Day Trading is a zero-sum game

Previously, I had discussed that day-trading is a zero-sum game, meaning that in every single-trade, someone gains and the other loses.

Someone provided an inaccurate counter example in which Entity A buys an asset for $10 and then it appreciates and then sells it to Entity B for $20, and then Entity B sells it to Entity C for $30. They say that since A & B both made money, this is evidence that both people can profit in a single trade.

This is a misunderstanding since this was not an example of a single trade, but of three trades. A bought the asset from the original seller. So the $10 gain that A made would have been made by the original seller if they didn’t make that trade. In the next trade, B bought the $20 asset from A and then sold this asset for $30. Indeed, both A and B realized a $10 gain, but both A and the original seller would have been better off not selling since the trade was profitable for the entity they sold it to, and thus they missed out on that gain.

So even though both A and B profited, they didn’t profit off of the same trade.

Entity A made a gain from the prior trade and realized it when selling to B, and B gained from their trade and realized when they sold to C. This is an example of 3 trades (from original seller to A, from A to B, and from B to C).

In any single trade, it is impossible for both parties of that single trade to make a gain.
This is better illustrated with short selling. If A short sells B a call and then the call appreciates in value, then B has made a gain proportional to A’s loss.

It’s possible that A made a gain off of a previous trade (such as if this was a covered call strategy where they bought 100 shares and then short sold the call to hedge their bet), in which case they would profit off of the stock’s appreciation and would lose due to the sold call, and still make a net profit.

TLDR; in any single trade, one always makes a gain at the expense of another.