39. Tech is playing State in the last conference game of the season. Tech is trailing...

39. Tech is playing State in the last conference game of the season. Tech is trailing State 21 to 14 with 7 seconds left in the game, when they score a touchdown. Still trailing 21 to 20, Tech can either go for two points and win or go for one point to send the game into overtime. The conference championship will be determined by the outcome of this game. If Tech wins they will go to the Sugar Bowl, with a payoff of $9.2 million; if they lose they will go to the Gator Bowl, with a payoff of $1.5 million. If Tech goes for two points there is a 30% chance they will be successful and win (and a 70% chance they will fail and lose). If they go for one point there is a .98 probability of success and a tie and a .02 probability of failure. If they tie they will play overtime, in which Tech believes they have only a 20% chance of winning because of fatigue. a. Use decision-tree analysis to determine if Tech should go for one point or two points. b. What would Tech’s probability of winning the game in overtime have to be to make Tech indiff erent between going for one point or two points?

Expert Solution

The decision Tree for Tech

Expected Payoff from going for a 2 pointer = 0.3 * 9.2 + 0.7 * 1.5 = $3.81 million

Expected Payoff from going for a 1 pointer = 0.98 * (0.2 * 9.2 + 0.8 * 1.5) + 0.02 * 1.5 = 0.98 * 3.04 + 0.02 * 1.5 = 3.0092

Since the expected payoff from going for a 1 pointer is lesser than going for a 2 pointer, So Tech should go for 2 points.

b) Let the probability for winning in Overtime be x

So Expected payoff from Going for a 1 pointer = 0.98 * (x * 9.2 + (1-x) * 1.5) + 0.02 * 1.5

If Tech has to be indifferent between going for a 1 pointer or a 2 pointer, then

0.98 * (x * 9.2 + (1-x) * 1.5) + 0.02 * 1.5 = 3.81

or 9.016x + 1.47 - 1.47x + 0.03= 3.81

or 7.546x = 3.81 - 1.5

or x = 0.3061

or x = 30.61%

So if the probability of winning in overtime is 30.61%, then Tech will be indifferent between going for a 1 pointer and a 2 pointer.

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Rahul Sunny answered 2 years ago

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