Tiger Lilov's video about the Zadar Open 2012 motivated me to look at the relevant data in some detail. The issue involves a non-grandmaster player (NGM) who played against grandmasters (GM) with such surprising strength that many people wondered whether he had an unfair advantage, possibly in the way of computer assistance.
I took a sample of moves from games 58, 75, 87, 100, 117, and 136 in which the NGM played GM. The NGM won three of these games and lost one. The other two ended in draw by mutual agreement. The question raised by Tiger concerns the use of computer generated moves - specifically moves recommended by Houdini 3 Pro. Since I don't have access to Houdini 3 Pro, I used Houdini 3 and collected data from the tournament PGN file provided by chessbase.com. The sample data are summarized below.
To exclude rote opening moves, I tallied the data from move 10 in each game. I counted 321 moves in these six games - 160 by the NGM and 161 by the GM players. Of the 321 moves I identified 195 as "computer moves" because each move coincided exactly with the move recommended by Houdini at a depth of 19 to 20 half moves. The other 126 moves are likewise identified as "non computer moves". So we find that almost 2/3 of the moves in all six matches, 60.7% to be exact, are coincident with Houdini recommendations.
Of the 160 moves made by the NGM 115, or 71.9% , coincided with Houdini moves while the 161 moves made by GM contain only 80 Houdini moves at the considerably lower rate of 49.7%. We can carry out a statistical test to determine whether the observed difference in the rate of computer moves could have happened by chance in the small sample of moves taken.
The Chi-Square test shows that if the GM and the NGM had the same propensity to make Houdini moves, the probability of realizing the observed difference in this sample is 0.3%. In non medical statistics, we normally consider a probability of less than 5% to be something we would not expect to happen. So in this case, the sample data show that there is in fact a real difference in the computer move rate between the NGM and the GM. In particular, we conclude that the computer move rate of the NGM is higher than that of the GM.
The additional question raised by Tiger is whether the NGM's computer move rate is unusually high. To answer that question I took a sample of moves from the 2012 world championship between Anand and Gelfand counting from move number 10 to move 29 or the end of the game if the game was shorter than 29 moves. Of 398 moves in my sample, 280 or 70.4% were computer moves with Anand slightly higher at 73.5% and Gelfand somewhat lower at 67.2%. In this context, we can see that a computer move rate of 71.9% is actually as unusually high as Tiger had suspected as it is comparable to the rate of the reigning world champion.
Incidentally, the positive relationship between player rating and rate of computer moves shows that computer moves are not an aberration but consistent with good chess and the high rate of Houdini moves by the NGM may imply only that he was simply playing well.
Another question raised is the the occurrence of long sequences of consecutive Houdini moves by the NGM. The longest sequence of Houdini moves by the NGM in my sample is 14 moves. There are two of these sequences - one starts from move 15 in game 75 and the other from move 13 in game 87. The longest sequence of such moves by the GM is 4 moves and these occur in all the games. These sequences often occur because of a series of exchanges. I found 40 instances of consecutive Houdini moves in the sample, 20 by the NGM and 20 by the GM. The average length of these sequences for the NGM is 5.15 moves. The average length for the GM is almost half that at 2.75.
The t-statistic for this difference is more than 12 which implies that the observed difference could not have occured in our sample if there were not a real difference in the propensity to make sequences of Houdini moves. We conclude that the data provide sufficient evidence that the NGM has a higher propensity to make sequences of Houdini moves - just as Tiger had suspected.
By way of comparison, the average length of Houdini move sequences in the Anand-Gelfand 2012 world championship match is 4.17 (Anand 4.19, Gelfand 4.15). The NGM's average sequence length of 5.15 exceeds the length achieved in the world championship by about one move.
The data seem to show that the NGM tends to play a lot like Houdini. As to the question of how the NGM developed this ability, we really have no actual data to go on and thus all we can do is speculate. It could be that the NGM has played so many games with Houdini that he developed a Houdini-like pattern in his moves. It is also speculated that the NGM used devious high-tech methods to access Houdini during the match and that therefore he enjoyed an unfair advantage over the GM.
Yet, although there is insufficient evidence to conclude that the NGM used any of the high tech cheating devices described by Tiger, the important message in Tiger's videos may be that these devices exist and they are not very expensive; and that alone should be sufficient reason to install the cell phone jammers in tournament halls that Tiger has proposed.