How can I use chess piece value to balance my homemade TCG?
When Glorfindel linked you to the Chess piece relative value article, he was providing an example of how you can compare relative strengths in very simple situations.

In the case of your game, you would need to:


Pick a card which is fairly simple, and whose value is preferably quite small.
Give that card a value of 1.
Compare every other card to that card, and give them values based on their relative strength.
Use those values to calculate the total value of each deck, and compare those to each other.


For example, if you have a card that says "Do 1 damage", then you might decide that it's your value 1 card. Then a card that says "Do 2 damage" has a value of 2. A card that says "Flip a coin. If it's heads, do 2 damage" might have a value of 1, because on average it does a point of damage.

However, here's the nasty part - if steps 3 and 4 are easy to do, and can be done consistently, then your game will not be very fun. So such value calculations can only ever be approximate, and you will want to use them to get starting points to create what you think might be balanced decks, and then playtest those decks to see how accurate you are. Because, for example:


Players usually prefer safe bets to risky ones, so the "flip a coin" card will not be considered of equal value to the "do 1 damage" one, even though on average they're the same. But, if you need to deal 2 points of damage to your opponent to win otherwise they will win on their turn, then the "flip a coin" card has a 50% chance of letting you win while the "do 1 damage" card has 0%.
A creature with 1 strength is probably better, most of the time, than a card that does a single damage. But how much better? Does it matter how long the creature is likely to stay in play?
How do you value a rock-paper-scissors set of cards? The value of one is dependent on whether your opponent has the one it beats, or the one that beats it.
The valuation completely ignores things like card combos. Two cards can be completely useless on their own but game changing together, so how to value that?


Hence - do something quick and simple that you can then verify with actual playtesting. Anything else is too much effort for too little reward.