Try working with the second blank first. The second blank is talking about what a player will be forced to do if he’s stubborn. The clue is that the “mistakes” the player makes will lead to the “prevailing strategy of his or her opponent.” Because of these clues, we know that a word that means “to give in” would be a good match. Capitulate is the only word that works, as dissent means to disagree and repudiate means to reject. Now look at the first blank. The first blank is referring to something all great chess players know. The clue tells us that they know stubbornness will almost surely lead to mistakes that force a player to capitulate to the prevailing strategy of his or her opponent. As you can see, we needed to solve for the second blank first, as we would not have known what stubbornness would lead to without doing so. Recycle the word stubbornness as your word for the blank. Obdurate is the only word that works for the first blank. Finicky means to be overly particular, and vituperative means to be combative.