Lesson 2 - The Rule That Starts Trading for You - Automatically

The room felt even quieter now - as if the Academy itself leaned in, waiting for the next piece to fall into place.

Ava flipped open her notebook, revealing a single line written at the top of the page:

x · y = k

Tao stared at it.
Two variables. One constant.
Deceptively simple.

“This,” Ava said softly, “is the rule every liquidity pool lives by. A single equation that decides how much of each token the pool must hold at any moment. The pool’s symmetry isn’t a suggestion - it’s a law. And this law is its heartbeat.”

Tao leaned closer, tracing the symbol with his eyes.
“So x and y… the amounts of the two tokens?”

“Yes,” Ava replied. “Token A and Token B. Their quantities shift constantly as people trade against the pool. But no matter how violently the market moves outside, the product of those two amounts must stay equal to one thing - k, the constant.”

Tao exhaled.

“So the pool has one instruction:
‘Whatever happens, keep x times y equal to k.’”

Ava nodded.
“And that instruction forces the pool to bend. If one token is taken out, the other must increase in quantity to keep the equation balanced. If one side rises in market price, the pool must hold less of it. If one side falls, the pool must accumulate more.”

Tao’s expression shifted - curiosity turning into recognition.

“That means the pool never holds what the market holds. It always holds what the equation demands.”

“Exactly,” Ava said. “Most newcomers think liquidity providers earn yield while holding the same tokens they deposited. But that’s not true. The moment you enter the pool, you surrender your fixed position. The system begins moving your tokens for you, redistributing them to satisfy the constant product.”

Tao felt the weight of that.
A quiet, almost unsettling realization.

“So even before any loss appears… the pool is already shaping my position. Without asking.”

Ava folded her hands.

“It has to. If it doesn’t bend, the market breaks the pool. The equation is the only thing keeping trades fluid - and that fluidity is what liquidity providers get paid for.”

Tao let silence settle between them as he studied the page again.

x · y = k
A simple rule.
A relentless one.

“Then the pool doesn’t simply react to the market,” he said slowly. “It protects itself from the market by pulling the provider’s tokens into whatever shape the equation demands.”

Ava’s eyes warmed.

“Now you’re seeing it. And this is the moment most people never reach - the realization that liquidity provision isn’t passive at all. It’s collaborative. You and the system hold each other in place. And the strain of that collaboration is where impermanent loss begins to take form.”

Tao sat back, almost breathless from the clarity unfolding.

“So Impermanent Loss (IL) isn’t a glitch.
It isn’t a punishment.
It’s the shadow cast by this equation.”

Ava nodded once.

“When prices diverge outside the pool, the equation forces the pool to move inside. That movement shifts your balance away from what you would have held outside it. And the gap between those two realities - your redistributed liquidity vs your untouched tokens - is where the loss emerges.”

Tao closed his eyes briefly.

The pool wasn’t random.
It wasn’t unfair.
It was obedient - to a rule so strict it bent everything around it.

When he opened his eyes again, the chart on the screen looked different.
Less chaotic.
More like a system breathing under constraint.

“What’s next?” he asked quietly.

Ava turned the page.
A new heading waited there like a doorway.

“What Happens When the Market Moves Without You”

She tapped the title once with her pen.

“Next lesson,” she said. “We study the moment the market and the pool fall out of alignment - and why that fracture is the birthplace of impermanent loss.”