WheelMigo

A random letter wheel for word games and the classroom

Name-a-word games, phonics warm-ups and 'I spy' rounds all start the same way: someone needs to pick a letter without anyone arguing about it. A wheel with the alphabet on it settles that in one spin.

Quick answer

WheelMigo does not ship a letter template, so type or paste the letters A to Z, one per line, into the entry list and spin. With all 26 letters each one has a 1 in 26 chance (3.85%) per spin, and the wheel does not copy English letter frequency, so Q comes up as often as E. A plain spin repeats a letter within 5 spins 33.6% of the time; switch on No repeats this round and every letter comes up once before any returns. Delete or disable hard letters such as Q, X and Z to make the game easier.

Key points

  • There is no letter template: enter the letters yourself, one per line (up to 1,000 entries, each up to 120 characters).
  • With A to Z, every letter has the same chance, 1/26 = 3.85% per spin. English words do not use letters equally, so a uniform wheel is harder than it looks for letters like Q, X and Z.
  • With repeats allowed, the chance of at least one repeat is 3.8% after 2 spins, 11.2% after 3, 21.5% after 4, 33.6% after 5 and 69.8% after 8 (exact birthday-problem arithmetic).
  • Covering all 26 letters with plain spins takes about 100.2 spins on average (26 × 3.854, the coupon-collector value). No repeats takes exactly 26.
  • There is no weighting setting. To favor a letter, list it on more than one line: a second E turns 26 entries into 27 and gives E 2/27 = 7.4% instead of 3.85%.
  • Entries can be more than a letter. A line such as 'S - something you can eat' turns the wheel into a prompt generator.

If you searched for a random letter generator, you probably want one of three things: a starting letter for a category game, a letter for a spelling or phonics activity, or a quick way to hand out letters to a group. WheelMigo covers all three, with one honest caveat: it has no ready-made alphabet template, so you build the list yourself. That takes about a minute.

Build the letter wheel in a minute

  • Open WheelMigo and clear the example entries. The entry list takes one entry per line, so you can paste the whole alphabet at once.
  • Type or paste A to Z, one letter per line. Uppercase is easier to read from across a room.
  • Remove or disable the letters you do not want. A common cut is Q, X and Z, which leaves 23 letters at 4.35% each (1/23).
  • Decide whether repeats are allowed. Leave them on for a quick game where each round is independent, or turn on No repeats this round for a full alphabet pass.
  • Spin. The result is recorded in the history list with its round number, so you can check later which letters have already been used.

What 'random' means here

Every enabled line is a slot of equal size, and the spin picks one of them with the browser's cryptographic random source, using rejection sampling so no slot is favored. With 26 letters that is exactly 1 in 26 per spin. It also means the wheel knows nothing about language: Z is as likely as E. That is the right behavior for a fair draw, but it changes the game. In a word game, a run of Q, X and J will feel unfair even though it is just as likely as any other run.

How often will a letter repeat?

With repeats allowed, each spin is independent, so the same letter can come up twice in a row. The chance that k spins from 26 equally likely letters are all different is 26 × 25 × ... × (26−k+1) / 26^k, and the table shows one minus that, rounded to one decimal place.

SpinsChance of at least one repeat (26 letters, repeats allowed)
23.8%
311.2%
421.5%
533.6%
646.3%
869.8%

The first row is just 1 in 26: the chance a spin matches the previous one is 3.85%. A repeat is still less likely than not after six spins (46.3%), but by the seventh it is more likely than not (58.7%). A game that needs five or six different starting letters in a row should use No repeats.

Plain spin or alphabet pass?

Use a plain spin for a one-off decision, such as the starting letter of a single round. Use No repeats this round when you want to work through the alphabet: WheelMigo removes each result from the wheel until you start a new round yourself, so 26 spins give 26 different letters. With plain spins the expected number of spins to see every letter at least once is 26 × (1 + 1/2 + ... + 1/26) = 26 × 3.854 = 100.2, and even after 26 spins a particular letter has been missed 36.1% of the time ((25/26)^26). The no-repeat rounds article explains the same trade-off with name lists.

Ideas that work with a letter wheel

  • Category games: spin a letter, then everyone writes a country, animal and food that start with it. Cut the hard letters first or allow one free re-spin.
  • Phonics and spelling warm-ups: use only the letters you have taught so far, so the wheel stays within the lesson.
  • Alphabet walk: with No repeats on, assign each letter to a student or a topic until the round is complete.
  • Starting letter for a story or word chain: spin once, then each player adds a word that begins with the last letter of the previous word.
  • Prompt wheel: type lines like 'B - something you can hear' so the wheel gives a letter and a task together. Each entry can be up to 120 characters.

Making the wheel match how English works

If you want the wheel to hand out common letters more often, repeat those letters on extra lines. For reference, the standard English Scrabble set has 98 lettered tiles, of which 42 are the vowels A, E, I, O and U, which is 42.9% of tiles. A plain A to Z wheel gives vowels 5/26 = 19.2% of spins. Listing vowels more than once moves the odds toward the tile set, but be aware that the wheel then treats each line as a separate slot, so the chance of a given letter is its line count divided by the total number of lines.

What the wheel will not do

  • It does not check spelling, give word suggestions or keep score. It only picks from the list you provide.
  • It does not adapt to a lesson on its own. Choose the letters for the activity before you spin.
  • It does not remove a result you dislike. If a result cannot be used, say so before the game and agree how many re-spins are allowed.

How this works

The entry rules (one entry per line, at most 1,000 entries, at most 120 characters each, repeats allowed by default, optional No repeats this round) are read from WheelMigo's own source. WheelMigo has no letter template, so the 26-letter list is user-built. The odds are exact: the chance that k independent picks from N equally likely entries are all distinct is N × (N−1) × ... × (N−k+1) / N^k; for N = 26 the at-least-one-repeat chance is 3.8% (k=2), 11.2% (k=3), 21.5% (k=4), 33.6% (k=5), 46.3% (k=6), 58.7% (k=7) and 69.8% (k=8). Average coverage with plain spins is the coupon-collector value N × (1 + 1/2 + ... + 1/N) = 26 × 3.8544 = 100.2 spins. The chance a specific letter is missed in 26 plain spins is (25/26)^26 = 36.1%. The Scrabble vowel share uses the standard English tile set: 98 lettered tiles (blanks excluded), 42 of them A (9), E (12), I (9), O (8), U (4). No pedagogical or learning-outcome claims are made.

Frequently asked questions

Does WheelMigo have a random letter generator?
There is no dedicated letter template, but the wheel works as one. Type or paste A to Z, one letter per line, and spin. Each enabled letter has an equal chance, 1/26 = 3.85% with all 26.
Can I leave out letters like Q, X and Z?
Yes. Delete those lines or disable them. With Q, X and Z removed you have 23 letters, each with a 1/23 = 4.35% chance per spin.
Will a letter repeat?
It can. With repeats allowed, there is a 3.8% chance of a repeat after 2 spins, 33.6% within 5 spins and 69.8% within 8. Turn on No repeats this round to get each letter once per round.
Can I make common letters come up more often?
There is no weighting setting. List a letter on more than one line: with E listed twice among 27 lines, E has a 2/27 = 7.4% chance per spin.
Can I use it for a spelling or phonics lesson?
Yes, as a way to pick a letter or a prompt. Use only the letters you have covered, and add your own tasks as entries. The wheel does not check answers or track progress.

References

  1. WheelMigo — No-repeat rounds: the math
  2. WheelMigo — Classroom brain break spinner
  3. WheelMigo — Truth or dare wheel
  4. WheelMigo — Pick a random number from 1 to 100
  5. Wikipedia — Birthday problem
  6. Wikipedia — Coupon collector's problem
  7. Wikipedia — Scrabble letter distributions

← All articles