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I'm betting this can be done an infinite number of times as long as you have your commander replenish units, and the last units alive are dual wielder enemies. This is highly valuable for winning islands with just one infantry unit
Base Stone 1 2 3 4 5 6 7 8 9 10 11 12
1st Upgrade -3 -1 1 3 5 7 9 11 13 15 17 19
2nd Upgrade -11 -8 -5 -2 1 4 7 10 13 16 19 22
The base profit from the un-upgraded Stone is 1 per turn. On turn 5 the base profit is equal to the profit from upgrade 1 minus the cost (10 - 5 = 5). On turn 7 the second upgrade is equal to the base profit (but not the first upgrade, interestingly). By turn 8 the second upgrade beats all other options.
This means that you should always take both upgrades as early as possible if there are at least 8 turns left in the game. If there are only 6 or 7 turns left, a single upgrade is slightly more profitable and if there are 5 or less, don't bother upgrading at all. But you can usually manipulate the remaining turns to make it work in you favor, so I recommend always upgrading twice on the turn you assign the Stone.
Not quite. The break-even point is the point when you have covered the total cost of the upgrades and are beginning to turn a profit. That is the third use for the 1st upgrade (3 turns x 2 gold = 6 minus 5 for the cost 1 gold profit) and the 5th for the second (5 x 3 - 14 = 1). What you are referring to is the number of turns until the profit exceeds the profit gained from earlier upgrades. But even then, the second upgrade is cheaper than you suggest (7 turns vs 9) because it gets to use the profit from upgrade 1.