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

Question

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 Tech scores a touchdown. Still trailing 21 to20, Tech can either go for 2 points and win or go for 1 point to send the game into overtime. The conference championship will be determined by the outcome of this game. If Tech wins, it will go to the Sugar Bowl, with a payoff of $7.2 million; if it loses, it will go to the Gator Bowl, with a payoff of $1.7 million. If Tech goes for 2 points, there is a 33% chance it will be successful and win (and a 67% chance it will and lose). If it goes for 1 point, there is a 0.98 probability of success and a tie and a 0.02 probability of failure. If the teams tie, they will play overtime, during which Tech believes it has only a 20% chance of winning because of fatigue.

Use decision tree analysis to determine whether Tech should go for 1 or 2 points.

Please show all work and calculations so that I can study this example problem better.

Explanation / Answer

Tech has two options, two alternates for decision making as follows:

First--- Tech goes for two points        and Second--- Tech goes for one point

Under both the alternates, there are two uncertain possibilities or states or outputs to happen, mentioned as successful and failure. In other words either Tech is successful or met with failure under both the options.

Under First option/action---depending on the outcome, if successful Tech will go to Sugar Bowl with payoff of $7.2 million; if loses go to Gator Bowl with a payoff of $1.7 million. Further it is mentioned that there is a 33% chance of success and thus 67% chance of failure. Therefore the expected payoff under First option/action that is, if Tech goes for 2 points Expected payoff = $3.515 million (7.2*.33 + 1.7*.67)=(2.376+1.139)

Under Second option/action---depending on the outcome, if successful teams tie and play overtime and then depending on the outcome of overtime play, either Tech go to Super Bowl (on success) or Tech go to Gator Bowl (on failure). It is mentioned that Tech has 20% chance of winning thus 80% chance of failure, therefore expected payoff for overtime play = $2.8 million (7.2*.20 + 1.7*.80)=(1.44+1.36)

It is given that .98 probability of success and .02 probability of failure in case Tech goes for 1 point under the Second option/action.

Therefore the Expected payoff under Second option = $ 2.778 million (2.8*.98 + 1.7*.02)=(2.744+0.034)

From the above calculations, Expected payoff (3.515) for First option (go for 2 points) is more than the expected payoff (2.778) for Second option (go for 1 point) Therefore Tech should go for 2 points.

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