Card Pool Mechanics
Each player has their own pool. There are 8 copies of each card, except only 6 copies of Incarnation cards. Exchanging and absorbing don’t return cards to the pool!
Effects that gain a specific card create an additional copy of the card, including Daoist Rhyme Omen choices other than At Own Pace. Generally, effects that draw specific kinds of cards create additional duplicate copies of cards in your pool, notably, Immortal Fates like Mental Perception and Inheritance of Cloud Sword.
At Own Pace takes a card out of your pool, and the same is probably true of other simple draw effects such as Thunder Tribulation. Wu Ce’s Virtuoso Immortal Fate, Best Choice, probably takes a card out of your pool, and the same is likely also true of other effects that draw card(s) from a specific phase. Wonderful Strokes creates new copies. Card upgrade effects like Enlightenment Elixir don’t take anything out of your pool.
Not only do exchanged and absorbed cards not return to the pool, exchanging or absorbing a card makes the remaining copies of the card less likely to be drawn. The exact workings of the mechanic is unknown. It doesn’t apply to Practice Writing, and probably not to other cards with absorb or exchange abilities either.
An exchange won’t give you another copy of the same card.
Each round, your first exchange has an increased chance to draw a current-phase card.
If you stay at a phase and keep exchanging long enough, you become increasingly likely to draw Deviation Syndrome, a useless card with the text “There are no other cards!”. In Meditation phase, it happens after seeing approximately sixty to seventy cards (not always the same number).
I think it takes long enough to happen that it shouldn’t deter you from early-phase reroll strategies, but you should probably move on if it does happen to you in a game.
One hypothesis I thought of that’s almost plausible is that perhaps whenever you exchange or absorb a card, a random number of additional copies of that card are removed from your card pool.
But it doesn’t explain why sometimes you get a couple more successful exchanges (drawing normal cards) after drawing your first copy of Deviation Syndrome.