One example of playing the board by seeing what kind of player each of my opponents was:
I recently played an 8 person World 2.1 Singles game. I started in Europe as the pink player. The Green player started in Parana and South Africa. The Blue player built up really strong in the Middle East and the rest of Africa in the north, while the red player slowly took over the rest of Asia.
I was lucky in this game to be the farthest player away from Green, because Green was the most aggressive player with lots of armies. I had a pretty nice stand off against red and blue, all three of us slowly building around Moskva, Iran, Pakistan, and Komi/Kaz. Of course, none of us wanted to attack each other, since the third could easily swoop in.
It turned out that the green player was pretty vindictive. If anyone attacked him, he would lash out unrelentingly. He did this early on against yellow, and I resolved to stay out of his way and hope the others would hold him off. Eventially he got hold of Oceania and red had enough - felt he was getting too strong (in the meantime, I was taking over North America, trusting that Blue and Red would hold each other off from attacking me in europe). Red attacked green, and green went after him with a vengeance.
Blue saw this as an opportunity to take the rest of Africa away from green. Tactically speaking, it was the right move. Green didn't have the resources to take on blue, so he should have felt that the game was balanced enough (him in Africa, me in europe and NA, and green in Oceania, La Plata, and much of Asia), and he was just a bit stronger than the the rest of us. (Again, at this time I was in a conquest against Silver, and there wasn't really anything I was going to do about it.
The problem with Blue's move, though, was that he didn't count on what kind of player green was, even though the guy had shown it twice, lashing out against yellow and then red. All I had to do was wait for them to tear each other apart.
Green of course, struck back, giving me time to take out the silver player and build up my armies on my borders. Green also made some really bad diplomacy moves, making promises he didn't keep and offers that didn't make sense, so that none of us were going to trust him at all. So when, in the middle of an attack on blue, green noted that I (pink) was getting too strong, and that blue should attack me, this only made blue angry. All I had to do was say nothing. My first instinct is to object or argue, but I found it easy to stay out of the trouble until they had weakened each other just enough for me to swoop in and take an insurmountable lead against both of them.
It wasn't so much a display of my own diplomatic brilliance as it was an example of taking advantages of the bad diplomatic mistakes of others. Had Green been more careful or Blue less erratic (I guess, both, really), they both could have teamed up on me to take me down to size. If I had said anything, I'm sure they would have.
I'm mostly just musing on how those kinds of mistakes can be fatal. I understand when a player is going to die and they want to do as much damage as possible to the person who took them down, but lots of players just play with reactions. One player bursts into their land, and they turn it into their personal vendetta. How many times have you heard a player say, "That's it! I can't take it anymore,
. Take THAT!" Those are the times I just sit back and silently thank the universe for patience.