Memory Match

Every card is face down and every shape appears on exactly two of them. Turn one card over, then turn a second. If the two shapes agree, the pair stays face up and is out of the game; if they do not, both go back down in the same places they came from. That is a turn, and a turn is always two cards — never one, never three. You have finished when no card is still face down, and your score is the number of turns it took.

• Nothing is hidden from you except what you have not looked at. There is no shuffling between turns and no card ever moves.
• A miss is not a wasted turn. It is the only way to see two new cards, and what you do with what you saw is the whole game.
• With two players, the person who finds a pair goes again — so a player who remembers four locations takes all four in one visit to the table.

"Blind turn matches" is the chance that two cards turned over with no knowledge at all happen to agree: one card leaves 15 others on a 4 × 4 board and exactly one of them is its partner, so 1 in 15. "Perfect recall" is the average a player who never forgets a card and always takes a pair they already know would score — measured here by playing 20,000 real deals of each board with exactly that strategy. Those two columns bracket the game: the first is what luck alone gives you, the second is the ceiling.

The arithmetic floor is one turn per pair — 8 on the 4 × 4 board, 18 on the 6 × 6 — and it requires being right about every single card before you have seen any of them. It is not a target. The real target is the perfect-recall figure in the table above, which works out at 1.55 to 1.59 turns per pair across all four boards: 12.4 turns for eight pairs, 28.5 for eighteen. That ratio barely moves with board size — it drifts up by four hundredths between the smallest board and the largest — and it is the reason a 6 × 6 board that could in principle be cleared in 18 turns essentially never is.

So: on the 6 × 6 board, thirty-something turns is a strong game, forty is a normal one, and anything under thirty means you were remembering almost everything you saw. A hint costs one turn on your recorded score, which is about what the information is worth, so hints and turns can be compared directly.

Because a turn is two cards, and while two are face up the board is judging them. This is the rule that nearly every digital memory game gets wrong: it starts a timer to turn the cards back down and leaves the rest of the grid live in the meantime, so a quick player can turn over four or five cards before the timer fires. Pairs then get credited that were never both on screen at once, the turn counter drifts away from what you actually did, and cards occasionally vanish. Here the board is genuinely locked between the second card and the verdict — and if you do not want to wait, a tap or a key ends the pause early instead of stacking up a flip behind it.

Two players share one device and take turns. A matched pair scores a point for whoever turned it, and that player goes again; a miss passes the turn. The last pair ends the game and the higher score wins, with ties possible on the even-numbered boards. Playing on means the game rewards a good memory twice over — once for the pair you take, and again for every extra pair you can take before you have to hand the device back.

It also makes a miss expensive in a way the solo game never does. When your second card fails to match, you have shown your opponent two cards and then given them the turn. Strong two-player play is partly about which unknown card you open second, because that is the one your opponent is most likely to be able to use immediately.

Each deal is a pure function of a 32-bit number, shown as "Deal #" under the board, so the same number is the same board on every device and "Replay this deal" gives you the identical grid to try again. Across the first 200,000 seeds this game produces 200,000 different boards at every one of the four sizes — measured, not assumed, by the test that ships with it. The shapes vary too: the pool holds 24 shapes and a deal uses between 8 and 18 of them, picked by the same seed, so two games in a row are not one cast rearranged.

For scale, a 4 × 4 grid of eight pairs has 81,729,648,000 distinct arrangements and a 6 × 6 grid of eighteen pairs has more than 1.4 × 10³⁶ of them. A deal number is 32 bits wide, so it selects from 4,294,967,296 of them — far more than anybody will play, and far fewer than exist, which is the honest way to put it. Every shape is drawn as SVG path data in the code, so nothing is downloaded and the board works with the network unplugged.