3BV - What Is It?


    The minimum number of left clicks you can clear a board with is called its 3BV.
   
    In 2002, sweepers noticed that some record boards were easier than others. In particular,
Vincent Yeh (Taiwan) scored 52 on an exceptionally easy Expert board. Stephan Bechtel
(Germany) was the first player to count clicks and mention it in the Guestbook, soon followed
by Lasse Nyholm (Denmark) and Matt McGinley (USA).

    In February, Georgi Kermekchiev (Bulgaria) asked the Minesweeper Addicts group if
someone could write a program to count clicks. He also suggested that 3BV/s was a better
measure of skill than just time, and called for a 3BV/s ranking. Noteably, this was again called
for in 2005 and now exists on the site of Gregroire Duffez (France).

    In June, Benny Benjamin (Australia) wrote a program to analyse the 3BV of game
screenshots. He then passed it to Yoni Roll (Israel) who translated it from Visual Basic into
Delphi. An interesting feature was the MRB file format, which uses only 250 bytes per
screenshot. Benny Benjamin created the name "Bechtel's Board Benchmark Value".

    In October, Stefan Pettersson sent me his beta version of Global Mines, asking for
comment from elite players. He soon heard of 3BV and incorporated it into his second release.
Global Mines displays 3BV stats after the game finishes and lists click ratios. However, it did
not list 3BV/s. Features of the program included storage of your best 100 games, and encrypted
submission of games to an online ranking with saved boards and stats. Unfortunately, Stefan
cancelled his project in November due to lack of resources.

   Sorin Manea (Romania) took 3BV a step further in 2003 and created the Recorder. His
program was the first to display stats while you played. Stats are saved to a text file from which
you can sort games and save videos.

   The Clone was released by Rodrigo Camargo (Brazil) in 2004 and offers more advanced
features than the Recorder.

   Dmitriy Sukhomlynov (Ukraine) released Arbiter in 2005 with similarly advanced features.

   Some argue that 3BV is biased, being only an accurate measure for No Flag players. It is
difficult to analyse efficiency of Flagging players. For instance, Petterson's program correctly
counts right clicks and chording, but adds the left click from chording to the left click count. The
Recorder does not count chording, making it impossible to tell what your real clicks are. The
Clone accurately counts chording and left clicks, but misses a subtlety that several players exploit:
You can flag, then chord, without relifting your right finger. Thus, while the Clone is technically
correct to distinguish these actions, it is not obvious when flagging has been efficient. Steffan
Stachna (Germany) and Damien Moore (Canada) first mentioned this technique in 2002.

    Another subtlety of 3BV is that boards are occasionally finished in fewer clicks. This is due to
clever flagging, and is not known to always be possible.

   Another consideration is that 3BV is best described as a correlation between a board and its
ease. Stephan Bechtel noted in 2002 that he had scored 20 seconds on both a 38 and 72 3BV
Intermediate board. Such cases tend to be anomalies, but do make an interesting point: 3BV is
a good correlation, but not a perfect one.

   Several formulae have since been suggested for more accurate measures of skill. However,
none capture the ease of a board and relate it to skill more simply and effectively than 3BV.














Damien Moore
Rewritten in depth Mar 16, 2006
Original article Nov 2002