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Very interesting problem, given the unexpected result - I solved it a bit differently than he did, but I got a similar answer (-72 cents per hand). But I'm not clear on what this has to do with collusion?? The author is discussing collusion, but I don't see any collusion at work here, just a setup that puts you at a disadvantage. (This could even be a casino game, the house gets two cards, you get one, and you pay $10 to get a card and $30 more to play it).

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Very interesting problem, given the unexpected result - I solved it a bit differently than he did, but I got a similar answer (-72 cents per hand). But I'm not clear on what this has to do with collusion?? The author is discussing collusion, but I don't see any collusion at work here, just a setup that puts you at a disadvantage. (This could even be a casino game, the house gets two cards, you get one, and you pay $10 to get a card and $30 more to play it).
It's implied that the other two players are splitting profits/losses, and given the setup, you cannot have a positive expectation. You will lose, its a mathematical guarantee over any significant sample size. One of the other guys might lose also, but since theyre on the same roll, it doesnt matter. Collusion is two or more players knowingly putting another player/s at a disadvantage by working together. These players are working together to create a system which, while perfectly legal, makes it impossible for an opponent to win.
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Okay, I guess it is an example of collusion. I was thinking that it didn't really count since they weren't adjusting their play to help each other, but I guess one player is always intentionally playing suboptimally to create an ovarall advantage for the partnership, so it qualifies.

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