Discovering every recipe by random combining: how long will the last one take?

When discoveries come at random and some are much rarer than others, the final missing piece can take longer than all the others together. This shows how to estimate the real effort of completing a collection with uneven odds, and why the usual rule of thumb fails.

Why this works

With uneven odds the rare pieces dominate, because you must wait for them alone at the end. The honest effort comes from counting every combination of pieces that might still be missing, not from the equal-odds rule of thumb.

When not to use it

Skip it for large collections of dozens of pieces, where the exact count becomes too slow, and simulate instead. Also skip it when players can trade or buy missing pieces, since then the collection is no longer a pure matter of luck.

In the full entry

• What to build, step by step
• Starting values and the reason for each
• 4 common mistakes and the fix
• 50 lines of example code with 5 checks that pass
• How your AI shows you that it works

Say this to your AI

Use the Spielerando entry "Discovering every recipe by random combining: how long will the last one take?" (read_entry collect-all-recipes-expected-tries) in my game. Build it step by step, and show me how you checked that it works.

Or skip this and connect the MCP: your AI then finds all of this by itself.Connect the MCP