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CronoDAS comments on [LINK] Counterfactual Strategies - Less Wrong Discussion
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Comments (14)
The game tree doesn't adequately describe the game.
The attacker has a 50/50 chance of seeing a calm sea or a stormy sea, and then must choose between attacking by land or by sea.
The defender has the choice to fight or to run. He doesn't know if the seas were stormy or not when it's time to make the decision, but he does know if the attack was by sea or by land.
If the attack was by land, it's always better for the defender to fight. This results in a draw (0 points).
If the attack was by sea and the defender chooses to fight, the defender wins a fight if the sea was stormy (-20 points for the attacker) and loses both the fight and the city if the sea was calm. (+30 points for the attacker.) If the defender runs away, the defender loses the city (+20 points for the attacker).
As calculated in the link, the optimal strategy for the attacker is to always attack by sea when the sea is calm and attack by sea 1/3 of the time when the sea is stormy.
If you want to know the significance of that fact, follow the link yourself. ;)
Did you mean to have the result of fighting on stormy seas to be -10 points for the attacker? As it stands, I don't believe the math works out exactly.
Thanks for the clarification. I removed the game tree image from the overview because it was misleading readers into thinking it was the entirety of the content.