In a TV game show, a contestent selects one of three doors; behind one of the doors, there is a prize, and behind the other two there are no prizes. After the contestant selects a door, the game show host opens one of the remaining doors, and reveals that there is no prize behind it. The host then asks the contestant whether they want to SWITCH their choice to the unopened door, or STICK to their original choice.

Is it probabilistically advantageous for the contestant to SWITCH doors, or is the probability of winning the same whether they STICK or SWITCH? (You may assume that the host selects a door to open from those available , with equal probability).

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