Instead of thinking about the two outcomes of the situation, it is better evaluated by the amount of change that will be experienced by the switch. You can either hold the 2x or the x with equal odds, so if you don't make the switch, it is fifty/fifty either way. If you hold the x and switch to the 2x, that is a net gain of x. However, if you hold the 2x and switch to the x, that is a net loss of x. Averaging these outcomes, you get 0.5(x - x)= 0, which shows that there is no net gain or loss in making the switch.
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