My favourite example of this is how no limit Texas holdem was solved.

This game is of course an imperfect information game (you don’t know your opponents hole cards). We have lots of great algos for perfect information games but not imperfect.

So what the researches did is they mapped hold em to a perfect information game by tweaking it: now nobody knows their hole cards and all players must publicly announce their strategy to a “referee”. Then the referee looks at the players cards and places bets on behalf of the players. A player’s strategy looks something like: if I have a pair of aces then I want to raise 94% of the time and call 6% of the time and fold 0% of the time etc etc.

You know your opponent’s strategy too (as they have announced it like you did to the referee) so you can now iterate and optimise your strategies which will approach a Nash equilibrium.