This is a solo mid AD Vayne carry build. You will hit like a truck with the armor penetration but you will also have some survivability with the MR and armor runes. 21/0/9 is pretty standard on AD carries, especially when you are solo mid you will enjoy that 10% exp and M/5 mastery. This build is reasonable but you cannot roam that well because a tri-force is pretty hard to farm. Once you get sheen you will be able to kill pretty easily and once you finish Madred's you will be able to take down tanks almost as fast as squishies.

Doran's Blade will give you the hp and damage you will need to take on a solo lane. An alternative build I use for Vayne v Vayne solo mid is Cloth Armor + Health Potions(5). Sheen will proc when you tumble so it is perfect for vayne. Tri-force gives you the necessary mana, HP, crit, AS, and the chance to slow. Madred's Razor is a great item for taking down tanks especially when paired with silver bolts. Bloodthirster is an optional damage item, depending on how the game is going you may want to skip this item and continue on to the banshee's vail. BV is a must on almost every character. The spell shield, HP, and MR are critial to surviving. The runes you start with already give you a little survivability but you will need BV. GA is a great item overall but could be replaced depending on who the other team's carry is.

Pretty standard. You wanna max out condemn first, then tumble and lastly silver bolts.

Ghost/Flash ONLY

This portion of the guide will tell you what items to start into a major one.
Boots->Berserker's Greaves
Sheen->Trinity Force

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While in solo mid, you should concentrate a lot on last hitting because a the trinity force will take a long time to get. You really won't be able to leave your lane to gank because you will need at least 100 last hits in the first 20 minutes to be on track with this build.

The trinity force (after the Berserker's Greaves) should come at the 18-22 minute mark, though I have gotten it at the 16 minute mark sometimes.