Buy Patchwork if you want a puzzle with no luck and a physical board; it is 2 players, about 30 minutes, ages 8+. Buy Lost Cities if you want a card game that packs small and gives the weaker player real wins; it is 2 players, 30 minutes, ages 10 and up.
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Both of these are the answer to the same question -- what do we play when one of us does not want to be attacked -- and they answer it in completely different ways.
Patchwork removes conflict by giving you separate boards. Lost Cities removes it by making the deck the antagonist.
02Luck is the real difference
Patchwork has almost none. The patch circle is shuffled at setup and after that everything is visible, so the better player wins consistently. It is a puzzle you get better at.
Lost Cities is substantially luck-driven within a hand. Commit to an expedition and the cards for it may never come, and no skill rescues that. Across three rounds skill wins out, but any individual round can go either way.
This is the deciding factor for most households, and it points opposite ways depending on your situation. Skill gap between you? Lost Cities, so the weaker player gets genuine wins. Evenly matched and want your decisions to be what decides it? Patchwork.
03Table footprint
Lost Cities is cards and a small shared area -- it works on a coffee table, a train seat, a lap. Patchwork wants a real surface: two personal boards plus a ring of tiles is a meaningfully larger footprint, and cramping it makes the puzzle harder to read.
If you play at a dining table, ignore this. If you play on a sofa, it decides the purchase.