After having played thousands of games of chess, I finally feel as though I'm beginning to see the patterns.   One observation that I've made which I call the "3 piece rule" is that having 3 pieces in the opponent's side is enough to create a checkmate opportunity.  Of course, it's always possible to win with just 2 pieces, but it seems clear that having 3 almost ensures that your forces can overwhelm the opponent king.  The combination can be a pawn, knight, and bishop or include more powerful pieces such as the queen and rook.  Regardless, the instant you move 3 of your pieces over to the other side, your opponent is in trouble.