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As a follow-up, suppose there is a 20% chance of scoring when adding the extra man from pulling the goalie (that's probably high). Suppose also that the chances of winning the next game by at least two goals is 30% (seems reasonable enough, but admittedly I'm pulling these numbers from my own imagination). That right there is incentive enough to sit on that extra attacker idea and hope you just win by two or more the next game.
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