Increase Catch Rate
This is not confirmed, but I have been using this technique on many games and have caught Kyurem, Mewtwo, Zapdos, and various other high level Pokemon, with measly Pokeballs.
Basically the idea is that each Pokeball has a catch rate/percentage. You have a better chance of catching a Pokemon with an Ultra ball than a Great ball. But, it's set the first time you throw it. The second time, you are slightly more likely if you use the same ball. The third time, you decrease the likelihood. So here's what I purpose : use two of the same ball, and then switch the ball you are using.
If it doesn't catch, you continue the cycle. For instance, you may go into battle with Reshiram and use the following combination: Ultra, Ultra, Poke, Poke, Ultra, Ultra, Great, Great, Poke, Poke, Ultra, etc.
I have used this on wild Pokemon other than legendaries, and I would say 9 out of 10 times that I use this I catch the Pokemon without even weakening it (anywhere between level 5-70).
*Note* If you are planning on using this technique, stock up on Pokeballs and other balls as well. I have gone through over 100 in a day.
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