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Well, strangely enough in 5 runs of the applet I stayed with my original guess all five times and won the $ 4 of those 5...
5 runs is not statistically valid and yet the initial intuition answer is reinforced not disproved.
Update:
I ran the simulation 12 times; 6 times without switching and 6 times with switching. Result: I won 4 times out of 6 in either strategy.
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