Date: Sun, 27 July, 1997
From: Jim Geary
To: cgp
Subject: But You Need to Know

Executive Summary:

Some players feel that because Maven has played so unbelievably well against them, that perhaps the tile-picking mechanism needs a little "fine-tuning" to truly be random. JG addresses this.

On Sat, 26 Jul 1997, LAWREN FREEBODY wrote: (tho echoing the sentiments of Marlon and perhaps others) 

 Spurred on in the hope of a fruitful discussion:
OK... 
 (analysis of random picking ness)

 considerations about the programmer(s). What we are talking about
 appears to be simple programming "fine-tuning". As an engineer
Writing a random-tile picking routine does not take a lot of engineering horsepower. To test this, I had an idiot programmer (me) write a routine to pick tiles at random. It took 18 minutes using pieces of programs I had previously written. I then tested this program by running it 1,000,000 loops and summarizing the data. Surprisingly, the results for each letter fell within acceptable statistical deviation of the expected result (10k * n : E(a)=90k..) I'll go out on a limb and say Brian Sheppard is a better programmer than I and can probably accomplish this task without hundreds of yet incomplete "refinements." If it is true (I don't know) that when passing tiles, your passers may endup being passees, then I would also bet that that was not BS's doing, as he has used the Maven engine probably more than the rest of humanity combined and would've noticed that. This has never happened to me when playing the original non-Hasbro Maven and I'll hazard that this inadvertant "refinement" was introduced at the Hasbro end. In any event this *would* be a disadvantage to the human player as quite frankly they will pass in situations where they shouldn't more often, not because of strategic problems (there exist some situations where the creative human will make a brilliant pass that would be difficult to achieve algorithmically, though I've seen Maven make some damn fine passes into a rich bag) but because of failure to find those ass-saving thru plays.

Now, to program a picker that intentionally c****s, that would take some doing and it would be by no means inadvertant. If we start with the premise that Brian Sheppard has no motivation to c****, then we can conclude that Maven does not c****. If you dispute this premise, please state your reasons publicly on cgp and CC them to SheppardCo@aol.com . 

 Maven seems to perform impeccably in endgame situations, very, very
 well in early to midgame situations, and brilliantly (though open for
 some interesting speculation) on opening racks. I think Maven plays
 fair, but hasn't figured out how to draw in true random fashion. And
 since Maven knows how Maven draws, it can (and does) play accordingly.
This is true. Maven *does* know how maven draws -- at random. Maven makes it's decisions based on the chance of drawing unseen tiles according to the appropriate distribution of the unseen tiles. Most humans play at the level where they make the best play that they can see. The best humans see the best play that they can make. Part of determining bestness is an awareness of what letters are in the bag. A few years ago in a tournament, I made an autopilot-type play and was rewarded with a screwed rack because I hadn't paid enough attention to the unseen tiles. Bob Felt was sitting next to me (thank goodness for small blessings) and said "what's the point of your even tracking?" I still hear that voice when I fail to pay attention to the bag at all times. I guarantee you that Maven hears that little voice and heeds it every turn. 
 I think the draw/play logic in early to mid-game is faulty. As I
 mentioned before, though in less detail, Maven takes some surprising
 risks, opening S plays and "easy" bingos on the triple, but amazingly
 its human opponent doesn't seem to have the right tiles, though they are
 still in the bag, and often in quantity.
Surprising by whose standards? There are not more than ten people in the game who understand the strategic aspects of scrabble better than Brian Sheppard. BS has incoporated this knowledge into Maven's algorithms. Unless you have internalized BS's theoretical writings, you are at a pronounced strategic disadvantage to Maven (who has). I am sure that BS understands the expense of slotting triple-triples. The mathematics of this action is pretty straightforward and has been thoroughly analyzed and probably incorporated into Maven. If one feels that Maven consistently gets away with unjustified risks, perhaps one's internal model of risk/reward needs refined. 
 Also, for those who like to watch how Maven "thinks," watch how it
 plays in moves 2 thru 7. If you get skunked or Maven skunks itself
 (this seems to go 50-50) the fate will NOT turn in moves 8 thru 13.
 Have fun with it.
This would seem to say that having a lead early in a game is a good thing. No argument here. If anything, this might be the one area where a human master might have the edge on Maven, as Maven does not base it's individual move choices on % winning chances. A human with damn near perfect vocabulary and vision along with completely sound strategic understanding should be able to outplay Maven to the tune of 50-55% because of their ability to differentiate situations that require nonlinear analysis. This is a very small group, but not one of them has ever stated to me privately or on cgp that they think Maven cheats or that their results are worse than what they expect. I'll extrapolate a little and venture that players who make it to the pantheon of Scrabble don't do so by blaming their losses on luck. In the summer of 95 when I was preparing for Superstars (ie playing a hell of a lot better than I do now), I played over 100 games with Maven and was happy to score 50%. I believe there was one run where I lost over 10 games in a row and another where I won over 10 in a row. In neither instance did I or my opponent think the other was cheating. 
 How sad! So close to perfect... random tile draws seem like a small feat
 compared to the wonder of programming that went into end game analysis.

I hope that after reading my post, you do not still believe that Brian Sheppard wrote a brilliant program yet couldn't get the tile picking right.

The reason Maven does so well against mortals is that Maven is so much better than them. The use of Maven in analyzing my games and simulating unclear situations has helped me improve greatly. Believing that the reason Maven wups you is due to some underhandedness will only stand in the way of using Maven to improve. The first step is admitting you have a problem..

Regards

JG

(now, of course, everyone knows the Deep Blue programmers cheated)

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