Simple thing, but it drives me crazy when I'm thinking of it in terms of GTO. If anyone can explain, it would be awesome.
"THE FOOL'S GAME":
It's a very simple two player game where you play with real money. Player who starts offers you some money, let's say he wants to give you 4 $. You can take this money and end the game or you can give him 2 options to choose from:
1. Give me more money (more than 4 $).
2. Take 4 $ from me and end with a 4 $ profit.
The GTO for me says: "Take the money he gave you and never give him 2 options to choose from."
The GTO for him says: "Never start this game with anyone."
Concluding - the GTO says: "Don't play this game." But what if there is a "fool guy" that doesn't care about all that, he wants to play and he offers you money ? Seems to be a simple solution - take the money. But when you try to analyze this more deeply it looks like this:
=> The fool guy's intention is to GIVE you money, because he knows you'll take it. So it means that he might be interested in giving you even more money. Why not ? Maybe you should give him 2 options to choose from so that he can give you more ?
=> Is he really a fool ? Maybe he knows what you'll think and he hopes you give him 2 options so that he can win ?
Does it eventually lead to a point where you have to decide if he's a fool or not ?