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How to win Memory in fewer moves: perfect play and a grid trick

Eigengames team · 6 October 2026 · 5 min read

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You turn over a fox. You have seen a fox before — you are sure of it — somewhere in the bottom half, maybe second from the left. You tap. It’s a doughnut. The fox turns back over, and now you remember two cards less clearly than you did a moment ago.

Memory feels like a test of how good your memory is. It is partly that, but it is also a game with an exact best strategy, and most of the moves people waste come from breaking it, not from forgetting.

What a perfect memory scores

A move in our game is two cards turned over. A matching pair stays open; a mismatch turns back. You finish when every pair is open, and your score is the number of moves.

Imagine a player who never forgets a card. How well can they do? Less well than you might think, because the first time you see a card there is nothing to match it with. We simulated that perfect player 20,000 times on each of our three sizes, and the numbers match the formula worked out by mathematicians Daniel Velleman and Gregory Warrington for the expected moves under optimal play, about 1.61 moves per pair (their paper).

For the perfect player, the middle 80% of games took 8–10 moves on Easy, 12–13 on Medium and 18–20 on Hard. So 12 moves on Medium is not “pretty good”; it is what a flawless player usually scores. If you hit 10 there, you were lucky as well as sharp. The last columns show where human limits bite. Holding the last four cards you saw costs almost nothing on Easy, two moves on Medium, and eight and a half on Hard. That jump is the size of the board outrunning the handful of items that short-term memory can hold at once (Miller’s “seven, plus or minus two” is the famous estimate; later research puts it nearer four). Hard is the only size where technique, rather than attention, decides your score.

The perfect strategy, in three rules

The optimal play is short enough to keep in your head.

1. If you already know where both cards of a pair are, take that pair. It costs one move and you never lose by banking it.
2. Otherwise, turn over a card you have never seen. If it matches one you remember, turn that one and take the pair.
3. If the first card is new and has no partner you know, turn over another unseen card for your second flip.

Rule 3 is the one people break. When the first card is a dud, it is tempting to “play safe” with a second card you already know, so as not to clutter your memory. We tested that habit with the same perfect memory: it costs about one and a half moves on Easy, two and a half on Medium and four on Hard. The new second card is not clutter. It is free information for later, and sometimes (more often as the board empties) it is the partner of the card you just turned over: a lucky match you would otherwise have had to spend a whole move to find.

Give every card an address

The best technique for the remembering part is to stop remembering pictures and start remembering places. Give the grid coordinates, as on a chessboard: columns A, B, C, D from the left, rows 1 to 4 from the top. Our Easy board is 4 columns by 3 rows, Medium is 4 by 4, and Hard is 6 columns (A to F) by 4 rows.

Then say each card’s address to yourself as you see it: “fox, B3”. Two words, said inside your head, last much longer than a glimpse of a picture. On Hard, go one step further and tie each picture to its address with a tiny absurd image: the fox is sitting on a bee (B), with three tails. It sounds silly, and that is the point; the method of loci used by memory champions works on the same principle of hooking items to places.

The fixed sweep order in the diagram helps rule 2 as well. If you always turn new cards in reading order, you do not need to remember which cards you have already seen: everything before your current position is seen, everything after it is new.

Spend your attention where it pays

Not every card needs to be remembered equally. A card whose partner is already open is gone. A card you saw once, a long time ago, is the one that slips. So after every mismatch, spend a second rehearsing just the two cards you turned: “doughnut A2, rocket D4”. When a picture you know shows up, go straight to its partner before you do anything else, because each move you delay is another chance for that address to fade.

And watch the clock less than the move counter. Our game ranks you by moves, not seconds. A mismatched pair stays up for most of a second, and a third tap turns them back at once, so there is no need to rush — but there is no reward for staring either.

Practice

Start on Medium and play three games using only the three rules and the reading-order sweep. Aim for 13 moves or fewer, which is within one move of a perfect memory. When that feels easy, move to Hard and add the coordinates out loud (or under your breath); a perfect memory scores about 19 there, and anything in the low twenties is excellent.

Pictures fade; addresses stick.

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