The following situation actually occurred in a 2009 college football game between Washington and Notre Dame. With about 3.5 minutes left in the game, Washington had fourth down and one yard to go for a touchdown, already leading by two points. Notre Dame had just had two successful goal-line stands from in close, so Washington’s coach decided not to go for the touchdown and the virtually sure win. Instead, Washington kicked a field goal, and Notre Dame eventually won in overtime. Use a decision tree, with some reasonable inputs, to see whether Washington made a wise decision or should have gone for the touchdown. Note the only “monetary” values here are 1 and 0. You can think of Washington getting $1 if they win and $0 if they lose. Then the EMV is 1 * P(Win) + 0 * P(lose) = P(Win), so maximizing EMV is equivalent to maximizing the probability of winning.
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