Scrabble point revaluation in the works?
“Za,” “qi” and “zzz” were added recently to the game’s official word list for its original English-language edition. Because Z’s and Q’s each have the game’s highest point value of 10, those monosyllabic words can rack up big scores for relatively little effort. So now that those high-scoring letters are more versatile, some Scrabble aficionados would like to see the rules changed — which would be the only change since Alfred Butts popularized the game in 1948.
Let’s kill two birds with one stone. Eliminate the role of chance in scrabble by having players buy their letters rather than draw them at random. Whenever a player needs to replenish his tiles, a tile is turned over and put up for auction. Players bid for the tile with points. A player who already has seven tiles who wins the auction selects one of his tiles to replace and puts that tile up for auction. This continues until all players have seven tiles.
This removes chance from the game and also eliminates the need to revalue the tiles because that will be taken care of endogenously by competitive bidding.
Update: Free Exchange at http://www.economist.com makes fun of me.
Cheap Talk 
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March 19, 2009 at 12:30 am
Scrabbler
This just adds another level of strategy to the game- it doesn’t completely remove chance. There is still imperfect information because of unknown tiles in the opponents’ racks, and the random order in which tiles will be drawn from the bag to be put up for auction (which is still the fundamental “luck” problem in the game).
And how does this at all endogenously help determine the value of the tiles? The relative values in the auction will be based on the ability of the tiles to score points for the player, which is still based on the play score which is based on the value of the tiles put into play!
If anything, the introduction of the new words (including QI) may have reduced the influence of chance in the game of Scrabble, as the likelyhood of a Q-stick (getting stuck with no play with the Q at the end) has been greatly reduced. The big point penalty for this (20 point swing) rarely is now a factor in the game.
More options of play leads to a more “fair” outcome.
March 20, 2009 at 11:41 pm
jeff
To understand how this re-values the tiles, take the analogy of treasury securities. There is a notional “interest” payment that you acquire when you buy one. But the true interest rate is the “yield” which depends entirely on the market price. If we double the notional value, the price would adjust leaving the yield constant.
Similarly, the number on the tiles would no longer play a role because the market price would offset them to ensure that they have their true value.
March 19, 2009 at 11:21 am
Game Theorist and Avid Scrabble Player
It’s a compelling idea, but as “scrabbler” points out there is still a lot of luck around the order in which the tiles are drawn. What might be interesting is if a random permutation of the tiles is picked beforehand, but fixed for the whole game. Then, auctions are held to replenish tiles as per the original idea, picking in order of the permutation. In this game racks are public knowledge, which I have always thought would be an interesting way to play the game.
Each auction is perhaps a second-price sealed bid auction? The problem with this is in the dependence between auctions; one must consider which tiles are coming, and how they complement the ones in your (and your opponent’s) rack. (This becomes the central strategic component of the game.) Other important details: Can one go negative in points? Are bids real numbers or integers?
March 20, 2009 at 11:37 pm
jeff
Indeed the combinatorial nature of the allocation problem is a serious complication. One way to do better than the sequence of auctions I proposed would be to hold a single multi-unit ascending auction for all tiles at the beginning of the game. Still, the inherent complementarities (i want q’s only if i also get u’s) will still cause problems.
June 18, 2009 at 4:26 pm
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August 6, 2009 at 7:37 pm
limeduck
ZZZ? As long as there’s still only one Z in the game, the only way to play ZZZ is by using both blanks (zero points) and the sole Z, pretty hard to justify even with the Z ending up on a multiple score spot or competing another word. Like many old fogeys, I think the OSPD jumped the shark after they took the dirty words out in the 3rd (?) edition.
January 17, 2013 at 12:29 pm
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February 6, 2013 at 12:02 pm
Wilbur Delbert
Wow, this paragraph is fastidious, my sister is analyzing these
kinds of things, therefore I am going to tell her.