So HIgh Evo strengths are how it's got the ability to consistently earn points even if you are floating energy on the turn. There's two main ways to play the deck, the Infanaut/She Hulk version, and the Abomination Afflication version. I'll go through the Abomination Afflication version as I feel that's the stronger of the two decks at the moment. Borrowing a build from Marvel Snap Zone.
The main idea is you use the early turns to build a point advantage and strong lane over your opponents, weakening their cards to discount Abomination which can cause a big 9 power swing on turn 5 or 6. And then the last turn you secure your win with one of a Big Hulk play to win a lane, or a Shang Chi/Enchantress to disrupt your opponents gameplan and win that way instead.
Try to aim to spend all but one of your energy each turn if you have your Evolved cards in play or Hulk in hand. If you have say, Sunspot and Misty Knight in play and Hulk in hand, that''s 2 power you are adding to the board immediately and 2 power added to Hulk for the final turn. Do note sometimes it is better to just play your cards though, No point inforegoing an Armor play just because you can get more points from floating one Energy if your opponent is going to killmonger and ruin you on turn 3.
A general rough playplan would look like so.
Turn 1. Oftentimes you just skip this turn to power up Hulk if he's in your hand, If you don't have Hulk, you can play Sunspot or Misty Knight this turn, but it's often favourable to wait a turn to get them a better lane. If you have Scorpion for turn 2 though, you want to play one of them now.
Turn 2. This is your Play Scorpion turn if you got him just so Scorpion hits the most cards possible, otherwise Sunspot and/or Misty Knight is good this turn. You can also set up Armor and Shocker here as well. Armor is key for not only defending a late game hulk, but also your Sunspot and Misty Knight from Killmonger as well.
Turn 3. Whichever 1 or 2 drop plays you haven't' had a chance to play previously, you do it on this turn. You can potentially set up a Cyclops this turn too if your opponent has committed 2 units to one lane, otherwise it's better to play Cyclops on 4 to position him better.
Turn 4. This is the Cyclops into a lane where he can deal the most damage. You can also use Thing here as well as an alternative if you've got at least 2 targets for him to hit (3 would be ideal). This is also around the time you should be thinking about Snapping or not for the game, looking if you have a powered up Hulk to close out and win the game, or the right tech cards to lock out whatever gameplan your opponent is trying.
Turn 5. If you've discounted abomination, this is probably the turn you are playing him. The only time I'd consider against it is if you think you will have 5 afflicted foes on your opponent or you haven't drawn your Hulk and want to save the big 9 power swing for the final turn. Otherwise you play one of your tech cards to disrupt your opponent or any of your previous other cards you haven''t played yet like Thing. You might play High Evolutionary yourself this turn if you have nothing further to do.
Turn 6. This is probably the Hulk turn whos' big enough power is hopefully strong enough to swing a lane for you, that or it's the time to play one of your tech cards to ruin your opponents gameplan and win the game that way. If you did manage to get Abomination to zero you can drop it with Hulk for one of the highest power turns possible. Armor can be used to defend your hulk as well if you fear Shang Chi.
There is other tech card considerations to run over Shang Chi and Enchantress as well, depending on what's bothering you more. Cosmo, Rogue, Luke Cage all worth considering as alternatives. I'll list some cards to watch out for at present for HIgh Evolutionary as well.
1. Red Hulk, the biggest issue for High Evolutionary at present since it's effect counters your effect of not spending energy each turn, as Red Hulk will gain 4 Power each turn you end without spending all your energy, something you wish to do. You do at least get an early warning if they have Red Hulk in hand, if you see Red Hulk, try to spread your power enough so you are winning enough lanes that they can't just win by playing Red Hulk to one lane, or try and throw your priority into the final turn and predict which lane they'll be using Red Hulk in and Shang Chi it out (No good if you have Armor though, they'll probably play it into that one.
2. Luke Cage, this not only undoes all your affliction lowering, but also prevents you from discounting your abomination as well. If you see it early, enchantress/rogue to get rid of it
3. Mobius M. Mobius. A bigger issue for the Inshenaut variant of High Evolutionary, but Aflliction doesn't like a full cost Abomination either, once again, Enchantress if you see it.
I hope that helps somewhat with playing the Abomination variant at least. I'd talk about some of the other variants like Infshenaut, but I dunno if you have those Series 3 cards like Magik and She Hulk to play them yet.
