This is what we call Gambler's Fallacy.
For example, suppose a fair coin is flipped 100 times. Using the law of averages, one might predict that there will be 50 heads and 50 tails. While this is the single most likely outcome, there is only an 8% chance of it occurring according to P(X=50\mid n=100,p=0.5) of the binomial distribution.
If you read the Law of averages correctly, you'll know that your chance doesn't increase nor reduce with the number of attempt.
For exemple, If you split Double down in 4 hits like you said, you will just roll 4x time more dice but your chance never increase. Let's admit that in the original 1 hit you do 20% crit chance, over a fight you then land 2 Double that are crit when you launch 10 of them.
So, 10 Double down, 2 are crits. Now if we are to increase that to 4x time you do 40 Damage of double down and 8 Crit. See ? 0 Difference (Because your damage, even if they are split will lead to the same result) 1200 x 2 = 300 x 8 = 2400. This will not change also because you still press 10 time one button inside the same window of time. This is called proportionnality. You may see more crit BECAUSE you roll more, but the end result would still be the exact same. More roll dice doesn't affect your crit chance and by extension doesn't touch variance.
To reduce the Variance you need to play with the crit chance or to readapt the potency for every single attack on your jobs to be more equal. Because 1200 x 1.5 (Crit DMG) is clearly more powerful than 300 x 1.5
If you were to have Double down at 15 sec of GCD and 300 potency for 1 hit it would be the exact same because now it's 1200 potency for 60 sec CD. Variance comes from the power of all the attack in total you have and which one is gonna crit and which one won't. If double down was 120 potency 10 times on a single button, that wouldn't change anythin because the button would still be a 1200 Potency value.
So basically, If you are lucky you will kick ass from anything. If you aren't, you will simply have a poor DPS.
TL: DR : Increasing the quantity of roll doesn't increase the chance.
