It's an interesting thought experiment dealing with behavioral economics.
Knowing myself, I would have to say I would take the 200k because I don't like sleepless nights of regret if I were to lose, knowing I could have banked the sizeable free money. I guess a base hit is better than swinging for the fences with a 50% chance of striking out and losing the game.
On the other hand, if the amounts were considerably less, but with the same percentage: Let's say 20k sure money or 50% chance of $500k, then I think I would go for it, since I am playing with the house's money and $20k wouldn't change my life that much anyway.
When it’s a windfall, the risk feels like play.
That being said, if I were betting with my own money of $20k with a 50% chance at $500k, I wouldn't do it. When it’s my own hard-earned cash? That’s sacred ground. To me, the pain of losing something you already have often outweighs the joy of gaining something new, but playing with a windfall that isn't too significant somehow changes things. In that case, I would feel like I don't have any skin in the game, so what the hell.