Santorini

First place your two workers, then on each turn move one worker to a touching square and build a level on a square touching where it landed. You may climb at most one level at a time but drop any distance. Step onto a level-3 tower and you win — and if you ever have no legal move-and-build, you lose on the spot. A level-4 dome can never be entered. Everything runs in your browser; nothing is uploaded.

Can you really be walled in? Yes, but rarely

Santorini has two endings — climb to level three, or run out of legal moves and lose where you stand. The second is the one people wonder about. It is real, and it is uncommon.

The second row is the interesting one. Players who overlook a winning step keep the game running — 43 plies against 31 — and a longer game is a fuller board, so being walled in becomes 8 times commoner. Suffocation is less a strategy in its own right than what happens when nobody finishes the game.

And it does not need a full board

The picture most people have is of a board choked with domes and nowhere left to go. The losing positions look nothing like that. Across 60 games that ended this way, the board at the moment of defeat held an average of just 5.9 domes, with 19.1 of the 25 squares still open — and even the tightest case left 12.

What has run out is not space but the space next to your own two workers. Suffocation is local, which is why it can be engineered against someone who has climbed somewhere committing — you do not have to fill the island, only their corner of it.

Every one of the 8,000 games reached a real ending, so neither row hides abandoned runs. The table is frozen; a fresh sample of 250 games runs on every build and comes out at 4.4% against the frozen 5.1%. These are random players, so they describe how often the ending turns up by itself rather than how often a strong player can force it.