Sebastian :I think you will find what you are experiencing is due to pin hole alignment & not wear & tear, pin tumblers are amazingly durable the first thing to go on a well used lock, only after years of use are the key cut's and and the tips of the bottom pins were they come into contact with each other, that and tired springs.
I normally refer to the pin order as #1 being the furthest at the back of the plug to #5 being the pin you can visibly see at the entrance of the keyway, to save any confusion I'll refer to them as set out above.
The pin hole alignment can be perfectly straight centre line/right off set centre line/left off set center line/or random, to find out what you have here's what I normally do:
Insert your tension wrench into the key way and apply medium to firm tension anti-clockwise, insert a diamond pick all the way to the back of the plug and rake two or three times, and make a note of what pins have set high and what pins have not, now turn the tension clockwise and do the same again.
If the rear pins set high when anti-clockwise tension was applied, & the front pins set high when clockwise tension was applied you have right hand centre line off set, if the opposite happened you have left hand centre line off set, & if middle to front set high in both directions (ie:no change) you have random.
I'm guessing you have a random pin alignment on your practice cylinder, and I'm also guessing that as your from europe youv'e purchased a euro practice lock, if so the next thing you want to do is cheating somewhat but it will answer the question to your problem.
As you have a practice cylinder it will be cut-away on the pin chambers so you can see what is happening whilst you are picking, if it is a euro cylinder the actuating cam should be off set at 30º in the locked position ie:sticking out at an angle pointing at one O'clock (There is a reason behind this but that's another story) if it is not a euro cylinder use a tension wrench. Hold the cylinder in your hand with the cut-away's facing you, apply light to medium tension by pushing the actuating cam with a finger or thumb, or use a tension wrench, take a pick with a pointed end and starting with for example pin #3 raise the
top pin above the shear line (Not both pins only the top one under the spring)
via the cut-away outside of the lock, not inside of the lock! Keeping a mental note (or write it down) of which order each pin will set, ie #3,#4,#1,#2,#5, once the plug is free to turn & the lock is opened you now know the picking order of your practice cylinder, then try picking the lock as standard using this pin order.
If you are still confused about what pin alignment is, go back to the MIT guide there are some pictures, Chapter 6
"Basic Scrubbing" Figure 6.2:
As for what direction to pick, my personal preference is from the rear to the front, some locks won't pick this way I know! but that is where a plug spinner comes into play.
What training cylinder have you got? there should be a brand name stamped on the front...for example
BKS.

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