The way TT is supposed to work (if they can get their formula right, it's almost there now), is that it's a self balancing system. Each puzzle has it's own rating, and if you beat it, it drops, and vice versa.
Because of this, one could expect that puzzles that are similar to each other and have the same level of difficulty, will adjust it's rating to about the same as each other.
This turns out to be a quite accurate prediction. I have sometimes seen two identical puzzles (or just reversed sides), and their rating has been very few points apart. A couple of years ago, when I myself was rated sub 1000, I had never seen a smothered mate puzzle. Then I got to 1050, and almost one of every 10 puzzles was smothered mate. When I reached 1200, they almost disappeared.
Now to your questions:
"Why are the puzzles given to you in such a small range around your rating?"
> If they are too easy, it's probably something you already learned to master before, and you will learn nothing new. And if they are too hard, you may not even be able to understand the solution, so again you learn nothing. Personally, I think the spread is well balanced.
"Instead you always "play" puzzles that have almost the same exact rating as you do and obviously that is a limited pool"
> I think the pool is thousands upon thousands of puzzles. I rarely see a puzzle that I have seen before. I often see a theme that I have seen before, for example the smothered mate puzzles between 1050 and 1200.
"High rated players have so few puzzles to play they have clearly memorized them all."
> Or they are cheating. Who cares. When you're that good at tactics, your main focus should be strategy. There's nothing left to learn.
"There were hundreds of thousands of puzzles so it seems odd to keep getting the same ones. "
> If you keep getting the exact same puzzles over and over at 1500 rating, then I agree, that's odd. The puzzle pool shouldn't be much different from the 1400 pool I'm at.
Unless you have been at that level for a long time. Hopefully then, that you remember having seen the puzzle before, also means you will solve it slightly faster than the previous time. Then you will get more points than the previous time. And soon, drip by drip, you will climb to 1600 where a whole set of fresh new puzzles awaits you.
It happened to me recently, I was stuck at 1250 for a year, then suddenly I climbed to 1400 in a month, and now, even on a bad day my rating does not drop below 1400.
"So tactics trainer has basically become a memorization tool. Memorize all the tactics at your level and then move up."
> Well Tactics Training is about pattern recognition, which is not much different from memorization.
I have so many questions about tactics trainer and there is so little information provided on the site.
Why are the puzzles given to you in such a small range around your rating? It creates a lot of repeated problems (even at the 1500-1600 level). The way the rating system works you could be given a much wider range... you would get more points for harder puzzles and less points for easier puzzles. Instead you always "play" puzzles that have almost the same exact rating as you do and obviously that is a limited pool.
High rated players have so few puzzles to play they have clearly memorized them all. They are gaming the system such that they top list now has 4000-5000 rated players. If you look at their recent problems you will see that they are solving everyone correct in about 3 seconds. Some you can barely make the moves at that speed even without thinking.
On the very old site a few years ago you could see the distribution of ratings of all the puzzles. There were hundreds of thousands of puzzles so it seems odd to keep getting the same ones. So tactics trainer has basically become a memorization tool. Memorize all the tactics at your level and then move up.