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Inifinite Tiles Scrabble II

Adjust the probability of letters being received to keep Scrabble Game fair
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This is for computerized Scrabble games.

There is a certain probability of receiving a given letter on a tile, e.g., 1/100 for a Q and 1/12 for an E. Qs are worth a lot more than Es. Thus, by receiving a disproportionate number of high-value tiles a player has a great advantage.

In this idea, the sum of the point value of the dealt tiles attempts to remain the same for all players during the course of the game, with some variation due to luck.

For example, if Player One receives QEAYSEI HWN for his first 10 tiles, then he has received a point value of 28 on his rack (keep in mind that you only receive seven tiles at a time) over the first 10 tiles. To make it fair, the dealer (computer) deals Player Two random tiles that also add up to 28. It can be made a little bit more random by adjusting the probability for letters such as to tend the distributions to have the same value.

In one implementation the sequence of tiles to be dealt is divided into chunks of ten. For each chunk of 10, each player will receive the same point value. E.g., the first 10 tiles will be worth 28, the next 17, the next 25, etc. The value for each chunk is randomly set by the computer without revealing the values to the players.

 — Goesta Berling, May 01 2020

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