Yeah, and also the following idea helps. Imagine you have 100 marbles, arranged in a 10-by-10 grid, perhaps. One of them is golden. You, blindfolded, choose one of the marbles at random. The likelihood you did NOT get the golden marble is 99/100 (there are 99 non-golden marbles).
Now imagine you're somebody else -- the person administering this thing. The name of the game is to push most of the remaining marbles away, leaving only one behind. The only rule is that you cannot push the golden marble away, if it's there. The chance that the golden marble is indeed still there, within the remaining 99 marbles, is 99/100. Therefore, the chance that, after you push most of the marbles away, the golden marble remains, is 99/100.
Now go back to being the person choosing marbles. The probability that the golden marble remains in the grid is 99/100. The probability that the golden marble wasn't pushed away, because you picked it so very luckily, is only 1/100. Therefore, you switch to the marble in the grid.
I call this "condensing the remaining multiple choices into one". The probability of any of the remaining choices being correct is being condensed into one physical object. Here, a probability of 99/100 is being shoved into one marble, so you should switch to it.
Slashdot Mirror
Yeah, and also the following idea helps. Imagine you have 100 marbles, arranged in a 10-by-10 grid, perhaps. One of them is golden. You, blindfolded, choose one of the marbles at random. The likelihood you did NOT get the golden marble is 99/100 (there are 99 non-golden marbles).
Now imagine you're somebody else -- the person administering this thing. The name of the game is to push most of the remaining marbles away, leaving only one behind. The only rule is that you cannot push the golden marble away, if it's there. The chance that the golden marble is indeed still there, within the remaining 99 marbles, is 99/100. Therefore, the chance that, after you push most of the marbles away, the golden marble remains, is 99/100.
Now go back to being the person choosing marbles. The probability that the golden marble remains in the grid is 99/100. The probability that the golden marble wasn't pushed away, because you picked it so very luckily, is only 1/100. Therefore, you switch to the marble in the grid.
I call this "condensing the remaining multiple choices into one". The probability of any of the remaining choices being correct is being condensed into one physical object. Here, a probability of 99/100 is being shoved into one marble, so you should switch to it.