Game Mechanics is a term used for game/card rules. These are conditions that must be followed in the game and are not considered destruction or loss by Battle or Effect.
The basic rule of yu-gi-oh is when you have 7 or more cards in your hand by the End of you own End Phase, you must discard until you have the maximum number of 6. If you play dark world and send card to the grave by this way. You cannot activate any of their effects because they were sent to the graveyard by game mechanics.
If you have Seal of Oricalcos or Rainbow Ruins and they each have to the ability to no be destroyed by card effects (oricalcos: once per turn). If a new Field Spell is activated, Rainbow Ruins or Seal of Oricalcos will be sent to the graveyard because it is not by effects, game mechanics prevent more than 1 Field Spell at a time.
If you have Gozen Match/Rivalry of the Warlord on the field and you're opponent has monsters such as Dai sojo of the Ice Barrier and Stardust Dragon on the Field, they cannot save Dai sojo of the Ice Barrier with his effects or Stardust Dragon to negate the effect because the trap card prevents either player from holding more than 1 type/attribute of monster, this is not destruction by effect.
There are cards in the game that prevent 2 or more copies of a card to exist on the field at once. Archetypes such as Malefics, Earthbounds, and monsters such as Guardian of Order and Alector, Sovereign of Birds.
If you have Malefic Red Eyes Black Dragon set and Malefic Rainbow Dragon in attack mode and your opponent attacks the facedown Malefic Red Eyes Black Dragon, after Damage Calculation, Malefic Red Eyes Black Dragon will be removed
If you control Phantom of Chaos, Call of the Haunted set and 2 copies Guardian of Order in the Graveyard. If you activate Phantom of Chaos's effect and banish 1 Guardian of Order and use Call of the Haunted to target the other Guardian of Order, then Phantom of Chaos will be destroyed after its effect resolve because only 1 Guardian of Order can exists.
Summery of Game Mechanics of monsters: If you have 2 cards that cannot co-exist, then the last card to be face-up will be destroyed.
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