4 ms·

Probability of drawing a given word from a bag of letters in Scrabble

16 points by georgecmu 13y ago

swayvil 13y ago
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 13y ago
  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 13y ago
    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.
    - llamataboot 13y ago
      "All models are wrong...but some are useful"
    - ronaldx 13y ago
      And your reply reflects the attitude of someone who hasn't fully understood probability. Best wishes ;)
rootbear 13y ago
Years ago, I tried to calculate how many opening positions there are in Scrabble with two players. I didn't get very far...
singlow 13y ago
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.
mrcactu5 13y ago
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#Probability_mass_function http://en.wikipedia.org/wiki/Multinomial_distribution#Probab... 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/

16 points by georgecmu 13y ago

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 13y ago
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 13y ago
  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.
  - llamataboot 13y ago
    "All models are wrong...but some are useful"
  - ronaldx 13y ago
    And your reply reflects the attitude of someone who hasn't fully understood probability. Best wishes ;)

rootbear 13y ago

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

singlow 13y ago

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.

mrcactu5 13y ago

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#Probability_mass_function http://en.wikipedia.org/wiki/Multinomial_distribution#Probab... 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/