[HarryT]

Spoiler:

It's a variant of the classic "which door is the lady behind" game, isn't it? Where the showman knows in advance where the lady is, and opens doors one at a time to reveal them to be empty. At the end, the contestant is left with two doors and has the choice of either sticking with their selection, or changing it. The winning strategy is always to change: the greater the number of initial doors, the more certainly he should change! Eg, if there are 10 initial doors, there's a 1 in 10 chance of winning by sticking with the initial selection, and a 9 in 10 chance of winning by changing selection.