Theory: Forced Acceleration of Game State and 3 Mem Tamers
Many players would opt to play their 3 mem tamer as soon as possible to make most advantage of the guarenteed 3 mem and the occational "profit" you get from the opponent passing turn to you by giving less than 3 memeory.
Its obvious that when players try memory choke each other fewer cards are played each turn thus slower game state, vice versa spending tons of memory lets both players play more cards each turn thus accelerating the game state.
Less obvious is that once any player plays a 3 mem tamer it actually forces both players to accelerate the game state as well, and because of this it may not be the best play to play the 3 mem tamer.
If you have the 3 mem tamer, you clearly have better capabilities to setup the board and make plays, this in turn forces the enemy to commit something to the board and answer or take the loss. Alternatively you could hard summon/activate an expensive card thus giving the enemy lots of memory (albiet less due to 3 memory guaranteed).
Note how regardless of which line of play is made it forces/strongly encourages the player without the 3 mem tamer to commit to the board. This means that if your hand is incapable of dealing with the board, you should reconsider whether you should play the 3 mem tamer. Not only are you effectively encourging the opponent to establish a board you can't clear, you also lose tempo (because 3 mem tamers essentially does nothing the turn its played).
TLDR: Don't blindly play a 3 mem tamer for the sake of "profiting" as much as possible, make sure you are can deal with the accelerated game state if you do decide to play it.

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