By now, if you have played Expert level some, you may be thinking that there must be a more advanced way of using the numbers to "see" the mines. If you're like me, trying to figure this out really makes your brain hurt.
It literally took me months of playing, and probably at least a year, before I figured out how to do it (okay, I'm a little slow). The good news is that it is simple and easy to learn and teach. I taught my wife in a few days, and within a month she was approaching my best scores!
Partial determinism involves looking at two numbers in adjacent cells. With complete determinism, we were always examining one number and its surrounding cells. Now we will examine two numbers and use their criteria to flag or clear cells.
Figure 13(a) displays a situation which, using complete determinism, cannot be solved. But using partial determinism, there is enough information here to allow us to progress quite rapidly.
Study Figure 13(b). This situation has occurred at the top edge of the Expert level. The two numbers we will be looking at are the two blue "1"s at the top of the center column of numbers.
There are two uncovered cells (highlighted with pink) next to the top "1" in Figure 13(b). The top "1" tells us that there must be one mine somewhere in these two cells. These two cells, highlighted with pink, are considered one "definite" mine, even though we don't actually know where it is. We have partially determined its location.
The lower "1", boxed in red, is satisfied by the same mine which satisfies the top "1". Since the lower "1" is satisfied somewhere in the top two uncovered cells, the uncovered cell below and to the left (marked with an "X") cannot be a mine, and can be safely cleared. The result is shown in Figure 13(c).
(a) A common situation that can be easily solved with partial determinism. (b) The top "1" restricts the location of the mine that also satisfies the "1" below it. Therefore, the cell marked "X" cannot be a mine. (c) The proper cell uncovered. Voilą!
The previous two paragraphs are very important. If you didn't get the logic on the first read, keep reading them over and over until you see the logic. A similar mantra will help you solve other situations using partial determinism.
Partial determinism will allow you to clear or flag a particular cell, but this information does not always lead to results you can use. Do not be discouraged by this. Every step toward a solution is a step in the right direction, and the additional information will come in handy later in the game, as you back solve around the situation.
If you study Figure 13(c), you can see that a "2" is now fully determined and can be flagged. These flags fully determine the third "1", which can be cleared, and a flag placed left of the top "1". From 13(a), where we had no hope with complete determinism, we have now made substantial progress.
Partial determinism takes more practice than complete determinism. You should expect to work a month or more (depending on how much you play) before you have this technique as part of your regular repertoire.
Some Comments on Play
At this point, if you have started using partial determinism, you should begin to develop "Sweeper Vision". This is a process by which you have learned to flag and clear cells, based merely on the visual situation presented to you. This "Vision" will allow you to very quickly play through common situations without effort, and without having to "stop and think" about what you are doing.
This capability is what you need to hone while playing. It comes naturally with practice, and as you improve you will be able to play almost without thinking about what you are doing.