Special Note: No, using 1 card at a time will not yield better results. It is a mathematically fallacy that is proven even more false the more you do it. Some people have experienced success using 1 HN at a time and rave about how it's better. These people are plainly wrong. They got lucky one time and if they continue doing it that way, much like gambling at a casino, it will balance out for their loss.
Skilling a High Rare (rare evolved into HR):
Lvl 1-2: 8 Skilled High Normals yielding 96% chance to skill up - Rough Price under 1HP
Lvl 2-3: 9 Skilled High Normals yielding 72% chance to skill up - 28% chance you will have to try again. Rough Price 1-2HP
Lvl 3-4: 9 Skilled High Normals yielding 54% chance to skill up - 46% chance you will have to try again. Rough Price 2-3HP
Lvl 4-5: 9 Skilled High Normals yielding 44% chance to skill up - 56% chance you will have to try again. Rough Price 2-3HP
Lvl 5-6: 9 Skilled High Normals yielding 39% chance to skill up - 61% chance you will have to try again. Rough Price 3-4HP
Lvl 6-7: 9 Skilled High Normals yielding 31% chance to skill up - 69% (giggity) chance you will have to try again. Rough Price 4-5HP
Lvl 7-8: 9 Skilled High Normals yielding 27% chance to skill up - 73% chance you will have to try again. Rough Price 4-5HP
Lvl 8-9: 9 Skilled High Normals yielding 27% chance to skill up - 73% chance you will have to try again. Rough Price 4-5HP
Lvl 9-10: 9 Skilled High Normals yielding 22% chance to skill up - 78% chance you will have to try again. Rough Price 6-7HP
Overall this should normally average out to somewhere around 30ishHP but could get as bad as 40+HP
Skilling an SR (HR evolved into SR)
Lvl 1-2: 9 Skilled High Normals yielding 72% chance to skill up - 28% chance you will have to try again. Rough Price 1-2HP
Lvl 2-3: 9 Skilled High Normals yielding 48% chance to skill up - 52% chance you will have to try again. Rough Price 2-3HP
Lvl 3-4: 9 Skilled High Normals yielding 36% chance to skill up - 64% chance you will have to try again. Rough Price 4-5HP
Lvl 4-5: 9 Skilled High Normals yielding 28% chance to skill up - 72% chance you will have to try again. Rough Price 4-5HP
Lvl 5-6: 9 Skilled High Normals yielding 24% chance to skill up - 76% chance you will have to try again. Rough Price 5-6HP
Lvl 6-7: 9 Skilled High Normals yielding 20% chance to skill up - 80% chance you will have to try again. Rough Price 6-7HP
Lvl 7-8: 9 Skilled High Normals yielding 18% chance to skill up - 82% chance you will have to try again. Rough Price 6-7HP
Lvl 8-9: 9 Skilled High Normals yielding 16% chance to skill up - 84% chance you will have to try again. Rough Price 7-8HP
Lvl 9-10: 9 Skilled High Normals yielding 14% chance to skill up - 86% chance you will have to try again. Rough Price 7-8HP
Overall this should normally average out somewhere around 40HP but could get as bad as 50+. The last few levels can get particularly bad.
In both rarity classes there is no reason to evolve the High Normals into Rares since the percentage increase is so small and requires four HN.