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December 11, 2010

Is Minesweeper for Windows 7 a Game of All Skill?

The chances of my winning six or more out of eight games of Minesweeper are .00012% given my previous winning average of 6%. This average held steady for thousands of games and hundreds of wasted hours on my former computer, which was stolen (see Blog Blocked by Breakin).

My new computer came with Windows 7 and I avoided searching the games folder for Minesweeper for over a week. After all, I had plenty else to do training a new computer. But I could only hold off so long. I considered winning the first game a good omen for my new computer. The second game was a bonus. Winning the third was suspicious. One loss was a deliberate experiment; the other was a mistake and not bad luck.

Minesweeper for Windows as it used to be was a game of both skill and luck. Sometimes you would have enough information to determine whether or not a square contains a mine. As fellow players know, uncovering a square with a mine in it terminates the game with extreme prejudice. Sometimes there just wasn't enough information and you were forced to guess. Skill helps you take the highest probability guesses but they were still guesses. There were times when you were down to two choices and knew a bomb lay under one of them. It was luck if you didn't get blown up.

choice with 50-50 odds (from Wikipedia)

Now, based on limited but statistically valid experiments, Minesweeper for Windows may have become a game of all skill. Without hacking the code, I'm not sure how this was done; but I can think of two possibilities – both could be true.

As a preface, Minesweeper for Windows has always cheated slightly in your favor. Even though it appeared that the location of mines was calculated in advance when the game started, you never uncovered a mine on your first click. According to Wikipedia, there is an algorithm for moving a mine away if it is under the square you clicked to begin the game.

According to a more general Wikipedia article about Minesweeper (the article cited in the previous paragraph is just about Minesweeper for Windows), there are versions of the game that never lead to situations which require guessing – presumably because they don't generate mine patterns which can't be deduced like the one illustrated above. It does seem that I am doing less guessing on Windows 7.

But I'm pretty sure I am doing some guessing – and that my guesses always turn out to be right when I have no other choice but to guess. This could be a benign shell game. If there are two choices as illustrated above, either of which might be right, the algorithm could always move the mine from the square you picked to the square you didn't pick if you made a bad guess. On the other hand, when I randomly clicked boxes at the beginning of a game instead of working where I had information, Boom!

Clearly I have no choice:

  1. must continue the experiments no matter how much times they take
  2. must update the Wikipedia entry on Minesweeper for Windows

hattip for an update on probability calculations to Ion Saliu.

Related posts:

Getting Back Online

Blog Blocked by Breakin

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