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hot_pastrami · 06-13-2003, 06:20 PM

Well, the problem with the 50/50 intuition is that it assumes that the first choice has no bearing on the second choice. But it does. Consider the two possible scenarios for the initial door selection:

1) You select the door that does contain the prize, which will occur one in three times. Monty can open either of the other two doors at random. His choice is unaffected.

2) You select a door which does not contain the prize, which will occur two in three times. Monty is forced to open the other non-winning door.

Scenario #1 will happen about 33% of the time, and scenario #2 will happen about 66% of the time, right? So, after you make your initial choice, it is safer to bet that #2 happened. So accordingly, it is safe to bet that he was forced to open the other empty door, and therefore it follows that the third door, the one you did not pick, contains the prize. I hope I explained that well, my brain is getting pretty tired.

The reason the Daily Number's odds don't change is that one day's selection has no effect on the other days' numbers, it's always a random draw. Statistics don't always follow intuition... for instance, if you flip a normal coin 100 times and it surprisingly comes up heads every time, what are the odds that it will come up heads again on the next flip? It seems outlandish, like it would become less and less likely for it to turn up heads. But against (my) intuition, the chances are still exactly 50%. That's because each flip of the coin is a random result independent of all the other flips. Wierd.

Anyway, have a good weekend everyone.

06-13-2003, 06:20 PM	#18
hot_pastrami I am meaty Join Date: Dec 2001 Location: Salt Lake City, UT Posts: 1,119	Well, the problem with the 50/50 intuition is that it assumes that the first choice has no bearing on the second choice. But it does. Consider the two possible scenarios for the initial door selection: 1) You select the door that does contain the prize, which will occur one in three times. Monty can open either of the other two doors at random. His choice is unaffected. 2) You select a door which does not contain the prize, which will occur two in three times. Monty is forced to open the other non-winning door. Scenario #1 will happen about 33% of the time, and scenario #2 will happen about 66% of the time, right? So, after you make your initial choice, it is safer to bet that #2 happened. So accordingly, it is safe to bet that he was forced to open the other empty door, and therefore it follows that the third door, the one you did not pick, contains the prize. I hope I explained that well, my brain is getting pretty tired. The reason the Daily Number's odds don't change is that one day's selection has no effect on the other days' numbers, it's always a random draw. Statistics don't always follow intuition... for instance, if you flip a normal coin 100 times and it surprisingly comes up heads every time, what are the odds that it will come up heads again on the next flip? It seems outlandish, like it would become less and less likely for it to turn up heads. But against (my) intuition, the chances are still exactly 50%. That's because each flip of the coin is a random result independent of all the other flips. Wierd. Anyway, have a good weekend everyone. __________________ Hot Pastrami!