"Manipulation" describes a mechanic, not a single game. Several games feature manipulation as core play:
| Game | Type | How Manipulation Works |
|---|---|---|
| Manipulation Rummy / Carousel | Rummy Variant | Players can rearrange melds on table (their own + opponents') to play more cards. "Manipulate" the board. |
| Rummikub | Tile Rummy | Same: break/reform runs/sets on table to empty rack. The classic manipulation game. |
| Mahjong (Western/Card variants) | Tile/Set Collection | Claim discards, rearrange exposed melds. |
| Fluxx | Card Game | Rules change every turn (New Rule cards). Manipulate win condition, hand limit, play count. |
| Innovation | Civ Card Game | Dogma actions manipulate board state: splay, tuck, score, attack, draw. |
| Glory to Rome / Mottainai | Multi-use Cards | Each card = role, material, building, action. Manipulate roles each turn. |
| Race for the Galaxy / Roll for the Galaxy | Tableau Builder | Phase selection manipulates everyone's turn order/actions. |
| Coup / Resistance / Avalon | Social Deduction | Manipulate perception — bluff, deduce, accuse. |
| Magic: The Gathering / TCGs | TCG | Stack manipulation, bounce, counter, reorder, steal, copy. |
Most likely: You mean Manipulation Rummy / Carousel (add to/melds) or Rummikub (tiles). Search "Manipulation Rummy rules" or "Rummikub rules" for full details.