It certainly goes against instinctive logic
QuoteIt certainly goes against instinctive logic Next we are not really that logical, even when told that it is always better to swap people remain blind to the reality.I bet there are more than a few instances where this flawed logic has found its way into computer programs.
As long as you don't know where the coin is, including the possibility of it being under the tray that was removed by the bar tender, yes, you have a 1:3 chance. As soon as you know that the coin isn't under that tray, you now have 1:2. There's no difference between the 3 trays with 1 coin, remove 1 tray with no coin under it---and the two trays with 1 coin under 1 of them. In the end of both cases you have two trays with a coin under one of them. You still have a choice. 1:2
... Someone else steps up to take your place. There are two ash trays sitting there. One is close to him, the other is pushed back a little. There is no 3rd ash tray because the bar tender took it away. What are the odds? 2 in 3, right? WRONG!!! They are 50:50.
If you still don't believe me then perhaps we could play this game for real a couple of hundred times smiley-money - when its your turn you always pick and stick with your choice, when its my turn I'll always pick then change.