The Four Card Trick - a variation on Monty Hall

[Simon]

The following is open to anyone - but will be of particular interest to those familiar with the Monty Hall conundrum.


There are four cards face down - two are Jacks, two are Queens. There is a host present who knows what each card is.

1.You choose one of the cards.

2a.You instruct the host to eliminate either a Jack or a Queen. It is your decision. You can flip a coin if you wish. He will follow your instructions and turn over one of the other three cards accordingly.

2b. Alternatively, the host is not involved. You simply turn over one of the cards yourself.

3. Whichever way it happened, let us say a Jack was eliminated.

4. At this point, you make a new selection. You can stick to your original card or choose one of the other two.

5. Finally, another card is eliminated. This time it must be the host who turns it over. He will show the opposite of the last so as not to spoil the game. In this case, he turns over a Queen.

There is now one Jack and and one Queen remaining. Your card is one of them.

Questions: Which is more likely to be the Queen? Are the odds 50/50? Does it make a difference whether you stuck or swapped? Does it make a difference whether you used the host for the first elimination?


All the best
Simon