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The Last Card Problem

Three short lessons for the grown-up beside a collector: why the first cards come fast, how long a whole set takes on average, and why the last few cost the most. Then roll a die until every face has turned up.

For grown-ups, from what DeckPals teaches children at Spark & Anvil.

  1. Lesson 1Collecting is waiting
  2. Lesson 2The collector curve
  3. Lesson 3Why the last card costs most
At the table · Two or more, ages 6 and up

Roll until every face appears

You'll need: One die each, a pencil and a strip of paper with 1 to 6 written along it.

  1. Before rolling, everyone guesses how many rolls it will take to see all six faces.
  2. Roll and tick each face the first time it turns up; count every roll, repeats too.
  3. Write down the count when the last face appears, then play twice more.
  4. Add up everyone’s counts, divide by the number of games, and compare that average with about 14.7, the long-run average.

Print the guidebook (all lessons + the table activity) →