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So, why is it, that on page 22 of HEPFAP, 2nd paragraph, it says that AA loses value as it becomes multiway?

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I disagree with another responder that this is an error in the book. You have to keep Sklansky's writings in perspective. Unless otherwise stated, he writes with the assumption that the game is relatively tight/aggressive. IN a game like this, the Aces do lose value as the pot gets multiway. I think between that book and ToP, he explains it all quite clearly.