Comments on: Monty Hall revisited

By: Peter Cameron

Peter Cameron — Wed, 21 Mar 2012 15:30:28 +0000

The Sudoku instructions in The Independent say “There is no mathematics involved; solve the puzzle with reasoning and logic”. You are saying something similar. But mathematics is nothing but reasoning and logic.

By: Woodstone Sorenson

Woodstone Sorenson — Wed, 21 Mar 2012 02:20:26 +0000

Complicated instructions for this puzzle based on mathematics are unnecessarily complex and misleading. This is a logic puzzle – not a question of probability.

You select one of three doors. (Try to select one with a goat. Your odds are two out of three.) If you select a door with a goat, your probability of winning becomes 100%. They don’t open your door (goat 1), they open the door with goat 2 and you choose the remaining door.)

Odds of winning – very simple – two out of three!

By: Peter Cameron

Peter Cameron — Mon, 12 Mar 2012 09:16:42 +0000

Indeed, anyone watching a chess game for the first time could easily understand that any piece can be moved anywhere, in which case the strategy would be rather different.

I almost added a last paragraph saying that, if Monty doesn’t obey the rules of the game, then the analysis is different.

By: Gabriel Verret

Gabriel Verret — Mon, 12 Mar 2012 07:14:10 +0000

I think much of the misunderstanding often comes from the way the problem is stated. It is very important to state the Monty knows where the car is and that he is picking a door hiding a goat on purpose.

For example, from your summary of the problem, a person seeing this problem for the first time could easily understand that Monty is just picking doors randomly and happened to pick a door with a goat, under which assumption the usually wrong answer becomes the right answer : it doesn’t matter if you switch or hold.