I have written a perl program to compute the number of possible scrabble games up to the point where the first player has placed a word on the board but not drawn tiles, and the second player hasn't done anything yet.
It works basically like this: Read in each word from the lexicon of length L up to 7 Find out how many racks contain the word without blanks = R0 Replace each letter in the word with a blank Find out how many racks contain that spelling = R(more subscripts) Replace each letter to the end with another blank Find out how many racks for that Add up all the Rs and multiply by 2 * L (for different placements) Add that to the total Go to the next word if there is one Print the result This does not include exchanges or passing or challenging or playing phonies or missing the center square or playing from a rack of 8 tiles or playing disconnected tiles or drawing tiles from the wrong bag or mis-designating the blank or taking a different amount of time on the clock, etc. I multiplied by 2 for the different placements because it makes me mad when people start vertically so that makes it distinct from starting horizontally. For example with this counting any 7 letter word can be played in 406 different ways, 203 horizontally and 203 vertically. 2 * 7 * (1 + 7 + (7 * 6 / 2)) = 2 * 7 * 29 For six letter words and shorter each possible spelling of the word (with blanks) is multiplied by a figure representing possible leaves. Possible leaves depend on what tiles are used to spell the word (including blanks and not blanks). The answer I get is: 1,403,470,757 * 2 = 2,806,941,514 I am reasonably sure the parts of the program are working OK though I could have missed something of course. My email is [email protected] so in case you want the program please request it by email and I will send it. I wouldn't mind if someone wants to check it. Kevin Leeds --- In [email protected], Russell Honeybun <tc...@...> wrote: > > Yes I too do not understand the incredible amount of faff about not making a > move. > > Too many words about nothing. :p I look forward to some results. > > > --- On Sun, 3/8/09, zax_...@... <zax_...@...> wrote: > > From: zax_...@... <zax_...@...> > Subject: Re: [quackle] Re: Scrabble Complexity > To: [email protected] > Date: Sunday, March 8, 2009, 9:22 AM > > You crazy lunkheads. You make it much too difficult with the infinite > passing, etc. > > Try figuring out the total number of opening moves if no phoneys and you have > to touch the center star and all passes and exchanges are considered equal > and count as one. > > Geesh, just because it is hard... > > Zax > > PS I won the Westinghouse Prize. For having the cleanest fridge. > > --- On Sat, 3/7/09, Steven Gordon <sgordon...@...> wrote: > > From: Steven Gordon <sgordon...@...> > Subject: Re: [quackle] Re: Scrabble Complexity > To: [email protected] > Date: Saturday, March 7, 2009, 8:16 PM > > If the number of total moves was bounded (as are the number of racks > and legal moves at each point in the game), the number of distinct > sequences of moves must be bounded, making the total number of > distinct games bounded. > > You can enumerate them all, but you will run out of numbers before you > run out of legal move sequences as long as the N-pass rule applies for > some finite N. > > Steven Gordon > On Sat, Mar 7, 2009 at 3:10 PM, G. Vincent Castellano <g...@ocsystems. com> > wrote: > > Ok, point, I was being too clever. Can I save face by claiming that the > > number > > of games is countably infinite as long as you require that all the games be > > of finite length? > > > > I concede that if you allow for games which never terminate, then my method > > will not enumerate them. > > > > I should probably stop now before I annoy the Real Mathematicians among us. > > --gvc > > > > Eugene Deon wrote: > >> *That's like saying you can enumrate the real numbers by starting with > > > >> the first decimal digit and building a tree with 10 children per node > >> off into infinity. * > >> > >> *I'm quite sure I can find a unique game of scrabble for every real > >> number. And the decision tree is trivial. Both players exchange 7 > >> every turn. One decision. It's what's on the rack that makes it > >> different.* > >> > >>
