How to prevent stalemate?

If both players have the same cards, than you already have your balance. However, it is a puzzle and it is still solvable. Unless options are open that a player has to gamble.

You need a slight imbalance for the game to keep the game going. So a card that only works some times is what you need.

My card E suggestion:
--> Bounce the card that the opponent has played back to the opponent.

Effects:
A: you gain 1 VP; was not played on you, so no effect.
B: your opponent loses 1 VP; was played on you, this backfired.
C: nullify your opponent card; no effect.
D: return your played card(s) to your hand; no effect.

Of course this would mean that 25% of the cases, you spiral downwards with VP.

Card F suggestion:
--> Double the card that the opponent has played. And play it as if it was your own card.

Effects:
A: you gain 1 VP; means that the player with Card F gains 2 VP.
B: your opponent loses 1 VP; means that the player that played B loses 2 VP, this backfired.
C: nullify your opponent card; no effect.
D: return your played card(s) to your hand; means this happens for both players. Perhaps taking one card of the opponent now?

I hope these suggestions have given some idea's.

Well, Tic Tac Toe, the title above my first post. Is a puzzle for 2 players. You don't want to loose, but try to win. However, if both players play perfectly. There is never a winner. And the end result is always the same. A perfect stalemate.

When I took a look at your 4 cards. I had the exact same feeling.
In fact, you can write out every possibility of how players could play their cards until they retake all the played cards.
There is a set of best optional order in playing the cards. But no doubt, the players might discover this sooner than you think. Eventually you get the same end result every time. A perfect stalemate. Or in your case, a draw.

***

In my opinion. A game has several possible aspects for being called a game. It is all about breaking through determinism caused by the mirror nature of puzzles.

1- An event can be countered by 2 or more options. Not just 1. Because 1 option is not a choice.
2- (Mechanical) randomness helps breaking mirror effects. If you play a game with the exact same choices every time. The outcome would be the exact same. But not with randomness.
3- The simplest RPS, is not a mirror, even though you only have 1 counter option each time. In other words, don't have balanced or equal options. Instead, have a windmill of options that goes around. Literately, get the game rolling.
4- If you need skill that is limited by your body and mind. A randomness by human nature.

If you combine 1, 3 and 4. You get:
- Trying to trick players into doing something, which would benefit yourself since you already plan on having the right option ready.
Adding 2;
- You might fail. :) But chances are slim to fail if you have sufficient skill.

I am sure there are many more possibilities to turn a puzzle into a real game. But these 4 are very important to me since I am a RTS player by nature. Although number 2 is less of importance when you play video games. But it was certainly needed when translating RTS to board games.