So I did some brain work on the second test and here's what I found. There are key phases in the game, at least 3 that decide the victor.
Check Mate is when a round reaches 19 tokens. The person who starts the round with 19 tokens taken away automatically loses.
Check however, is a little different. This is decided by whether or not the game ever gets a round with 15 tokens or 16 taken. Player 1 wins if they start the round with 16, they'll just take 3. Player 2, however, automatically wins if the round starts with 15 no matter how many tokens player 1 takes.
Pre Check is decided by whoever gets to control of 13 or 14 because either number gives the player the power to create Check.
And finally
Fork in the Road is 12. If a game ever reaches a round with 12, player 2 effectively wins no matter player 1's response. Player 2 gets control of Pre Check which gives them control of Check which lets them put the game in Check Mate.
So from my analysis, I have to say that the Angel Princess is pretty fucking stupid.