We’ve all been confounded by an all-vowel “hand” in Scrabble. What is the likelihood of it happening 3 turns in a row?
Some assumptions are necessary. Let’s use these:
- Two-player game
- English tile distribution
- Vowels are AEIOU (ie, exclude Y)
- The situation is drawing all vowels on the first pull, followed by being in that situation on the subsequent two turns.
- The subject draws first.
- The opponent plays first (this probably contradicts the game rules but is convenient for this experiment).
- The opponent plays a four-letter word on every turn, and that word is two consonants and two vowels.
- The subject is able to play two of their vowels on each turn, requiring a draw of two new tiles.
(If any of the above assumptions is logically impossible, please correct.)
An interesting bit is that blanks can be counted as either a consonant or vowel.
Distribution of English words and letter usage is disregarded for this calculation. Though if you want to throw it in for extra interest, great.