The letter M in Scrabble
2 in the bag · 3 points · 2% of all tiles
Drawing 7 tiles from a full bag, the letter M shows up about one rack in 7 — the 13th likeliest tile to see of 27 (tied with 9 others, since every tile with the same number of copies has exactly the same chance).
How many you can expect
Most racks hold none at all — 86.4% of them, and 0.42% hold two or more. On average a rack carries 0.14 of them.
Exact chance of holding each number of M tiles in an opening rack of 7.
Is it a bingo tile?
A rack picked at random can play all seven tiles 12.6% of the time. A rack holding at least one M manages 11.3% — only 0.90× the baseline, which makes it the 14th best bingo tile of 27. Measured against ENABLE, which is public domain. The official lists are both bigger, so both would give a higher number — a little higher for NWL, appreciably so for Collins.
The reason is countable rather than folklore. 19% of the 19,424 seven-letter words in ENABLE use an M somewhere in them. A tile that appears in more words is a tile more racks can build around, and that is the whole of the effect above.
One caveat worth stating: this is a fact about whole opening racks holding an M, averaged over every set of six tiles it could arrive with. It is not a leave value. Whether to keep this tile mid-game depends on the six tiles beside it and on what is left in the bag, and a tile that is good on average can still be the wrong keep.
What it’s worth carrying
M is worth 3 points, which puts it 11th highest-scoring tile of 27 — tied with 3 others at the same face value. Face value tracks rarity by design, but not as hard as people assume: the whole set is worth 187 points, and the five one-of-a-kind tiles (J, K, Q, X, Z) carry only 22% of that between them. The ten one-point letters carry 36% — more than the whole high-value end, because there are so many of them.