Memory Information Lab: measure what remembering changes

The precise question this tool answers

You are about to start a turn with no card currently face up. Some unmatched cards have been seen and remembered; the rest are unseen. You open an unseen card first. If its mate is one of your remembered cards, you take that known mate. Otherwise you choose one other unseen card. What is the chance of completing one pair on this turn? This is narrower than predicting how many turns the whole round will need.

Keep the information model honest

Count only locations and identities you remember correctly. A vague feeling that a card was near the top is not a known singleton. Each remembered card in this calculator must belong to a different pair, and no complete known pair remains in the count. Matched cards are already removed. Unseen identities are assumed to be uniformly distributed among the remaining unseen positions. The calculator cannot read your game, reveal cards or compensate for a forgotten location.

Worked example: the same six pairs, more knowledge

With no remembered cards, after the first reveal its mate is one of the other eleven cards: 1/11. After remembering two different non-matching cards, ten unseen cards remain. Two of those ten match a remembered singleton. If neither is opened, the second unseen reveal has one matching card among nine.

The two-singleton calculation is 2/10 + (8/10 × 1/9) = 13/45. It is not 2/10 + 1/9: the second branch happens only when the first reveal has no known mate.

A failed match can still change the next decision

A mismatch that reveals two previously unknown, different identities gives useful information if both locations are retained. It does not earn points, and knowledge is not guaranteed to survive in your memory. Before the cards turn down, attach a compact location label to each: for example, “top-left cloud” and “bottom-right fern.” In the next turn, a recognised face can turn what would have been a guess into a known second reveal.

Known pairs and long-term claims

If a complete known pair is available, taking it produces a certain match. That is a different situation from the singleton-only policy calculated here. The page does not prove an optimal strategy for all future turns or advise delaying a known pair. In Playfield’s six-pair game, each match earns 100 points; more efficient recall reduces the number of attempts, not the value of each pair. A complete round still contains six matches.

A small experiment you can repeat

Compare six pairs with zero, two and four singletons. Explain each increase using the two possible branches rather than memorising the percentages. Then set three pairs and two singletons: four hidden cards remain, giving 2/4 + (2/4 × 1/3) = 2/3. Finally set all remaining pairs to known singletons. Every hidden card now has a remembered mate, so the stated policy succeeds with certainty under the model. This certainty depends on accurate memory and the stated setup, not a promise about your next click.