
Rethinking the value of Scrabble tiles - jlewis_st
http://blog.useost.com/2012/12/30/valett/
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dfan
"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.

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jlewis_st
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
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.

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Tloewald
Changing the values of tiles will change the game, so you'll have a new
mismatch. I think that a simpler fix would be to ban plays of fewer than three
or four tiles are placed (I'd say four since three is still too easy). You can
still score off the stupid two letter gotchas, but you have to place a three
or four letter word down to score anything.

The game would end when all players had two few tiles to play.

~~~
robryan
I am speaking of Boggle, where the scoring is based on unique words.

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caf
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
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.)

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

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cdelsolar
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.

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jlewis_st
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.

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zem
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.

~~~
javajosh
Maybe you and the OP should petition the Words With Friends people to give you
a statistically significant data-dump of real games so you can analyze and
revalue the letters.

It would be a service to us all.

~~~
furyofantares
That would be really interesting data to look at.

There would be a lot of factors to consider that might make it hard to apply
to re-valuing Scrabble, though:

1\. Most Words With Friends play is casual, and casual players are likely to
play very differently than competitive players.

2\. The data would show you what words players play given the current scoring
system, and wouldn't necessarily translate to another scoring system.

3\. Words With Friends is a different game than Scrabble (different board
layout, different bingo scoring, different number of tiles and different tile
frequency).

4\. Players end up playing the majority of the tiles they draw, so the
frequency with which they play a letter may have a closer relationship to how
many of the printed tiles have that letter than it is to the frequency of the
letter in the corpus.

~~~
hdevalence
Regarding 1: perhaps one could segment the players based on their scores ---
the people I know who play scrabble competitively generally have a
significantly higher average word score.

~~~
furyofantares
True - in competitive scrabble luck actually plays a pretty small role. It's
much closer to chess than it is to poker.

~~~
zem
on the granularity of an individual game there's a surprising amount of luck
even in the top levels of the game. for instance, i'm at best a high
B-division player, but i've won tournament games against two world champions
(and, on the flip side, lost to players rated far lower than me). it's the
overall performance in an (ideally 15-game+) tournament that lets the best
players consistently rise to the top.

~~~
caf
The luck element is a result of the malapportionment that the OP mentions
(it's good to receive the overvalued tiles, and who receives them is down to
luck).

~~~
zem
that's part of it, but not nearly as large a part as you'd imagine. there are
ways to defend against, e.g., someone getting the X both ways on a triple
letter score (the most common large "tile lottery" moment). harder to overcome
is someone simply drawing one bingo after another (possibly by being lucky
with the blanks and Ss), getting an early 100-200 point lead, and then simply
closing the board down (both players have low-scoring moves thereafter, but
you already have the lead), or having a close-fought game be irretrievably
lost because you get a final rack with six vowels, or none, or an unplayable Q
that hits you with a 20 point penalty _and_ let's your opponent play his final
rack out letter by letter, for a large number of points.

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StevenRayOrr
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.

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

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nathell
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.

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jlewis_st
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.

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

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dfan
Sorry, they're part of the game. It's like getting offended at a chess player
for castling.

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RyJones
I'd guess en passant is more surprising to neophytes than castling

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jacquesm
At a guess check-mate is the most surprising to neophytes. It gets them every
time no matter how often it happens.

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lmm
Huh? If checkmate is confusing you can just play until you take the opponent's
king, with minimal difference to the game.

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opk
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.

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

