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Given that he has a better Scrabble rating than a computer algorithm, there has to be an element of poker at this level - otherwise if it were pure probability

Given that he has a better Scrabble rating than a computer algorithm, there has to be an element of poker at this level - otherwise if it were pure probability and memorization of the words (which a computer would have done perfectly, with no room for error), then a human could not outrank a computer. I'm wondering (for the professional scrabble players out there) - do you play words differently depending on your competitor? That is, do you leave a vulnerability with some players, that you wouldn't with others? Or do you play the same game every time. I was surprised that element of Nigel Richard's Scrabble game wasn't discussed.

icelancer 12y ago
It could just be that the Scrabble AI is not sufficiently advanced to explore the entirety of the decision tree. For all board states X, there are many deep trees that increase in complexity at boards X+1, X+2, etc (though it's arguable that it decreases in complexity in the late game, or can a game can be played "closed" to reduce the chances of bingos). It may not be purely metagaming that causes the difference between AI and humans; the algorithm probably plays a far-from-perfect game.
- ghshephard 12y ago
  The other advantage a computer (probably?) has over a human, is the analysis of probabilities of words being available given whats known about the word play of the opponent given their current (unknown) tiles, and tiles already played. That is, I suspect it's possible, but difficult for a human player to surmise the probability of tiles hidden in an opponents pieces based on the words they've recently played (or not played) - but being able to do so, based on a count of which tiles have already been played and are visible on the table, is probably more challenging - but straightforward for a computer. Are the games that players have played publicly available? While I presume that players at this level have memorized all 270K or so words, they might have tendencies to favor some words versus others, in particular scenarios - that's another advantage that a computer would have - adjusting it's play based on a players history.
  - icelancer 12y ago
    >That is, I suspect it's possible, but difficult for a human player to surmise the probability of tiles hidden in an opponents pieces based on the words they've recently played (or not played) - but being able to do so, based on a count of which tiles have already been played and are visible on the table, is probably more challenging - but straightforward for a computer. I have played a very small amount of competitive Scrabble and a few of my friends are playing in the National tournament that this article references. What you describe is utterly standard by even mediocre tournament players. Tournament Scrabble players do a lot more than memorize good lists of 2s and 3s. It is truly impressive how deep the game can be.
- thret 12y ago
  The article claims there are just shy of 200,000 scrabble words. Why would it be so complex? The key is to use all 7 of your letters. The subset of valid words containing all 7 letters you hold shouldn't be that large, surely the board can be exhaustively searched to fit them?
  - deleted 12y ago
    [deleted]
  - adrianN 12y ago
    You don't have to use all your letters for the same word, and there are strategic considerations regarding which spots you place your words, since that might enable the other player to use the score multiplier tiles for their next move.
  - vijayr 12y ago
    200K words! I wonder how many does an average human know? 5k? 10k?
    - taejo 12y ago
      IIRC 15k-20k is usual for monolingual adult speakers of English. Since different languages have different total vocabulary size -- English's is particularly high -- it probably varies quite a bit across languages. I believe bilinguals tend to have a smaller vocabulary in each language, but larger if both are counted. You can estimate your English vocabulary at http://testyourvocab.com/ http://testyourvocab.com/ (BTW, if anybody knows a site that does a similar test for other languages -- particularly German -- I'd be interested).
  - Strilanc 12y ago
    You don't just want good words, you want to position yourself so your next move is also a good word. So you don't just have to iterate over the current board, you have to iterate over all possible upcoming boards. But it's even worse than that! You want to set up your opponent for a bad move, and vice versa, so you're trying to infer each others' tiles from past moves and bluffing starts to matter. So you also have to reason about counterfactual games where your opponent would have done the same thing, meaning you have to care about the entire game tree instead of just the sub-tree you're in... In the general case, solving games involving partial information requires super-exponential time. It's no picnic. (Of course in practice we use approximations, and those can work quite well.)
zem 12y ago
yes, against a weaker player you can play a more "risky" game - that is, risky in theory because it leaves potential vulnerabilities, but not very much in practice because you can be fairly confident your opponent won't capitalize on them. Nigel actually did that to me once; in a game that he was already winning he deliberately left a difficult lane open to give himself a chance at one last bingo, knowing that I would not see what he was up to, and had the satisfaction of bingoing out in a spot with four of his seven tiles constrained, and picking up a nice bit of extra spread.
MLR 12y ago
Identifying the best turn in any one play should be fairly trivial I think, but the strategy with keeping some letters in hand for a big play later on while still optimising for score is probably fairly complicated within the time limits. Or alternately the AI could just be fairly mediocre, I don't have enough expertise to judge.
yen223 12y ago
Maybe the ranking system is flawed? I don't think Nigel played directly against the computer.
codingdave 12y ago
A computer would only play perfectly if it were coded perfectly. Any nuances to the play style would have to be known by the programmer, and coded into the system. And that doesn't even count plain old bugs that would cause mistakes.
contingencies 12y ago
there has to be an element of poker at this level Pushing the boundaries of acceptable words (uncapitalized Chlorodyne being a good example) is one strategy.

icelancer 12y ago

It could just be that the Scrabble AI is not sufficiently advanced to explore the entirety of the decision tree. For all board states X, there are many deep trees that increase in complexity at boards X+1, X+2, etc (though it's arguable that it decreases in complexity in the late game, or can a game can be played "closed" to reduce the chances of bingos). It may not be purely metagaming that causes the difference between AI and humans; the algorithm probably plays a far-from-perfect game.

ghshephard 12y ago
The other advantage a computer (probably?) has over a human, is the analysis of probabilities of words being available given whats known about the word play of the opponent given their current (unknown) tiles, and tiles already played. That is, I suspect it's possible, but difficult for a human player to surmise the probability of tiles hidden in an opponents pieces based on the words they've recently played (or not played) - but being able to do so, based on a count of which tiles have already been played and are visible on the table, is probably more challenging - but straightforward for a computer. Are the games that players have played publicly available? While I presume that players at this level have memorized all 270K or so words, they might have tendencies to favor some words versus others, in particular scenarios - that's another advantage that a computer would have - adjusting it's play based on a players history.
- icelancer 12y ago
  >That is, I suspect it's possible, but difficult for a human player to surmise the probability of tiles hidden in an opponents pieces based on the words they've recently played (or not played) - but being able to do so, based on a count of which tiles have already been played and are visible on the table, is probably more challenging - but straightforward for a computer. I have played a very small amount of competitive Scrabble and a few of my friends are playing in the National tournament that this article references. What you describe is utterly standard by even mediocre tournament players. Tournament Scrabble players do a lot more than memorize good lists of 2s and 3s. It is truly impressive how deep the game can be.
thret 12y ago
The article claims there are just shy of 200,000 scrabble words. Why would it be so complex? The key is to use all 7 of your letters. The subset of valid words containing all 7 letters you hold shouldn't be that large, surely the board can be exhaustively searched to fit them?
- deleted 12y ago
  [deleted]
- adrianN 12y ago
  You don't have to use all your letters for the same word, and there are strategic considerations regarding which spots you place your words, since that might enable the other player to use the score multiplier tiles for their next move.
- vijayr 12y ago
  200K words! I wonder how many does an average human know? 5k? 10k?
  - taejo 12y ago
    IIRC 15k-20k is usual for monolingual adult speakers of English. Since different languages have different total vocabulary size -- English's is particularly high -- it probably varies quite a bit across languages. I believe bilinguals tend to have a smaller vocabulary in each language, but larger if both are counted. You can estimate your English vocabulary at http://testyourvocab.com/ http://testyourvocab.com/ (BTW, if anybody knows a site that does a similar test for other languages -- particularly German -- I'd be interested).
- Strilanc 12y ago
  You don't just want good words, you want to position yourself so your next move is also a good word. So you don't just have to iterate over the current board, you have to iterate over all possible upcoming boards. But it's even worse than that! You want to set up your opponent for a bad move, and vice versa, so you're trying to infer each others' tiles from past moves and bluffing starts to matter. So you also have to reason about counterfactual games where your opponent would have done the same thing, meaning you have to care about the entire game tree instead of just the sub-tree you're in... In the general case, solving games involving partial information requires super-exponential time. It's no picnic. (Of course in practice we use approximations, and those can work quite well.)

zem 12y ago

yes, against a weaker player you can play a more "risky" game - that is, risky in theory because it leaves potential vulnerabilities, but not very much in practice because you can be fairly confident your opponent won't capitalize on them. Nigel actually did that to me once; in a game that he was already winning he deliberately left a difficult lane open to give himself a chance at one last bingo, knowing that I would not see what he was up to, and had the satisfaction of bingoing out in a spot with four of his seven tiles constrained, and picking up a nice bit of extra spread.

MLR 12y ago

Identifying the best turn in any one play should be fairly trivial I think, but the strategy with keeping some letters in hand for a big play later on while still optimising for score is probably fairly complicated within the time limits. Or alternately the AI could just be fairly mediocre, I don't have enough expertise to judge.

yen223 12y ago

Maybe the ranking system is flawed? I don't think Nigel played directly against the computer.

codingdave 12y ago

A computer would only play perfectly if it were coded perfectly. Any nuances to the play style would have to be known by the programmer, and coded into the system. And that doesn't even count plain old bugs that would cause mistakes.

contingencies 12y ago

there has to be an element of poker at this level Pushing the boundaries of acceptable words (uncapitalized Chlorodyne being a good example) is one strategy.