How to use a random letter for a categories game
Games like Scattergories, Categories and “Name, Place, Animal, Thing” all start the same way: pick one letter, then everyone writes an answer for each category that begins with that letter before the time runs out. In Scattergories a 20-sided letter die decides the letter, each list has 12 categories, and the timer runs for up to three minutes. A random letter generator replaces the die, so you can play anywhere — on a phone, on a video call or in a classroom.
- Choose “A–Z”, 1 letter and UPPERCASE, and press Generate.
- Read the letter out loud and start a timer (2–3 minutes works well for 10–12 categories).
- When time is up, everyone reads their answers. Answers that start with the letter and that nobody else wrote score a point.
- For the next round, generate a new letter. To avoid repeating a letter in the same game, generate all the letters at once with “No repeats” and use them in order.
Easy and hard letters
Every letter is equally likely in the generator, but letters are not equally useful in English. Peter Norvig’s count of 3.56 trillion letters in Google Books shows how often each one is used:
| Letters | Share of all letters |
|---|---|
| E | 12.49% |
| T, A, O, I, N | 9.28%, 8.04%, 7.64%, 7.57%, 7.23% |
| S, R, H, L, D, C | 6.51%, 6.28%, 5.05%, 4.07%, 3.82%, 3.34% |
| U, M, F, P, G | 2.73%, 2.51%, 2.40%, 2.14%, 1.87% |
| W, Y, B, V | 1.68%, 1.66%, 1.48%, 1.05% |
| K, X, J, Q, Z | 0.54%, 0.23%, 0.16%, 0.12%, 0.09% |
Source: Peter Norvig, “English Letter Frequency Counts: Mayzner Revisited” (Google Books data).
The start of a word is different from the middle. Norvig found that T is the most common first letter, while E is about four times rarer at the start of a word than elsewhere and N about three times rarer. So a high overall share does not always mean a letter is easy in a categories game.
Many groups agree on a house rule before they start: if Q, X or Z comes up (together about 0.44% of all letters), generate a new letter. Others keep them as a bonus round with extra time.
The odds, worked out
With A–Z and repeats allowed, each draw is independent and every letter has a 1 in 26 chance (3.85%). That makes it easy to work out the odds yourself:
| Question | Calculation | Chance |
|---|---|---|
| A specific letter on one draw | 1 ÷ 26 | 3.85% |
| A specific letter at least once in 10 draws | 1 − (25 ÷ 26)¹⁰ | 32.44% |
| At least one vowel in 3 letters | 1 − (21 ÷ 26)³ | 47.31% |
| At least one vowel in 5 letters | 1 − (21 ÷ 26)⁵ | 65.63% |
| Some letter repeats in 6 draws | 1 − (26 × 25 × … × 21) ÷ 26⁶ | 46.34% |
| Some letter repeats in 10 draws | 1 − (26 × 25 × … × 17) ÷ 26¹⁰ | 86.35% |
Vowels are A, E, I, O and U, as in the generator.
The last two rows are the “birthday problem” for letters: with only 26 possibilities, repeats come quickly. Ten rounds of a letter game will almost always repeat a letter unless you switch on “No repeats”.
How many letter combinations are there?
| Length | Repeats allowed | No repeats |
|---|---|---|
| 2 letters | 26² = 676 | 26 × 25 = 650 |
| 3 letters | 26³ = 17,576 | 26 × 25 × 24 = 15,600 |
| 4 letters | 26⁴ = 456,976 | 26 × 25 × 24 × 23 = 358,800 |
Ordered strings, so AB and BA count as two different combinations.
Random letters are fine for game codes, seat labels and test data, but too short for anything secret. Four letters give fewer than half a million combinations, which a computer can try in a moment. For passwords, use the Password Generator or the Passphrase Generator instead.
Ideas for the classroom and at home
- Alphabet warm-up: draw a letter and ask everyone to name an animal, a food and a country that start with it.
- Phonics practice: draw lowercase letters and have children say the sound, not the name, of each one.
- Spelling game: draw 5 consonants and 2 vowels and see who can make the longest word from them.
- Vowel or consonant: use the “vowels only” and “consonants only” sets to build word-making rounds like the ones in TV letter games.
- Story starters: draw a letter for the main character’s name and another for the place where the story happens.