I have thought of the reason why it appears that we have more chances to open an area when
clicking in the corners or on the edges than in the middle. I have calculated the probability to
open an area in different situations. Here is what I have found. I have supposed that THE
MINES ARE RANDOMLY PUT ON THE BOARD ( we already know that in reality the
randomness is not a perfect, but let’s see… )
BEGINNER ( 10 mines on 8 × 8 = 64 squares )
1st click
2nd click
No mine on the square you’ve chosen. There After the first click, there are 10 mines left on
are 10 mines on the 63 other squares, so 53
63 squares ( 53 empty squares ). To open an
chances out of 63 that there is no mine on
area clicking in the middle, you need 9 of
each square surrounding the one you’ve
those empty squares. Not just 8, like when it
clicked on.
was the first click.
( 53 )8 = 25.09 %
( 53 )9 = 21.11 %
63
63
( 53 )5 = 42.14 %
( 53 )6 = 35.45 %
63
63
3
( 53 ) = 59.54 %
( 53 )4 = 50.09 %
63
63
Middle
Edge
Corner
The same thing can be done for inter and expert…
INTER ( 40 mines on 16 × 16 = 256 squares )
1st click
2nd click
( 215 )8 = 25.54 %
( 215 )9 = 21.53 %
255
255
5
215
(
) = 42.61 %
( 215 )6 = 35.92 %
255
255
( 215 )3 = 59.94 %
( 215 )4 = 50.54 %
255
255
Middle
Edge
Corner
EXPERT ( 99 mines on 16 × 30 = 480 squares )
1st click
2nd click
( 380 )8 = 15.69 %
( 380 )9 = 12.45 %
479
479
( 380 )5 = 31.42 %
( 380 )6 = 24.93 %
479
479
( 380 )3 = 49.93 %
( 380 )4 = 39.61 %
479
479
Middle
Edge
Corner
3 things to say about it :
 I don’t feel like verifying all that, starting hundreds of game for each situation.
Maybe you or someone else will take time to do so…
 I have compared my results concerning the expert board with those obtained by
Paul Kerry and published on your site. The comparison lead us to conclude that
even if the randomness is not perfect, it is not very far to be…
Place for the first click.
Theorical percentage of openings if we consider
that mines are randomly put on the board.
Percentage of openings obtained by Paul Kerry
( on a total of 424, 196, and 135 games )

Middle
15.69
Edge
31.42
Corner
49.93
14
31
44
It’s amazing to see that the probability to open an area is slightly bigger on an inter
board than on a beginner, despite of the fact that the density of mines is the same
for both. It’s because the density isn’t exactly what is took into account in the
calculation. All that is due to the fact that the first click is never a mine.