Rethinking the value of Scrabble tiles

Rethinking the value of Scrabble tiles(blog.useost.com)

112 points by jlewis_st 13 years ago | 52 comments

dfan 13 years ago |

"More broadly, I think Valett can provide the foundation for answering other interesting questions in word games, such as how to quantify the difficulty of Boggle boards."

Well, you can already quantify the difficulty of Boggle boards pretty well just by counting up all the points you can make on them (it's a small enough problem that you can do that pretty fast). I think the topology of the board is important enough (whether those I N and G blocks are next to each other or not makes a _big_ difference) that a simple histogram of letters isn't going to be sufficient.

jlewis_st 13 years ago | |

I was thinking that you could sum up the transition probabilities from the actual transitions available on the board as the main measure. Then you could use frequency by length to weight legal Boggle plays (3/4 letters and up, so 2-letter words wouldn't even count).

You're right that with a Boggle board you could just count up the available Boggle points by finding all the possible words, but that might miss some aspects of how hard the words are for a human to find.

robryan 13 years ago | | |

If you had enough real games data you could see how often a word is found when present and use that is a weighing factor. Although the arrangement if a word might also impact the likelihood to be found.

caf 13 years ago |

For valuing Scrabble tiles, Valett also needs to include the representation of the letter in common prefixes and suffixes that can be prepended or appended to existing words. I believe that one reason that G is so playable is the common -ING suffix.

DLWormwood 13 years ago | |

I believe that is part of what his definition of “ingoing and outgoing entropy” is refering to. That said, it does seem weird to heavily bias for the 2-3 letter and 7-8 cases. I would think the moderate length words should not get such short shrift, since these words tend to be the ones used to determine when the various letter and words value tiles get hit in any given game. (Full disclosure: not a regular Scrabble player.)

zem 13 years ago | | |

regular scrabble player here. 2, 3, 7 and 8 are absolutely way more valuable than all the other lengths.

cdelsolar 13 years ago |

Competitive Scrabble player here :) -- the reason the C goes down to two points despite having no two-letter words is that it is actually a very good letter - basically, it's in a lot of high-probability bingos. In contrast, the V is one of the worst tiles in the game. It's telling that the Q stays at 10 despite QI -- the Q is by far the worst tile in the game.

In any case I've always wondered what the values of tiles should be if we were to use our current word list rather than the NY Times - thanks for this analysis. The blank is missing though, it would probably have a significantly negative value (-25 to -30?).

At the end of it all I'd rather keep the values what they are. Part of the beauty of Scrabble is the fact that there is chance. Despite the Z and the Q both being worth 10 points, one realizes pretty quickly how much worse the Q is.

jlewis_st 13 years ago | |

Yes, my distaste for C is probably because I'm not a good enough player, haha. I received an email mentioning the CLARINETS heuristic for choosing tiles to leave in one's rack, and in that context the drop in C's value makes sense, as you say.

zem 13 years ago |

as a competitive scrabble player, one mistake that I think he might have made is overweighting corpus-based probability versus game playability. his transition-in and transition-out weights are a good start, but there's also the fact that n+1 letter words that can be made by "hooking" (adding a single letter before or after) n letter words are far more useful than those that cannot. also the layout of the premium squares, and the letter distribution of the bag, factor into how playable certain tiles are. intuitively, at the least I'd expect one more point for the U, and for the V to catch up with the Z, though of course it's very easy to fool yourself about these things when using strategies based on the current letter values.

StevenRayOrr 13 years ago |

The problem, of course, is convincing us "old hat" Scrabble fanatics to change our minds on the point values. "Only 5 points for an 'X'? Nonsense!". Then again, competitive Scrabble and the original foundation of the game have little in common, methinks. Rather frequently I think about the Scrabble-likes (Words with Friends, Literati, etc) and the boards themselves. I am more curious about the designs and placements of the premium squares than the value of the tiles.

Interesting analysis though.

ChuckMcM 13 years ago |

That is a very nicely done analysis. I too have wondered what a 'modern' valuation of letters might look like, this approach seems reasonable.

nathell 13 years ago |

Little known is the fact that Butts actually did some manual fine-tuning of the frequencies he obtained from NYTimes. E.g., he decreased the number of S's to four in order to mitigate its affixability to almost every singular noun and enhance the gameplay.

jlewis_st 13 years ago | |

I did simple analysis of overall letter frequency and how that would map to a 98 tile set (not counting the blanks) and this is what I got:

A: 7 B: 2 C: 4 D: 3 E: 11 F: 1 G: 3 H: 2 I: 8 J: 1 K: 1 L: 5 M: 3 N: 6 O: 6 P: 3 Q: 1 R: 7 S: 9 T: 6 U: 3 V: 1 W: 1 X: 1 Y: 2 Z: 1

It makes a lot of sense to reduce the number of Ss for the sake of gameplay, and it seems like Butts redistributed those extra tiles amongst the vowels.

transfire 13 years ago |

2-letter Scrabble words are more offensive than curse words, and anyone who insists on them deserves only two: "F" and "U".

opk 13 years ago |

One advantage of using the NY Times over the full OSPD for determining letter scores is that it gives precedence to words that people know and use. Casual players don't memorise lists of two letter words. Having imperfect letter scores adds an element of luck to the game which can make it more fun.

BasDirks 13 years ago |

article claims to be written 1 year from now: "30 DEC 2013 - JOSHUA LEWIS"