Tit for Tat
Be nice, then copy. The strategy that beat everyone.
What it actually is
Tit for Tat is the dumbest smart strategy ever written down. In repeated games you start by cooperating, then on every turn after that you simply do whatever the other player did last time. That is the whole program: be nice first, then copy. It wins because it is nice (never defects first), retaliatory (punishes betrayal immediately), forgiving (goes back to cooperating the instant they do), and legible (the other side learns exactly what you'll do). Complicated strategies that tried to be clever and exploit opponents lost, because they got mistrusted and then punished forever.
Where you'll see it
In 1980 Robert Axelrod ran a computer tournament where game theorists submitted strategies to play the repeated Prisoner's Dilemma against each other. Anatol Rapoport submitted Tit for Tat, four lines of code, and it won. Axelrod ran a second, bigger tournament, telling everyone that the four-line program had won and daring them to beat it, and it won again. It never once scored higher than the opponent it faced, yet it took the whole tournament because it lost small, won small, and never got dragged into a mutual death spiral.
Spot it in yourself
You defect first "just to be safe," or you keep punishing someone for one old slight long after they've made peace. Nice-first-then-mirror beats both: stop pre-emptively screwing people, and stop nursing grudges past the last move they actually made.
The bias underneath
Tit for Tat runs on reciprocity, and the Ben Franklin Effect is the cleanest reciprocity bias in the set: your attitude toward someone bends to match how they last treated you, so a cooperative move earns cooperation back and a defection earns retaliation.
Read about Ben Franklin Effect