On the First Click in Microsoft's Minesweeper
by Tim Kostka


The first click on beginner
I ran through the 50,000 some boards in the Beginner board cycles and recorded the number of times each block opened up a space for each board. In the graph on the right, the numbers in each block tell the percentage of the time an area was opened when clicking on that block first. As was expected, the corner proved to be open the most and the center spaces were open the least
The reason for the lower percentages around the top-left corner are discussed in the TLM article.

The first click on Intermediate
On Intermediate, I did the same thing with the 25,000 some boards in the intermediate board cycles. The same thing happens, except the percentages are slightly higher.

The first click on Expert
Same deal here, except since Expert's board cycle is so big, this was out of 60,000 sequential boards. The percentages are lower due to the increased mine density and the influence of TLM is extended to six blocks due to the increased mine dinsity.

Size of the first click opening on Beginner
This graph tells the size of the area opened on the first click. For each board in the cycle, I saw if an area would be opened by clicking on a certain block, and if it was, then I calculated the size of that opening. For example, if an area opened that was a 3x3 square (a blank space surrounded by 8 numbers), I would mark down a 9. For the corners the minimum size of an opening would be four (a blank space and 3 numbers), and for the edges it would be 6. These values were then averaged for each block over the entire 50,000 some boards in the beginner board cycles.
As you can see, the tendency is that the middle produces larger openings that blocks closer to the sides. And this of course is perfectly logical and exactly what one would expect.

Size of the first click opening on Intermediate
This was out of around 25,000 boards and resulted in exactly the same pattern as Beginner.

Size of the first click opening on Expert
This was out of just over 70,000 boards, and, again, resulted in the same pattern as the other two. The decreased size of the openings is due to the increased mine density in expert mode.


© 2006 Tim Kostka