First off this week, a quick recap. I've been using *CBTree* to help me learn
the White side of the Exchange Variation of the Ruy Lopez. At the end of
Part Two, after the moves 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 dxc6, we saw
that *CBTree* provided me with the following menu of choices:

MOVE | FREQUENCY | % | RESULT | ELO |
---|---|---|---|---|

5.0-0 | 1288 | 76% | 0.54 | 2290 |

5.Nc3 | 217 | 13% | 0.56 | 2297 |

5.d4 | 150 | 9% | 0.47 | 2274 |

5.d3 | 21 | 1% | 0.50 | 2234 |

5.h3 | 11 | 1% | 0.36 | 2200 |

5.Nxe5 | 6 | <1% | 0.33 | 2296 |

5.c3 | 2 | <1% | 0.50 | 1995 |

5.b3 | 1 | <1% | 0.50 | 2200 |

Since I'm studying this opening from White's perspective, I have a choice to make here. Which line do I want to concentrate on? I'll need to use the process of elimination to make my decision.

Most of the lines look pretty similar from the standpoint of results, all
hovering within a handful of points of 0.50, so they all look to give White
and Black about even chances. However, the last three moves on the list
appeared in less than ten games each, so we can label them "untested". I
might try them against *Fritz* later, but right now I'll bypass them. 5.d3 and
5.h3 both look pretty passive, so I'll cross them off the list too.

So which of the three remaining moves will I concentrate on? I already know from my outside reading that the Ruy Exchange tends to be pretty drawish, because it usually leads to a mass exchange of material. 5.d4 looks like it would achieve that end much more quickly than the other two lines, so I'll study it (despite the fact that, of the three candidate moves, it seems to be the one that most favors Black). Another plus to choosing 5.d4 is that there are 150 games (out of the original 1729 games) from the database that follow this line, so by choosing this path I've cut the amount of data that I need to wade through by more than 90% of the original total.

Let's digress and consider this "outside reading" business for a moment. Steve's Rule #3 for using a statistical game tree program reads as follows: don't be afraid to consult books and other outside knowledge to help you study the game tree. In many cases, this approach will give you information and insight that goes beyond mere statistics. (For example, I read somewhere that 5.d4 was the standard move prior to the 1960's. Then Fischer popularized 5.0-0 and castling became the norm).

So what's next? After 5.d4 we see:

MOVE | FREQUENCY | % | RESULT | ELO |
---|---|---|---|---|

5...exd4 | 142 | 95% | 0.45 | 2288 |

5...Bg4 | 6 | 4% | 0.92 | 2216 |

5...Nf6 | 2 | 1% | 0.50 | 2200 |

Odds are that my class-level opponents will be playing 5...exd4, since the other two moves have been played very infrequently. Even if they play one of the other two moves, I doubt that they're going to have any more information on them than I do. So I'll skip the latter two moves for now and come back to them later.

After 5...exd4, we see:

MOVE | FREQUENCY | % | RESULT | ELO |
---|---|---|---|---|

6.Qxd4 | 140 | 99% | 0.45 | 2279 |

6.Nxd4 | 2 | 1% | 0.25 | 2203 |

Forget the numbers. There is no way that I'm going to play 6.Nxd4 because it puts the Knight on a doofy square (where it can be easily attacked by a Black c-pawn) and sets up a possible Queen swap on d1 that will prevent me from castling. So 6.Qxd4 is the only choice.

MOVE | FREQUENCY | % | RESULT | ELO |
---|---|---|---|---|

6...Qxd4 | 127 | 91% | 0.45 | 2295 |

6...Bg4 | 11 | 8% | 0.59 | 2225 |

6...Be6 | 2 | 1% | 0.25 | 2200 |

Here comes a typical question that might be posed by someone unfamiliar with
the science of statistics: "Since 6...Be6 is way better for Black, why isn't
it played more often?" In Aristotelian fashion, we might answer the question
with a question: "Is 6...Be6 really better, or does it just *look* better?"

Examining the stats we notice that 6...Be6 was played in just two games; Black won one and the other was a draw. Two games does not constitute a good statistical sampling.

We're all familiar with ads proclaiming that "four out of five dentists recommend Brand Yeeech toothpaste". But what does this really mean? It means absolutely nothing, because we have no idea what type of statistical base is being used to come to that conclusion. If thousands of dentists were interviewed and 80% of them recommended Brand Yeeech, I'd be impressed. But it's more likely that only five dentists were consulted, and four of them practice in small towns where the tiny grocery carries only Brand Yeeech and no other toothpaste brands. So of course these four recommend it; they have no choice.

Fortunately, *CBTree* gives us an opportunity that Madison Avenue fails to
provide: the chance to look behind the statistics and see how they were
derived.

If I highlight 6...Be6 and click on "Games" at the top of the screen, I see
that Black's sole victory is Game #282 of the database (Mieses-Janowski,
Cambridge Springs, 1904). Upon firing up *ChessBase* or *Fritz* and playing
through the game, I see that Mieses (White) was actually a piece up at one
point but later got his Knight trapped by a Black Bishop and a swarm of
Black pawns in the endgame. Obviously, Black's victory was not due directly
to his having played 6...Be6. So we can conclude that 6...Be6 isn't in and
of itself better for Black -- it just worked out that way in one of the two
games in the database in which it was played. The other game was a draw, so
after averaging 0.00 (the Black win) and 0.50 (the draw), we get 0.25. The
raw statistical data suggests that Black is winning after 6...Be6, but our
research proves otherwise.

This brings up Steve's Rule #4 for using a statistical tree program: before
drawing conclusions from the numerical data, make sure the numbers are based
on a ggod statistical sampling. What constitutes a "good statistical
sampling?" This will vary depending on the overall starting size of the
original database and the number of games in the branch you're currently
examining. Since the particular branch we're looking at contains a total of
140 games, I think that a mere two games is *way* too small a sampling from
which to draw conclusions. By the way, this might seem to be in direct
violation of my first rule for using statistical trees (don't run a tree
program on a large batch of unrelated games) but that's just an illusion;
the key word in Rule #1 is "unrelated". What we're searching for here is a
happy medium: too much data and your head will explode, too little data and
you risk being misled by the numbers.

Personally, I'm skeptical of numbers derived from fewer than 10 games. In
such cases I do exactly what I described a few paragraphs ago: I play
through the games to see what happens later on. Did the move in question
directly contribute to the result or did some other factor later in the game
decide the issue? Steve's Rule #5 for using a statistical tree program comes
into play here: **always** play through complete games to see what's "behind"
the numbers.

Now back to our tree: I remember a time when 6...Bg4 was a hot topic of
debate on *Compuserve*, so I make a mental note to check later to see what all
the shouting was about. Right now, though, I'll stick with 6...Qxd4:

MOVE | FREQUENCY | % | RESULT | ELO |
---|---|---|---|---|

7.Nxd4 | 125 | 98% | 0.44 | 2284 |

END | 2 | 2% | 0.50 | 2280 |

Four more players call it a day, leaving us with 125 games. Clicking on 7.Nxd4, we get this:

MOVE | FREQUENCY | % | RESULT | ELO |
---|---|---|---|---|

7...Bd7 | 62 | 50% | 0.37 | 2325 |

7...c5 | 21 | 17% | 0.48 | 2285 |

7...Bd6 | 20 | 16% | 0.58 | 2284 |

7...Nf6 | 10 | 8% | 0.60 | 2200 |

7...Bc5 | 4 | 3% | 0.38 | 2218 |

END | 3 | 2% | 0.50 | 2367 |

7...g6 | 2 | 2% | 0.50 | 2200 |

7...Be6 | 1 | 1% | 0.00 | 2200 |

7...f6 | 1 | 1% | 0.00 | 2200 |

7...Ne7 | 1 | 1% | 1.00 | 2200 |

Yipes! Time for the "process of elimination" again! Basically, I can cut out
all but the top four moves, since the bottom five ("END" being excluded, of
course) have a statistical base of less than ten games. The upper four moves
have a large enough statistical base to allow me to draw some preliminary
conclusions. Looking at the raw numbers, I see that 7...Bd7 is played about
half the time here and results in an average effectiveness of 0.37. Since an
evaluation of "Black has a slight advantage" is scored as 0.40 by *CBTree*,
we'll round off 7...Bd7's evaluation to a slight plus for Black. The
remaining three variations round off as either an even position or as
slightly better for White. So there's really nothing alarming here.

Between these four variations, we're left with 123 games to study, which is still an impressive chunk of data (though nothing like the original total of 1729 games!).

How do we tackle this data? A good way to do it is to examine the set of games for each one of these four moves, looking for (and playing through) the games that contain commentary. There are several ways to go about doing this.

If our Ruy Lopez Exchange database has an opening classification key, we can
just look up and click on each of the four variations and get the game list
for each one. If the database has no key, but we have a copy of *ChessBase*, we can
direct *ChessBase * to automatically generate an opening key. If we don't have
*ChessBase*, we'll have to do it the old-fashioned way: use the "Games"
command in *CBTree* to call up a list of the games for each variation, write
down the game numbers, and then check them manually in whichever program we're
using to view the games. (A neat shortcut in *CBWin* or *CB6* is to set up the
board position after the candidate move and then hit **SHIFT-F7** to have a list
of the games containing that board position sent to the Clipboard).

Using an opening key, we click on the 7...Bd7 variation. Games with
commentary are easily identifiable by the letters **V** and **C** on the right-hand
side of the games list. In this particular case, there are nine of them. I
would concentrate on these nine games first since they contain variations
and commentary by stronger players. After studying these games and learning
the ideas contained within them, we can look at the unannotated games and
look for the same patterns, themes, and similarities. We then repeat this
process for the other three candidate moves.

After we do this, we can then return to *CBTree* and extend our variation
search an extra eight or ten positions down the road from each of our four
main candidates at Black's seventh move. We do this to search for hidden
traps and pitfalls.

Here's an example: let's say that I'm interested in playing a variation that
*CBTree* shows was played in ten games and is evaluated as 0.90. Looking at
the games list, we see that nine of the ten games ended as wins for White
and just one was a Black victory.

The initial reaction would be to say, "Hot diggety! Sure looks good for White!" So what could be wrong with this picture? Upon closer examination, we see that all of White's wins occurred before 1985. Black's sole win took place in 1986, and our candidate variation never appeared since. Smelling a rat, we play through the next few moves of the game in which Black was victorious. Sure enough, our "dream move" for White gets busted by Black and leads directly to White's downfall. Evidently in 1986 some brainy mug cooked up a theoretical novelty that finally turned the tables on White.

While this scenario may sound overly simplistic, it serves to illustrate the
point: number are not always to be trusted. A similar scenario may have a
different ending; Black's sole victory might have come because White blew
his early advantage and lost a hotly-contested endgame. The only way to know
for sure is to use *CBTree* to check ahead in the game tree, use one of our
other programs to play through the complete games in the database, and use
our brains to analyze the data we uncover.

By now you have the idea of how to use *CBTree* (or any other statistical game
tree program). The main use for these programs is as a sort of road map to
guide us through the labyrinth of variations. The numerical statistics,
while certainly useful, are really of secondary importance. The main purpose
of a tree program is to help locate and isolate specific games and
variations for study and then use the games themselves to discover the
positional and tactical themes that arise from these opening positions.

So don't be enslaved by the "tyranny of numbers"! Use your statistical tree
program as a trusted guide and refer to the numbers as handy guideposts.
Above all, remember to use the various tools at your disposal to discover
the truth behind the numbers. Think for yourself!

*To avoid massive confusion and aggravation, don't run a tree program on a large batch of unrelated games. Organize your data before generating a tree. Corollary: Confusion is bad; cut corners wherever possible.**Don't rely on numerical data that may be based on an incomplete statistical sampling (for example: don't trust the "average Elo rating" for a move unless 90% to 95% of the games in the database give Elo ratings for BOTH players).**Don't be afraid to use books or other outside sources to help you study and understand the game tree.**Before drawing conclusions from the numerical data, make sure that the numbers are based on a good statistical sampling (the exact figure here varies with the situation; a general rule of thumb is to be leery of results based on fewer than ten games).**Always play through complete games to determine what lies behind the statistical data.*