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Driver A comes to a 3 way path junction but is not sure which one to take. Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would bring him to town. Driver A is not heading to town but the seaside. Should he change to path 2?

Driver B encounters the cyclist before he can decide which path to take to the village. Is his chance less than driver A because he cannot switch?

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If we presume that the seaside and town are different directions, each driver has $\frac 12$ chance going on path $1$ or $2$ and $0$ chance going on path $3$. This is not a Monty Hall situation because the cyclist is not reacting to the driver's choice.

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    The guarantee part is to allow the original game to proceed to state 3(to switch or not) ALL the time but if we can proceed to state 3 somehow when monty 'guess' the same door, the decision to shift in probability by switching still depends on the player.2012-12-11