is confident they can handle it. Was that a mistake, a bluff, or a brilliant gambit you don't understand yet?
When we talk about "replayability" in games we're usually thinking of them offering variety by presenting different possible situations and moves. But even identical moves and positions may mean different things. (And of course, as Ben Abraham points out any game is replayable in the sense that any book is rereadable - even if the events and words are the same, we have changed.)
There are only nine games of Rock-Paper-Scissors, and three of them are ties.
(The words in this post are based on actual events, but I have on two occasions lifted them from truth into
fiction. The first game may not have been an exact scholar's mate, but it was a close approximation with perhaps an additional move. And let the record show that I thwarted Martin's attempt - at which point he lost interest for he was unprepared for the challenge of a spoken-word Chess game without having chosen his moves in advance. But in a nearby universe these could both be true.)