A “veridical paradox” is a situation that produces a solution that seems absurd, but is correct nonetheless. The video below shows one such paradox, a mathematical problem named after game show host Monty Hall. On the show Let’s Make a Deal, at the climax of the show, a contestant was given a choice of three boxes/curtains/doors. Behind one was a fabulous prize, behind the other two, a “zonk” or something of little value. After the contestant chose a box, Hall would then reveal what was in one of the other unchosen boxes, showing one of the zonks. He would then ask the contestant whether they wanted to switch their choice to the other remaining box.

According to the math, the contestant should always make the switch. The video below explains why, even though it sounds counterintuitive, this increases your odds (and makes the choice more obvious by switching to a scenario with 100 boxes).

## David Crotty

David Crotty is the Editorial Director, Journals Policy for Oxford University Press. He serves on the Board of Directors for the STM Association, the Society for Scholarly Publishing and CHOR, Inc. David received his PhD in Genetics from Columbia University and did developmental neuroscience research at Caltech before moving from the bench to publishing.

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## Discussion

7 Thoughts on "Monty Hall and a Veridical Paradox"

I first learnt about this at university and had a blazing (albeit good natured) row with a friend who asserted it couldn’t possibly be true. In the end we settled it by running the ‘game’ 100 times. Never has “I told you so” felt more satisfying!

Why does opening one door not change the problem to which of two doors is the car behind? That is, why does the probability remain 2/3 instead of becoming 1/2?