Tool
Scattergories Letter Picker
Letters weighted by how playable they are — the honest opposite of a uniform draw.
Scattergories Letter Picker
S is the most likely at 11.2%; the three least likely are X (0.1%), Z (0.2%), Q (0.4%). A uniform draw would give every letter 3.8%, including X.
A letter draw weighted by how many common English words start with it. S comes up often; X almost never.
This is the only tool on the site that is deliberately non-uniform for the player's benefit, and there is a switch to turn it off so you can compare.
A uniform letter draw gives X and Q a 3.8% chance each, which over ten rounds means a roughly fifty-fifty chance that at least one round is a dead round.
How the Scattergories Letter Picker works — and why it's fair
Each letter carries a weight roughly proportional to how many common English words begin with it. S is the heaviest at 105, C is 92, P is 82; at the other end X is 1, Z is 2, and Q and Y are 4. Those weights total 940, so a weight of 105 is an 11.2% share. The draw is a cumulative-sum walk over them, the same mechanism the weighted picker uses.
That makes S exactly 105 times more likely than X. In uniform terms both would sit at 3.85%; weighted, S is 11.2% and X is 0.11% — which turns an X round from a once-every-twenty-six-draws event into a once-in-nine-hundred one.
The switch matters because the two draws answer different questions. Uniform is fair to the letters; weighted is fair to the players. Over a ten-round game drawn uniformly without replacement, the chance of hitting X or Q at least once is 63% — so most games contain a round where nobody can name a country beginning with the letter, which is not a hard round but a wasted one.
Letters are additionally drawn without replacement within a session, so a game does not hand out the same letter twice in five rounds. The pool refills only when every letter has been used, which for a normal game never happens.
The weights are approximate and derived from rough counts of common word-initial frequency, not from a corpus study. They are right to within the accuracy that matters — the ordering is correct and the extremes are correct, and no game depends on whether M should be 50 or 55.
Turning weighting off is a legitimate choice for a group that wants the challenge, and the tool states the uniform probability explicitly so the trade is visible rather than assumed.
When the Scattergories Letter Picker is fair — and when it is not
What it does guarantee
- The weighted draw gives every letter a chance proportional to its playability, and the percentages are shown.
- Letters are drawn without replacement within a session, so no letter repeats until all have been used.
- The uniform option is available and its probability is stated, so the comparison is explicit.
What it does not
- The weighted draw is deliberately not uniform. X is roughly a hundred times less likely than S.
- The weights are approximate, derived from rough word-initial frequency rather than a corpus study.
- It cannot know your category list. Some letters are easy for animals and hard for countries.
Two worked examples
Weighted draw
- Weights total 940. S is the heaviest at 105 — 11.2% of draws.
- X sits at weight 1, so 0.11% — roughly one draw in nine hundred.
- Over a ten-round game, the chance of drawing X at all is a little over 1%.
Uniform draw
- Every letter has exactly a 1-in-26 chance, or 3.85%.
- Drawing 10 of 26 without replacement, the chance of hitting X or Q is 63% — 1 − C(24,10)/C(26,10).
- Fair to the letters, and close to two games in three containing a dead round.
Games where a bad letter ruins a round
Scattergories and its variants are the direct case, and the dead-round problem is specific: a category list of ten with a letter nobody can use produces ten blanks and a round everyone wants to skip, which is a worse outcome than a slightly easier round.
Word association and category games at parties use it for the same reason with less structure, where the cost of a dead round is a lull rather than a blank scoresheet.
Classroom vocabulary games use the weighting to keep every student able to contribute, since a hard letter penalises the students with the smallest vocabulary hardest — which is the opposite of what the exercise is for.
For a genuinely uniform letter draw with no game framing, the letter generator does exactly that. For weighting arbitrary entries rather than letters, the weighted random picker is the general version of this mechanism.
Frequently asked questions
Is the weighted draw unfair?
To the letters, yes, deliberately. To the players it is fairer than uniform, because a round nobody can answer is a wasted round rather than a hard one.
How much less likely is X?
Exactly 105 times less likely than S, because those are the two weights. Weighted, X is 0.11%; uniform it would be 3.85%.
How likely is a dead round with a uniform draw?
Over ten rounds drawn without replacement, the chance of hitting X or Q is 63% — close to two games in three.
Where do the weights come from?
Rough counts of how many common English words begin with each letter. They are approximate; the ordering and the extremes are what matter.
Can a letter repeat in a game?
Not until every letter has been used. Letters are drawn without replacement within a session, and the pool refills only when exhausted.
Should I use uniform or weighted?
Weighted for a normal game. Uniform if your group wants the challenge and accepts that a dead round is part of it.
Does it account for my category list?
No. Some letters are easy for animals and hard for countries, and the weights are a general-purpose approximation.
Are the percentages shown accurate?
They are computed exactly from the weights in use, so they describe this tool's behaviour precisely — the weights themselves are the approximation.
How is this different from the letter generator?
That one is uniform, which is the correct default for a general-purpose draw. This one is deliberately weighted for playability, which only makes sense inside a game.
Related tools
Random Letter Generator
Pick a random letter A-Z — for games, name generators, or classroom drills.
Random Word Generator
Draw English words with length and starting-letter filters — and see the pool shrink.
Weighted Random Picker
Give each entry its own odds — and see the exact probability table before you draw.