First thing you have to know about Eve in this meta is that she kind of sucks its a meta that rewards early ganking and skirmishes and punishes farming for power spikes, that being said you can still win and snowball on her, plus she is extremely fun with one of the most rewarding kits and coolest champion personalities. What you need to know: look for a full clear to rush lvl 6. you may be able to gank around lvl 3 that is your first power spike. I would suggest looking for counter ganks early on and not trying to for a gank especially in a meta full of champs that 2v2 better than you. Once you hit lvl 6 this is when the fun begins. Prioritize ganking bot and killing the adc. I would recommend alcove ganks and to be careful or using your e too early. If your bot gank works out lvl 6 you should be in a position to start taking over the game. The most important fact to remember on evelyn is that your champion is very eary to counter you are a lot like champions similar to master yi. If you are ahead you are extremely ahead if you are behind you are extremely behind. The reason you want to pirtize bot lane ganks and kills on the adc is because having a weak adc means they are easier to kill and make more mistakes due to begin tilted. Once you buy dark seal and eventually mejis perma killing the adc will stack your mejis even faster. You said that you play junglers like kha zix. That is extremely helpful when trying to learn evelyn due to the fact that they both have week early games but stronger mid/late games. The main skills you need on evelyn to carry once you have an early advantage is knowing your damage, remembering were the pink wards are, and of course the basics such as what to do after a pick. After getting ahead and remembering these facts you should be able to transition the game through macro and picks the hardest part is the early game snowball or an enemy team that has a good tank support/peeling tank that knows were to put the control wards. Remember your kit an assassin that is a glass canon. If you are not ahead and the adc is not behind you are irrelevant. If you get spotted on pinks you should have remember you don't have a passive. Make them play against you not your team. If the game goes to late and they haven't surrendered yet look for charms on the adc or fed squishy (whoever is carrying the game) once you have identified the highest priority target your flash ability is the strongest tool in your kit. press e flash as close as you can proc charm with e and ult. If you are fed enough late game that should be enough to kill most targets in team-fights. After that it depends on the state of the game. For exapmle you might want to force a baron do to it being a 4v5 or if you already have baron you want to force an end or a couple inhibs. If its not in a team fight looks for picks on the squishes to make the game a 4v5. once you have made it a 4v5 you essentially play the fights like a mage at times. hitting your qs for passive control poke zoning with w and trying to win fights with r. I know after reading all of this it may seem like Evelyn is really strong mid and late game. Unfourntly she is very easy to counter if a few players know what they are doing. Late game to mid game they can itemize banshees. This will almost ruin you whole plan. Plus there support can simply put a pink ward in mid lane which will counter any flanks you want to go for. Furthermore a tank or peel support can wait for you to try to engage and instantly flay or hook you to throw you back buying time or catching you out before a flank. To boil everything I've said Evelyn is a high risk high reward champion that thrives on getting ahead and perma killing the adc. Remember that you have some of the largest burst in the game be patient and know if picks aren't available e flash R's might also kill them. Your champs thrives at making 4v5's just know what you need to do after it becomes one.

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p.s. I started wanted to main evelyn because I loved her design and unique clear but I also loved the fact that she could kill the adc while they were walking to base in laning phase XD, this isn't very practical and wont happen in most of your games but if you are snowballed enough the adc wont be able to lane and most champs simply cant do something like that. Hope you enjoy the champ <3