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BGonline.org Forums
The Backgammon Solution
Posted By: Rick Janowski In Response To: The Backgammon Solution (Bob Koca)
Date: Sunday, 16 October 2016, at 5:43 p.m.
Thanks Bob but I find your argument a little difficult to understand. Is it possible that you could use a form of English which non-Mathematics graduates or non-Mathematics under-graduates could more easily follow?
I stated: “There are two joint winners of the tournament. After drawing lots, one player is asked to pick one of the two envelopes. He opens the envelope which contains £2000. He is told that it is not known whether this is the intended prize for the winner or the runner-up and that runner-up prize is 50% of the winner’s prize. So the other envelope will contain either £1000 or £4000. The player is then given the option of sticking with his original choice or switching to the other envelope.”
It also seems that you may not have fully understood the meaning in the question so I will try to explain. In effect, one envelope was opened which contained an amount of money, Q, and in the other envelope the amount will be either 0.5Q (in the event that Q in the opened envelope contained the winner’s prize) or 2Q (in the event that Q in the opened envelope contained the runner-up’s prize). Because we know that Q = £2000 it may be deduced quite easily that the unopened envelop contains either £1000 or £4000); if Q had some other value then these values would naturally change. Consequently, assuming there are no issues relating to bankroll management (e.g., Kelly Criterion), the actually of Q not relevant to the question of whether to stick or switch, just as theoretic take points in backgammon are not dependent on the value of the stake.
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