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July 26, 2011


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Thanks for the shout-out, David! This is using TWL; I'll have to try it with the SOWPODS dictionary for sure.

This is a nice summary of the paper. I was going to blog about this, but now I don't have to!

I'll add that the simulation of the two Scrabble "Bots" is accomplished by writing an R wrapper to a the underlying C++ code. Rather than re-implement a difficult bit of analysis in R, he just calls it directly, which is always a smart technique.

Maybe you or Andrew can answer a question that puzzled me. On the histograms on p. 7, the first graph shows the variation in score that is attributed to variation in the pulled tiles. But what is the second? The paper says "standard deviation of score differences," but why are all the standard deviations greater than 30? Weren't there any close games in the 10,000 simulations? I'm missing something....

What happens to that pregenerated double-ended sequence of tiles when one player throws back a bunch of his letters? Or do the AI players never throw anything back, no matter how bad it is?

SOWPODS is based on OSPD and Chambers Dictionary, not the OED. Its successor, the Official Tournament and Club Word List, is based on SOWPODS and Collins Dictionary.

@AC - the AI players do exchange when it makes strategic sense. When one of the bots exchanges, the replacement tiles are randomly selected from the Reserve list (see Fig 2 above) and the old tiles randomly inserted back into it. It's explained in the arXiv paper.

@Paul - thanks for the correction. I have a copy of Chambers sitting here on my desk that I used to use when playing in the UK, so I should have remembered that. I miss ZO and KI.

It seems to be an experiment to show the Q is unlucky (by 2 points?) in the grand average.

Some players might be better than dealing with Q than others so it suggests the idea of Q-skill

Not only are there 26 different letters, but there are a large number of racks to draw so scrabble players have skills that might be measured by a long list of different rack combinations. Someone might have learned all the FISH words while someone else might have spent time studying words with IEST. So FISH is luckier for the first player, but IEST is more likely so the second player probably benefits more overall.

It might be distracted and missing something, but isn't this paper implying that Scrabble is merely about maximizing your points. Something akin to what Neoclassical Economist say about humans as rational profit maximizers?

I've played lots of Scrabble and think this seems naive. You are trying to make sure that your score>opponents score. In other words, defense matters as well as offense. As much as I enjoy these simulations, I don't think they pick up on that idea and so miss enormous nuance.

I agree luck matters, though.

This is very interesting analysis, mind if I cite some of it (linking back here naturally) to my Scrabble mailing list?

The negative effect of the Q fits in with a lot of advice I've read from advanced players, who tend to ditch it as soon as they can. The X is relatively versatile, as you can use it as a two-letter word with any vowel tile.

I wonder what weightings for 'luck' of the tile vs skill of the player look like - is the simulation playing the 'best possible' word each time?

I don't think the end result of the experiment (luck vs. skill in scrabble) is very interesting or surprising. I would rather see where Scrabble falls in the "how much of it is luck" scale vs. other popular games, poker, backgammon, chess, Go and so on.

I'm working on a nano module that plugs into your brain to give you access to every known word but for now you will have to use http://scrabblecheat.com

This is all very well and good, and duplicates a lot of results already known to professional Scrabble® players. But I think the study is flawed in one important area -- bots and expert players don't play in the same way. For one small example, bots will never bluff, nor will they fall for a phoney, no matter how plausible.

These are interesting numbers, but based on the comments, people want to know more. DB makes a valid point, it would be interesting to play this data against other games, like backgammon online.

I really enjoy to read this awesome blog post.

Hey, everybody that has criticism, or doesn't think this is interesting, why don't you
1. carry out your own experiments on scrabble with said criticism or
2. read something else.

I found it very interesting and was thinking about this problem for a few weeks before I found it.

Factoring out luck is easy : just show all players the same set of randomly drawn letters ! Then let every player privately enter his best solution on the board. Each player adds his own score to his personal total. The solution with the highest score is put on the common board, and all players continue with the same rack of remaining letters plus the newly drawn ones. You can play with an infinite number of players as long as you fix a time limit per draw. Leaving the game causes no disturbance. Entering a new game can happen on fixed times - every hour or so.

I'd like an iPhone version in Dutch, please !

Copyright Bart Viaene - Leuven, Belgium if I'm the first with this idea :-)

Wow, I did some work on Scrabble algorithms and must have missed this one. Thank you for the great article. While reading I was thinking about other approaches to solve this.
In reality I recently talked with a finalist from a national Scrabble tournament and she kind of admitted that she lost against a very good opponent and not because of bad luck :)

Great Article! Luck def is a huge component if you have players of similar skill levels. If you had 2 robots going against each other, it 100% would come down to luck of the draw.

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