Last Slice

Rules

Last Slice is played on one ring of slices — a donut, cut into wedges. A seam at the top marks where the ring is considered "already open," so from the very first move there are two ends to nibble from.

On your turn, eat 1 or 2 slices from either end of what's left. The little numbered buttons next to each end show your options — tap "1" for a small bite, "2" for a bigger one. Eaten slices fade, and a colored line traces along the ring showing who ate what, growing in from both ends as the game goes on.

The ring keeps shrinking until nothing is left. Depending on the win rule you pick: and are either racing to take the very last slice (last to eat wins), or trying to avoid it (last to eat loses) — the classic sour trick.

On Hard, the computer plays this one perfectly, so once you're behind, only a mistake from your opponent gets you back in it. Who goes first alternates each new game.

New to this one? Medium is a good place to start — it plays the right move about three times out of four, so an occasional slip is usually enough to swing things your way.

Controls

Slices are numbered 1 through however many the ring has, clockwise from the seam at the top. Each turn eats 1 or 2 slices from whichever end of the remaining stretch you pick.

With a mouse or touchscreen: tap the "1" or "2" button next to either end of what's left.

With a keyboard: type which end -- "left" or "right" (or just "l" or "r") -- into the box below the board, optionally followed by a period and a count of 1 or 2, like "left.2." Leaving the count off takes 1. Press Enter or Eat to confirm.

Type status (or just the start of it, like "sta") and press Enter or Eat at any time -- even when it isn't your turn -- to have the ring's current state read back to you.

Roots

This one's straight-up Nim underneath the donut skin: a shared pool, take 1 or 2 at a time, and depending on your settings, either race for the last piece or dodge it. Nim is one of the oldest studied combinatorial games — the "don't take the last one" version is sometimes called misère Nim, and a specific take-1-or-2 variant is also known as the 21 Game.

Under the hood

Eating from the left end or the right end feels like two different choices, but they're not, strategically. The only thing that actually matters is how many slices remain in total — taking 1 or taking 2 from either end has the exact same effect on that count, so a move that eats from the left and one that eats the same amount from the right are functionally identical. The two-ended donut is really a single number in disguise.

That number is also all either winning convention needs to solve the game exactly. Whether the rule is "last to eat wins" or "last to eat loses," the AI works the same way: for however many slices are left, does taking 1 or taking 2 hand the opponent a position they can't escape? It's coded as a small recursive lookup rather than a hardcoded formula, but the pattern underneath is the same well-known one that's solved every take-1-or-2 game like this for centuries — there's a specific remainder you want to leave your opponent, and once you're controlling that, you control the rest of the game, under either convention. Easy ignores all of that and moves at random. Medium plays the mathematically correct move about 75% of the time and slips the rest. Hard always plays the winning move, though when more than one move counts as equally good (eating 1 from either end, say), it picks between them at random — so even Hard's choices sometimes just come down to which side it feels like nibbling, not real strategy.

That's also exactly why the skill ceiling here is genuinely low. Dishpan Hands, built on similar Nim-family bones, ended up with meaningfully more branching complexity specifically because it layered on the flip mechanic and the once-per-coin lock — rules that break the game out of a single clean number the way Last Slice never does. Once a player learns that pattern here, the outcome is often visible many moves before the game actually ends.