Welter's game, a little Nim-like combinatorial game

Hi HN! Here's a little game I (and my buddy Claude, cf. the obvious CSS gradient tell on the title) set up to explain to my kids some of things we were working on at work.

So in the game you're taking turns moving coins down a line until no moves are possible. If you've taken a course on combinatorial game theory, you'll have come across the game of nim and you can think of this one as a variant of nim where there can only be a single coin in every square. The theory of how to play it isn't quite as well-established as for nim though; play with enough coins and I certainly find it quite tricky to mentally reason about whether a position is good or not.

One fun fact about Welter's game is that its winning positions form the codewords of a particular error-correcting code called the constant weight binary lexicode (Conway and Sloane, 1986). What that means is that being good at the game is the same as being good at decoding messages in that code. Probably more fun to just play the game though.