saving vs. consumption as default actions

Lately, for good reason, there has been many advice columns telling people how to plan for personal financial goals. It always used to boggle my mind when I heard exhortations to save, where “save” is used in the sense of an action among which to choose, parallel to things like “invest” or “work”. Until I realized, some years back, that to save is a parallel action of choice to some.
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A little Markovian problem

Here it is: 

A has a fair coin and B has a fair coin. They flip coins together, but only keep track of their own sequences of heads and tails. A stops if the sequence “HHT” appears. B stops if the sequence “HTH” appears. Which player is more likely to stop first?

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