The Monty Hall problem in three cards

Let's make a deal. Take two players, a dealer and a contestant. The dealer deals three cards face down, one of which is the Queen of Hearts. The contestant selects one card but doesn't turn it over. The dealer then turns over one of the two remaining cards, that card cannot be the Queen. The contestant can then choose to stick or swap their card and then wins if their card is the Queen.

If they swap their chance of winning is 2 in 3, if they keep then it is 1 in 3. Note this is not an even chance since the dealer turning over a card hasn't changed the original odds. Play multiple times to demonstrate this.

This game was taken from "How long is a piece of string?" by Rob Eastaway and Jeremy Wyndham. A good book let down by the chapter on epidemics.

History

In the 1960s and 1970s, when Monty Hall was the host of Let's make a deal, the prizes were behind three doors which the contestant picked rather than cards. One was a car, the other two were goats. In the game below there are no prizes, not even a goat.