
Probability of drawing a given word from a bag of letters in Scrabble - georgecmu
http://stats.stackexchange.com/q/74468/24258
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mrcactu5
When I set it to "advanced" level, I wondered how my computer scrabble player
got 6 bingos in a row.

Scrabble is perfect information. You don't know your opponents tiles, so they
may as well be in the bag. At any given stage, you know the count for each
letter:

    
    
      A: 3
      B: 0
      C: 1
      D: 1
      E: 5
      F: 1
      G: 0
      ...
    

Then you can calculate the odds of any given word using Multinomial
distribution.
[http://en.wikipedia.org/wiki/Multinomial_distribution#Probab...](http://en.wikipedia.org/wiki/Multinomial_distribution#Probability_mass_function)

I would wonder how we could simulate human players, whose dictionaries are
incomplete? And even if we know the word, we may not be able to do all the
shuffling in our head (or even with the tiles).

There used to be JumbleTime
[http://www.jumbletime.com/](http://www.jumbletime.com/) to practice
identifying 4, 5, 6, 7 or 8-letter words. Certain people were consistently on
the leaderboard. Now the best I can find is DailyAnagram
[http://www.dailyanagram.com/](http://www.dailyanagram.com/)

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singlow
When tournament Scrabble players have probability questions they usually turn
to Quackle, a GPL program created by Jason Katz-Brown and John O'Laughlin that
can simulate scrabble games. Not sure if it has a way to find this particular
answer.

------
rootbear
Years ago, I tried to calculate how many opening positions there are in
Scrabble with two players. I didn't get very far...

------
swayvil
This calculation should include the probability of various events
interfering/participating in the process of drawing the word : wind, rain,
gravitational flux, novas, sudden muscular spasms, moods, random compelling
thoughts, etc.

I guess the first component in any "realistic" model is what to ignore.

~~~
ronaldx
I'm not sure what you're trying to say, but I'm replying anyway.

If there's a sudden gust of wind, say, there's a possibility you might draw a
different tile than you would have otherwise. But, this wouldn't make
individual tiles any more or less likely. As long as we can agree that wind
has a purely random effect, it does not need to be part of the probability
model.

Putting tiles into the bag and redrawing them may, however, result in
particular patterns. For example, it would be reasonable to believe that LIFO
has some influence: last in, first out. This would depend on the individuals
involved in shuffling and drawing the tiles, but some patterns common to human
players could be identified with some study.

I would suggest that word combinations could be more likely to appear than the
given random model predicts (and non-word combinations less likely), as the
groups of tiles may hang over from previous games.

~~~
swayvil
Well, what I'm saying that your model, while useful, will be unrealistic if it
does not take into account the billion other variables in play. Some words
weigh more (in ink). The meaning of words bear upon the mood of the
wordpicker, influencing his hand. Etc. And that this is the case with models
in general. (And your reply reflects the attitude of modelers, in general).

Call it humor.

~~~
ronaldx
And your reply reflects the attitude of someone who hasn't fully understood
probability. Best wishes ;)

