Quick odds look:
The odds of getting doubles on 4d6:
1st die can't be double. 2nd has 1/6th of being double. 3rd has 1/3rd of being double. 4th has 1/2 of being double. 5/6*2/3*1/2 (the odds of failure on each die after the first) = 5/18th odds of not getting doubles.
2nd set has 5/6*2/3 = 5/9th odds of not getting doubles.
3rd set has 5/6th odds of not getting doubles.
Winning on the first two sets: 13/18*4/9 = 26/81.
Winning on the 1st and 3rd: 13/18*1/6 = 13/108.
Winning on the 2nd and 3rd: 4/9*1/6 = 2/27.
Running through a decimal calculator because I'm lazy, the chances of a Hand winning are about 51.5%. Betting on the Hand is better by a fair factor, especially after you calculate the boon from a win.
On the other hand, playing three rounds has a better-than-one-eighth chance of getting a bunch of Orcs to beat the crap out of you. So that kind of makes it a wash.