Even if you are not a proud member of the Thieves guild and don’t plan on stealing anything (I don’t know how you do it), you will need to break into some locks. So where can you find those illusive picks?
I’ll let you know where to buy lockpicks in Oblivion Remastered, and how you can make sure you’re breaking as few of them as possible, regardless of your security level. You’ll never need to leave an unopened chest again.
The easiest way to get lockpicks is by looting them, especially from goblin caves or mines. Most of the locked chests found inside these will give you multiple lockpicks at once, and you’ll often find one or two in every other goblin you kill.
If you do want to purchase them, though, you can do so from Shady Sam outside the Imperial City. Exit the city through the stables and head northeast, always hugging the wall. You’ll eventually run into him. He’ll always have 30 lockpicks available for purchase. If you buy them all, another batch of 30 will be in stock on the following day.
Joining the Thieves Guild and/or the Dark Brotherhood opens more purchasing options. All fences sell lockpicks, and so do the Dark Brotherhood merchants. If you don’t intend to join any of these factions, you’re limited to Shady Sam for the entirety of your playthrough.
As with anything in Oblivion, practice makes perfect. The more lockpicking you do, the higher your Security skill will be, and the easier the minigame becomes. If you’re not against save-scumming, you can also brutalize the quicksave/quickload buttons before any difficult lock.
You can get good at lockpicking as a player, though. You’ll have noticed that the pins do not go up at the same speed. Some of them will go up and down really fast, while others will move slowly, hanging a bit at the top. This is influenced by your Security skill and by the lock’s difficulty.
As long as the difficulty isn’t way higher than your security skill, though, you can always get slow-moving pins, and the odds can be turned in your favor. The speed of the pins doesn’t change when you press them, it only does so when they reach the bottom.
So you want to press a pin until you see it move slowly. You might not be fast enough to lock it in once it reaches the top, but you only need to react before it goes all the way down to the bottom, which is easy. When you find a slow pin, keep pressing it before it reaches the bottom and it will maintain the speed. Repeat this until you get the timing of it hitting the top right and you will have a much higher success rate.
Just keep in mind that interacting with any lock that pops up as red will be considered a crime, so do make sure that you aren't seen doing it. Also remember that stolen items cannot be sold to normal merchants, and that includes Shady Sam. You'll be forced to join the Thieves Guild and selling them to one of the fences.
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