He doesn't make it to the third day if you take the chest...
I used to think the same, that you can reach the Barbarian's castle in 4 days... the question is, what to do with the Barbarian who has run away?
No, he reaches it on the 3rd day in any case. The chest is taken on the 2nd day.;)
As for the Barbarian, I don't know, I should have tried to "break" his strategy by applying "Extra Session" repeatedly!
P.S. By the way, I wrote about this in detail in an article, which is significantly different from the one written in the 2nd issue of the Heroes newsletter.;)
Sincerely, VDV_forever