Answer to Problem 1 (part 3)

The result matrix is tabulated below. Of the twelve combinations, five result in Russia losing a supply center while seven result in no change.

Note that the five successful cases all result in different board positions, some of which are much better for Turkey than others. Since every defensive column has a failure for Russia and every offensive row has a failure for Turkey, there are no sure-fire strategies for either side.

If the only consideration was whether Turkey gained the supply center (let's say it would be his 18th center), then all of the results would be equivalent. In this case the attack "Bla -> Rum" would be said to dominate the attacks "Bul -> Rum" and "Arm -> Bla -> Bul", since it succeeds whenever they do, but the others sometimes fail where it succeeds. The dominated moves would therefore be irrational choices and could be removed from further consideration.