I mentioned this to a friend of mine who teaches maths.
His reply (word for word) was "ah, that old chessnut, always change your mind" [ ie switch your choice ].
So I asked him to explain.
He said its a poor example to be able to understand, its far easier to understand how it works with a more extreme example.
The important points are you made you initial choice when all options were available, but you second choice is after the [wrong] options have been reduced.
His example ;
Take a pack of cards, and spread them all out on a glass table.
Then make you choice for which you think is the Ace of Spades (AOS).
Then get a friend to look under the table, and tell you 50 wrong cards to remove (but not yours).
This leaves you with your choice, and one other card.
However, the odds are not even, the chances the other card is the AOS are huge.
The odds you initially chose the AOS correctly is 1 in 52 [low], so the odds of it being in the other cards is 51 in 52 [high].
Now your friend has removed 50 incorrect cards, the chances of the remaining card being the AOS are still 51 in 52, so always change your mind, and pick that card.
It would only be 50/50 if your friend had removed the 50 cards before you made your first choice.
I understand now.
