Infinite Tiles Scrabble

In traditional board-game scrabble there is a finite set of tiles and for each letter, there is a finite number of those. For example there is one Q, one Z, one J, a couple of Ys and Hs, and a whole lot of As, Es, and Os. And so forth. The rarer letters have higher point value. Q, Z, and X have 10. However, the common letters are just worth one point.

The luck of the draw is very significant in the outcome of the games. If one player gets a Q, that player will be able to get at least 10 points from playing it and can get many more points from a clever play involving bonus squares. Thus, being lucky to get a disproportionate number of high point tiles can sway the outcome of the game.

There are 100 tiles in a standard scrabble. Thus, for any given tile, there is a 1/100 chance of it being a Q, for example. Conversely, there is a 12/100 chance of a tile being an E. Of course, once a Q is received by one player, the chance of another player drawing a Q is 0.

However, in Infinite Tile Scrabble, the probability of a tile being a given letter never changes. Thus, when someone plays a Q, the next tile drawn still has a 1/100 chance of being a Q and a 12/100 chance of being an E.