Today’s puzzle is a new twist on The Monty Hall problem, arguably the greatest maths puzzle of all time.

(According to Gemini, who trawled the internet for me, it is the most discussed and debated recreational maths puzzle of all time.)

Here’s how it goes, for those who may be unaware of it. You are a contestant on the US game show Let’s Make a Deal. Monty Hall, the host, asks you to choose one of three doors. Behind one door is a car. Behind the other two are goats. To win the car, which is what you want, you must choose the correct door.

You choose a door. Before your chosen door is opened, however, Monty Hall opens one of the other two doors that he knows has a goat behind it.

He opens the door and it reveals a goat. He now offers you chance to switch your choice to the other door.

Do you stick, or do you switch?

The intuitive reaction is that it makes no difference. If there are two doors left, surely each door has a 50/50 chance of having the car? This reasoning is fallacious. If you stick with your original choice you have a 1/3 chance of winning the car, but if you switch you double your odds to 2/3. Switch!

Now here’s today’s twist, which has recently been doing the rounds on the net. The set up is the same – but once Monty Hall has opened the door with the goat, you want to win the other goat, not the car.

Monty Hall and the golden goat

You are a contestant playing the Monty Hall problem. However, you secretly know one of the goats is the former pet of an eccentric billionaire who lost it and is willing to pay an enormous amount for its return, way more than the car is worth. You really want that goat. The host is unaware of this. After you pick your door, as is traditional, the host opens one door, which he knows doesn’t have the car. He reveals a goat, which you can tell is the ordinary goat and not the secretly valuable one. The host offers to let you switch doors. Should you?

I’ll be back at 5pm UK with the solution.

PLEASE NO SPOILERS. Please discuss goats, and GOATS.

UPDATE: Read the solution here.

Credit: The earliest reference seems to be here.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.