Accordion

Accordion is the simplest layout in the catalogue and the hardest game in it. Fifty-two cards in a row; move a pile one or three places to its left when the top cards share a suit or a rank; the row squeezes shut behind it. That is the entire rule set. And it wins about one game in a hundred. There is no hidden information and no stock — just a line of cards and a long chain of decisions where an early convenient move quietly kills the position twenty moves later. Its historical form was stricter still and effectively unwinnable, which is why the three-position move exists at all. Most players learn to treat a five-pile finish as a good day.

The whole deck is laid out in a single line, one card per position. A pile may be moved onto the pile immediately to its left, or onto the one three positions to its left, provided the two top cards match in either suit or rank. Whatever gap that leaves closes up as the piles shift left. Keep compressing and the line shortens like a squeezed accordion. Getting the entire deck into a single pile wins — and hardly ever happens, so many players count five piles or fewer as a result worth having.

The choice between the one-left and three-left move is where the whole game lives, and taking the immediately-available move is usually the mistake — a three-position jump keeps two piles in play that a single-step move would fuse. Think about what a move sets up two or three compressions ahead, because the line reshuffles itself every time you close a gap. At roughly one win in a hundred, judge yourself on how short you got the line rather than on whether you cleared it.