Scrabble Tile Distribution

What the shape of the bag tells you

Twelve E tiles, nine A, nine I, eight O and six each of N, R and T. Those seven letters are 59 of the 98 lettered tiles — three fifths of the bag is made of seven letters, and all of them are worth one point. That is not an accident of design; it is what makes long words possible at all.

At the other end there is exactly one each of J, K, Q, X and Z. You will draw each of them about once per game, and what you do with that one tile is worth more than several ordinary turns.

Tracking, and why it wins close games

Every tile on the board is a tile that is not in your opponent’s rack. Late in a game, when the bag is empty, subtracting the board and your own rack from this distribution tells you exactly what they are holding — not approximately, exactly.

The two things worth tracking even early are the blanks and the four S tiles. While any are unseen, a bingo can land; once all six are accounted for, the board is much safer to open. The solver shows unseen tiles beside the results for this reason.

Combine it with the tile values to see where the 187 points in the bag actually sit — and note that roughly a quarter of them are in five tiles.

The vowel problem

42 of 98 tiles are vowels, so a rack of five vowels is not bad luck, it is arithmetic. The fix is to dump them two at a time in short words rather than exchanging a whole rack: the two-letter list has AA, AE, AI, OE and OI in it precisely for this.