Did you know the population of ponies have never heard of Rock Paper Scissors? Unsurprising, given the lack of fingers necessary to play such a truly insightful and fascinating game with such an interesting history.
Alicorns, however, have a special pony-equivalent variation called Hoof, Horn, Wings. A Hoof beats Horn (Twilight Sparkle would object vehemently to the idea of brawn beating brain, but Ogres & Oubliettes players could make a convincing argument otherwise), a Horn wins against Wings by attacking from a distance, and Wings beat Hoof by flying out of reach. Since Alicorns are the only ones with the appendages to play such a game, it's well-known among royalty, and some unicorns who know how to create images with magic, quickly.
Princess Celestia is a particularly big player of the game: you'd be surprised at just how often incredibly big decisions as princess basically boil down to being decided by such a game. But of course, such a simple game of chance invariably gets a bit dull, and so on occasion she does house-rule in another play: the DOUBLE HORN.
It's been said that Bicorns don't exist, but then the same was said of Pinkie's capacity to hold her breath for nearly a day when Trixie rubbed out her mouth and nostrils with the Alicorn Amulet, and she did, just out of spite. Anyway, this special Double Horn that she has introduced adds a twist of thought to such a game. Double Horn defeats Horn, the same way Hoof does, it also beats Wings like regular Horn, and loses to Hoof.
Princess Celestia has always favoured the Best-of-3 approach to these sorts of games, but really, introducing just one new play is hardly going to be mind-blowing: indeed, some may considering it rather unsporting. As a result, Celestia has another rule during any time she house-rules Double Horn in: if at any point regular Horn is played when the opposing pony puts forward Wings, whoever played Horn wins the match, regardless of score.
Of course, hopefully there should never be such a time when you need to pit your wits and/or your neck against her, but it always pays to be crazy prepared for such scenarios. Supposing you were challenged to such a game: there are a number of ways it can play out, so for each phase of the game, how should you approach it to maximise your odds of winning?