Wednesday, February 3, 2010

Quiddler

While playing Quiddler you've probably wondered about the highest-scoring word, highest-scoring hand, scoring distributions for English words, and things like that. Wonder no more! By my calculation (using a short program in R), here are the highest-scoring words by words length:

   len    value cards           word
1    1        0     0          
2    2       16     2             za
3    3       28     3            zax
4    4       44     4           zizz
5    5       47     5          jazzy
6    6       55     6         zaqqum
7    7       58     7        buzzwig
8    8       61     8       quizzify
9    9       65     9      unquizzed
10  10       69     9     quizzingly
11  11       69    10    buzzerphone
12  12       67    10   wickerworker
13  13       68    10  quinqueverbal
14  14       60    10 fingerprinting

The maximum-scoring words:

       word len value cards
buzzerphone  11    69    10
crackerjack  11    69    10
quirquincho  11    69    10
 quizzingly  10    69     9


(Here's hoping you draw lots of Z's.) So words from 2-14 letters are possible, using 2-10 cards. This boxplot show the distribution of words values by word length:

Not surprisingly, scores increase with increasing word length until you get to 11 letters, when most words have a zero score (they require more than 10 cards to form), but a few can still be made using Quiddler's two-letter cards...until 15 letters, when even this trick doesn't help any more.

Finally, there is a hand with 109 points (not including any bonuses): "zizz" (44), "zizz" (44), and "zer" (21). The base word list used was /usr/share/dict/words...don't ask me what a "zer" is.
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  1. BenFebruary 3, 2010 at 6:46 AM

    # What's the Quiddler point distribution of English words? What's the maximum-value word?
    # Enquiring minds want to know!
    # Here's the key function

    wordvalue <- function( word, letterpoints, maxlen, firstcall=TRUE, forceshort=FALSE, fmode=1 )
    # returns a list with max point value of word, and its corresponding tile length
    # setting 'forceshort' means to go for smallest number of cards, regardless of points
    # (default is most points, regardless of cards)
    # fmode=1, return value to user; fmode=2, return number of cards
    {
    # print( paste( "Entering:", word, " maxlen =", maxlen ) )
    cards <- v <- v1 <- v2 <- 0
    if( nchar( word ) ) {

    if( !maxlen )
    return( list( value=-999, cards=0 ) ) # no more letters allowed; bail

    v <- letterpoints[ letterpoints$letter==substr( word, 1, 1 ), "points" ]
    rest <- wordvalue( substr( word, 2, nchar( word ) ), letterpoints, maxlen-1, firstcall=FALSE )
    v <- v + rest$value
    cards <- rest$cards + 1
    # print( paste( "v1 =", v, " cards1=", cards ) )

    if( nchar( word ) > 1 ) {
    a <- letterpoints[ letterpoints$letter==substr( word, 1, 2 ), ]
    if( nrow( a ) ) { # how do I test for no match above?
    v2 <- a[ 1, "points" ]
    rest <- wordvalue( substr( word, 3, nchar( word ) ), letterpoints, maxlen-1, firstcall=FALSE )
    v2 <- v2 + rest$value
    cards2 <- rest$cards + 1
    # print( paste( "v2 =", v2, "cards2=", cards2 ) )
    if( ( v2 >= v ) || ( forceshort && ( cards2 < cards ) ) ) {
    v <- v2
    cards <- cards2
    }
    }
    }
    }
    # print( paste( "return", list( value=v, cards=cards ) ) )

    if( firstcall ) {
    if( fmode==1 ) {
    return( max( v, 0 ) ) # if -999, e.g., force to zero
    } else {
    return( cards )
    }
    }

    return( list( value=v, cards=cards ) )
    }

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