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I am in favor of making the capture of an unguarded lumber mill, mine, or any other resource, dwelling, or town within the first 6 days a reason for a restart. This rule could be formulated as follows: if, within the first 6 days, contact between a hero of one player and any object belonging to another player (hero, town, mine, neutral creature) leads to a change in the number of flags for any player, then a restart should occur.
Why do I think so? For the same reason that a restart occurs when two heroes make contact within the first six days.