A high risk / high reward operation. The phrase originates from craps
where a hard six is achieved by rolling threes on a pair of six-sided dice (3+3). Rolling a hard six has a probability of about 3% whereas rolling six by any other combination has about a 14% chance. A hard six pays 7 to 1 whereas a regular six pays only 7 to 6.
The phrase was used by the character Commander/Admiral William Adama in the television series Battlestar Galactica
Dude: You should ask her out!
Guy: But what if she turns me down?
Dude: Sometimes you just gotta roll the hard six.
Not only do you have to be lucky in achieving the right outcome, but you also have to avoid the wrong ones on the way. It implies a certain level of complexity or layers of contingency in order to come out ahead. In Craps, Hard 6 & Hard 8 are the longest odds (9 to 1) that hinge upon more than one throw of the dice (avoiding 7 or other combinations of 6 or 8, respectively).
Commander Adama's raid on a Cylon base in Battlestar Galactica. Firing a missle and hoping it destroys the base in one fell swoop is like betting on snake eyes (1+1). The odds are long (30 to 1) and hinge on one result. But coming up with a strategy that involves the use of decoys, anticipating enemy responses, etc., requires everything to go as planned but it gives you better (some would say more realistic) but still long odds (9 to 1). That's why "sometimes you gotta roll the hard six."
v. To achieve something partially through intense skill and partially through luck. Expression originated with Commander/Admiral William Adama in the 2004 television series Battlestar Galactica
Commander William Adama (to Lee Adama, Saul Tigh, Kara Thrace, and Laura Roslin at a mission briefing): "Sometimes, you gotta roll the hard six."
Sharon "Boomer" Valeri: "It's like Commander Adama says; sometimes you gotta roll the hard six."