What's the Formula for Pickpocket Detection?

In Skyrim, if you are sneaking, you can activate people (pickpocket) to look at their inventories. Looking is not illegal, but taking is. It informs you the percentage probability of pickpocketing without being detected. I want to know exactly how many Septims on a person (relative to Pickpocket level) = >50% chance of success to level efficiently.

The UESP has information about pickpocketing mechanics:

The chance of successfully pickpocketing an item is dependent upon the item being stolen. Heavier items and more valuable items are harder to steal but reward more exp for leveling. Most of the time stealing items worth more than 100 at earlier skill level and 500+ later on guarantee skill level increase. If you fail, the target will detect you and you will receive a bounty. Even if successful, there is also a chance that the target will hire a thug to kill you.

There is also a known bug about stealing large quantities of gold: Is pickpocketing large amounts of gold in Skyrim bugged?

You can see this information on the UESP bugs section:

After taking Rank 5 of the Light Fingers perk, instead of raising the stealing chance, this perk can instead drop it to zero when trying to steal large amounts of gold (around 1600-1700). For example, if you use a trainer to train Archery from 57 to 58, you can use Pickpocket to get your money back. When you have Rank 4 of the Light Fingers perk, the odds are about 62%, but if you take Rank 5, they suddenly drop to zero.

This bug is fixed by version 1.1 of the Official Skyrim Patch.

And relative to the formula used to calculate the sucess rate, I found this information on the UESP:

From page, including table:

Base chance 40% Pickpocketer's Pickpocket skill
+1% per point Target's Pickpocket skill 
-0.25% per point Pickpocketer is hidden 
+25% Item's gold value 
-0.1% per point Item's weight 
-4% per point Perks add the perk percentage 

Alchemy multiply chance by 100% + total alchemy bonus percentage 
Enchantments multiply chance by 100% + total enchantment bonus percentage

The maximum chance for success is 90%.
The maximum amount of gold pickpocketable on an awake target is 3,102 (1% chance on a 15 Pickpocket skill target). 1,500 of this comes from perks.

If you want the maximum chance (90%) of success, reduce the amount by 890 gold.Alchemy and Enchantments will increase the chances of a successful Pickpocket, but will not allow you to pickpocket more gold at small chances.