OK, it took me a bit to figure out how to play, but I really enjoyed the process of figuring it out! Testing my theory as to finalize in my mind what did what was great! And then there's the actual game itself!

As a huge fan of puzzle games, I really enjoyed it. My main criticism is that there isn't really any way to influence what tiles you'll draw, it's completely random as far as I can tell. While in one sense this is a good thing since it forces you to play around what you get, on the flip side, it's a negative since you're at the mercy of RNGesus, and since I can't help but view this as a type of solitaire, in which everything is deterministic (though there is also a bit of luck there, but it's still deterministic), I can't help but view the luck of the draw as a negative. 

I'd say a bag system, where you're guaranteed to get one of every tile before you can get another, but the two sides have independent bags could really up the level of strategy that goes into the game, cause then you'd be able to carry over the tiles from one bag into the influence that belongs to the other bag. It would also let you hypothesize as to what would come next. 

Of course, the bag system could also lead to the game becoming solved (much like how one version of tetris that uses bags become solved), but the turn limit almost fixes that. At most, you'd be able to fully cycle through a total of three bags, and since you need to swap sides, that would mean you have an average of only refilling your bags on each side once, and then dipping into half of the next bag, which would maintain your randomness factor. 

OK, I'm done drooling over my hypothetical strategy solitaire game (if you couldn't tell, I've uhh, played a lot of solitaire, and several different kinds of solitaire). 

Overall, great game, and I will thoroughly enjoy it (and will possibly be the only one to still play it in 5 years when I randomly remember that it exists). 

Puzzle/solitaire enthusiast score is a solid 7.2/10. (I wavered a lot between 6.8 and 7.5, so just settled for the middle). 

Edit: I just got to 9, so I'll stop there so I have time to check out the other games. So far though, this one is the most in my niche, so it gets the medal for 'the game I am most likely to play in the future'

Edit 2: I just got 11 

I got 10 planes! (proof: )

Edit: 12 now

 Initially I was confused, especially since the UI looked like this:

It was only after I zoomed out my browser tab that it looked normal. For a game with minimal instructions, the gameplay is surprisingly intuitive after one game. A very cool puzzle, but I do wish there was a bit more to it. I know that you probably feel the same way, so if you end up continuing to work on this, I'm excited to see where it goes. Good work!