Or maybe he just suspected there was something funny about the game, and that the first player had a winning play. Playing second he would buy more time to figure out what's going on exactly.

It might just imply that Gates reads Martin Gardner (who had a column in a popular periodical) or the equivalent, but I don't see why he wouldn't have been able to figure expectation values in his head?

It’s to offer substantial proof that Bill Gates is a God among men and Windows 11 should in fact have advertisements in the start menu.

It's really not that hard to work out that it's true when given 3 dice with this property, especially if you already know that it's possible or if your suspicion level is high due to the framing.

All you need to do is look at each pair of dice and compare. Especially for some sets of dice the comparison is trivial. Like look at the ones in the article with five 3s and five 4s, you don't even need to think to figure out which one wins more.

People like apocryphal stories about successful people. Celebrities, billionaires, professors. imo the story serves as a way to connect the reader to the article. The HN crowd tends to care less about these kinds of things, which is fine, but the audience is much broader.

See for example: http://www.borrett.id.au/computing/petals-bg.htm or the umpteen versions of http://math.bme.hu/~petz/vnsumming.html

My guess is that if this story is true, Gates was just familiar with the ruse. Having read about intransitive dice before this article, if someone proposed a game like this to me, I'd definitely assume that something was amiss and try to see if I could determine that it was the case. It does seem like an explanation is purposely left out to make it seem more mysterious than it actually is, though.

The punchline of the story is supposed to be that Gates just knows that if the world's most famous investor proposes a bet, you don't want to take the other side of it. If Buffett wants to go second, then so does Gates.