Codenames Clue Number Calculator

You are the spymaster. Each turn you are offered a clue covering some number of your words at some confidence — a broader clue always comes at lower confidence, which is the whole trade-off — and you choose how many to actually call for. Your team guesses until it is wrong. Nothing is uploaded, and no words are involved: this is the arithmetic of the number, not of the clue.

A clue has a ceiling, and the number cannot raise it

Guessing stops at the first mistake, so the second word of a clue only arrives if the first did. The i-th word is worth p^i, and a clue for k is worth p + p² + … + p^k — a geometric series. It converges, which means a clue can never deliver more than p / (1 − p) words however large the number.

A team guessing right 70% of the time cannot average more than 2.33 words per clue, and no clue number changes that. Calling five when your clue is worth two does not buy three extra words; it buys the chance to be wrong earlier. What the number is really doing is setting an upper limit on a total that your accuracy has already capped.

This is also why multiplying the number by your accuracy misleads. At 80% a clue for 5 looks like 4.0 words and delivers 2.69. The two agree only at a clue for one, and the gap widens at every step after it.

Read backwards, the ceiling is a demand

Inverting p/(1 − p) gives the accuracy an average requires: p = g / (1 + g). This is a floor, not a target — it is what you need for that average to be possible at any clue number at all.

Three words a clue needs 75% accuracy and four needs 80%. The jump from three to four costs five points; from five to six only 2.4. The demand rises towards certainty and never reaches it, which is another way of saying no amount of accuracy makes an unlimited average possible.

The clue numbers that lose the game are the divisors of 8

The starting team has 9 cards and the other has 8, so when both play well the race is decided by how many turns each needs: ⌈9/k⌉ against ⌈8/k⌉. That is a sawtooth rather than a slope. Whenever k divides 8 exactly, the second team finishes in 8/k clean turns and the first team's extra card forces one more — so the bad numbers are 1, 2, 4, 8, and nothing else.

At near-perfect play a clue of 3 wins the starting team 91.8% of games and a clue of 4 wins it 7.5%. Asking for more throws the game away, because 4 divides 8 and does not divide 9. The rule was checked against the exact recursion at every clue number from 1 to 15 and called the winner every time.

Note which number matters: it is the divisors of 8 — the second team's count. Clue numbers 3 and 9 both divide 9 and both favour the starting team, so this is not a symmetry.

How much of that survives ordinary play

Every row is the starting team's win probability. The sawtooth is still there at 80% accuracy — a clue of 4 remains worse than a clue of 3 — but it has shrunk from 84 points at near-perfect play to 1.3. Below very strong play the whole effect is a rounding error next to simply guessing right more often, which is the honest summary: the number matters much less than the accuracy, and it matters most exactly when accuracy is high enough that it shouldn't.

One thing the table settles in passing: going first does not pay for the ninth card. At every accuracy here, calling clues of one or two, the starting team is behind — its best showing is 45.2%. The extra card costs more than the tempo is worth.

What each rule is actually doing

The assassin gets the attention, but it is not what shapes the game. Turning each rule off one at a time, at a clue of 3 and 85% accuracy:

Removing the assassin entirely moves the result by 0.5 points. Letting a wrong guess not end the turn moves it by 4.7 — several times more. The assassin is the rule everyone fears and the turn-ending rule is the one that decides games, because it is what turns a clue into a geometric series in the first place.

Why believe the recursion

Every win probability here comes from an exact recursion over board positions, which is the kind of thing that can be confidently and completely wrong. So it is checked against games played out card by card, by code that never consults it — 1,200,000 of them.

Worst disagreement 0.24 percentage points. Those rows are frozen because 1,200,000 games is more than a page build can spend, but the test suite re-plays all of them and a smaller game runs live on every build so the frozen numbers cannot drift away from the code that made them.

What this does not answer

Nothing here knows any words. Whether a clue can honestly link four of your cards, and how much confidence that costs against linking two, is a question about language, and every accuracy on this page is an input rather than a result. What is computed is the exchange rate: how much accuracy an extra word has to be worth before reaching for it pays. Given how sharply the value of the k-th word falls — it is worth p^k, so at 80% the fifth word is worth a third of a card — that rate is steeper than it feels at the table.