A few years ago I was quizzed or maybe a quiz was posted on this site about a scenario in the old game show, "Let's Make a Deal." A contestant was shown three doors by the host, Monte Hall. Behind one of the doors was a brand new car. Behind the other two doors was a silly prize like a donkey or something. The contestant was told to pick one of the three doors. Monte would then open one of the other doors that had a donkey behind it. Then he would offer the contestant a choice: stick with his original door or switch to the third door. Then Monte opened the door the contestant finally settled on to reveal either the new car or a donkey. This was essentially offering a contestant a two-thirds chance of winning the new car - if the contestant went into this game with the strategy of always switching to the third door. Contestants who stuck with the original door had a one-third chance of winning the car. Monte's forced choice of a donkey door changed the odds of the scenario for the contestant once he opened it. However, many contestants over the years didn't understand the logic behind this game and stuck with their original choice of doors. The irrational thought process that went behind the decision to stick with their original choice probably was not wanting to regret switching if they originally picked the door with the car behind it. Some probably thought that once Monte picked a donkey door they had 50-50 odds of getting the car because it was behind one of two remaining doors. Better to stick with the original decision, to avoid regret and/or looking stupid. The Monkey Factor I wonder if the producers of "Let's Make a Deal" ever pondered using a combination of biasing the odds of which door the car is behind and biasing Monte's choice between the two doors when the contestants' original selection was the door with the car? Since some contestants used irrational thought processes in their decisions to stick with their original doors, why not use an exploitive strategy to pay out less cars? They could have done a statistical analysis of how car position and Monte's choice of donkey doors influenced the contestants' decisions. For example, say the statisctical analysis found that contestants chose door #1 more often than the others. Also, lets say that Monte's choice of opening the donkey door furthest from the door the contestant chose made the contestant less likely to switch than if Monte chose the middle door. Lets also say that if the contestant chose the middle door when the car was there, he would be more likely to switch doors if Monte chose the left donkey door than if Monte chose the right donkey door. This contestant bias toward the left door would make it profitable for the producers to put the car behind the middle door more often than 1/3 of the time. Then, if the contestant chose the middle door (with the car behind it) anyway, Monte could then open the left donkey door more often than half the time. Monte could be given a secret signal for which door to open. This strategy, based on this kind of statistical analysis, could have saved the producers money by awarding less cars over the long run. This would be what game theorists call an exploitive strategy. Of course, exploitive strategies are always vulnerable to counter-exploitation. Sharp game show enthusiasts might have noted such a bias and then never chose the middle door. Their strategy of always switching doors would then, because of the game show's bias in favor of the middle door, make it more likely for them to have to switch their selection to the middle door. This counter-exploitive strategy would make the sharp game show enthusiasts' odds of getting the car greater than two-thirds.
Yes! Donkeys are more profitable! Your algebraic treatment of Monkey's First Equation is hilarious! Casinos are cheating their players while under Gaming's watchful eye? LOLOL!!! NICE! :laugh:
