Power Wall

In the "TCG", the damage becomes 0 regardless of whether the cards are sent from the Deck to the Graveyard.
In the "OCG", the damage only becomes 0 if cards are moved from the Deck by the effect of "Power Wall".

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OCG Rulings

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It does not target.: Power Wall

When the effect of "Power Wall" resolves, in order to make the battle damage the player takes 0, send 1 card from the top of the player's Deck for each 500 damage. (In the case of 2000 battle damage, 4 cards are sent from the Deck to the Graveyard.)

If the player cannot send cards from their Deck to the Graveyard in order to make the battle damage they are about to take 0, "Power Wall" cannot be activated. (In the case of 2000 battle damage, because it is necessary to send 4 cards from the Deck to the Graveyard, "Power Wall" cannot be activated if there are 3 or fewer cards in the player's Deck.)

Even when the player would take less than 500 battle damage, "Power Wall" can be activated. (1 card is sent from the top of the Deck to the Graveyard, and the battle damage becomes 0.) However, when the player would take 0 battle damage, "Power Wall" cannot be activated.

The opponent's "Ebon Illusion Magician" with 2500 ATK attacks the player's face-up Attack Position "Cyber Dragon Core" with 400 ATK. As Chain Link 1 during damage calculation, the opponent activates the monster effect "During damage calculation (in either player's turn), if your other DARK Spellcaster-Type monster battles an opponent's monster: You can send this card from your hand or face-up from your field to the Graveyard; that monster you control gains 2000 ATK and DEF during that damage calculation only" of "Apprentice Illusion Magician". Even in this case, the player can activate "Power Wall". In that case, when "Power Wall" resolves, the battle damage the player would take in the current state is 2100, so they send 5 cards from the top of their Deck to the Graveyard. Then, when the effect of "Apprentice Illusion Magician" is applied, the opponent's "Ebon Illusion Magician" gains 2000 ATK and DEF, but the battle damage the player would take has already been reduced to 0 so they take no damage. ("Cyber Dragon Core" is destroyed and sent to the Graveyard normally.): During damage calculation after a DARK Spellcaster-Type monster declared an attack, if the monster effect of "Apprentice Illusion Magician" was activated, can "Power Wall" be activated in Chain?

When the effect of "Power Wall" is applied, the battle damage the player would take becomes 0, but the player's monster can still be destroyed by battle and sent to the Graveyard normally.: If "Power Wall" is activated, will the player's monster be destroyed by battle?

The opponent's "Ebon Illusion Magician" with 2500 ATK attacks the player's face-up Attack Position "Cyber Dragon Core" with 400 ATK. As Chain Link 1 during damage calculation, the player activates "Power Wall". The opponent chains the effect "During damage calculation (in either player's turn), if your other DARK Spellcaster-Type monster battles an opponent's monster: You can send this card from your hand or face-up from your field to the Graveyard; that monster you control gains 2000 ATK and DEF during that damage calculation only" of "Apprentice Illusion Magician". In this scenario, when the effect of "Apprentice Illusion Magician" is applied, the opponent's "Ebon Illusion Magician" gains 2000 ATK and DEF. Then, when "Power Wall" resolves, the battle damage the player would take in the current state is 4100, so they send 9 cards from the top of their Deck to the Graveyard. The player takes no battle damage from this battle, but "Cyber Dragon Core" is destroyed and sent to the Graveyard normally. Note that when resolving the effect of "Power Wall" in this scenario, if the player has fewer than 9 cards in their Deck, they cannot send any cards from the top of their Deck to the Graveyard, so they take 4100 damage normally.: During damage calculation after a DARK Spellcaster-Type monster declared an attack, if the monster effect of "Apprentice Illusion Magician" is activated in Chain to the activation of the player's "Power Wall", how does it resolve?

While the effect of "Waboku" is applying, the player takes no battle damage from the opponent's monsters. Therefore, they cannot activate "Power Wall" during damage calculation that turn.: Can "Power Wall" be activated while "Waboku" is applying?

Even while "Macro Cosmos" is applying, "Power Wall" can be activated. In that case, the cards that would be sent to the Graveyard by "Send 1 card from the top of your Deck to the Graveyard for every 500 damage (round up) you are about to take, also you take no battle damage from that battle" are all banished, but the battle damage from that battle becomes 0 as normal.: Can "Power Wall" be activated while "Macro Cosmos" is applying?

If the opponent's face-up Attack Position "Reaper of the Cards" with 1380 ATK declares a direct attack and the player activates "Power Wall", since the battle damage they would take is 1380, they must send 3 cards from the top of their Deck to the Graveyard to reduce that damage to 0.: If "Reaper of the Cards" declared a direct attack, can "Power Wall" be activated during that damage calculation?

If the opponent's Attack Position "Amazoness Swords Woman" (1500 ATK) attacks the player's face-up Attack Position "Cyber End Dragon" (4000 ATK), since the monster effect "Your opponent takes all Battle Damage that you would have taken from a battle involving this card" of the opponent's "Amazoness Swords Woman" would make the player take the battle damage instead of the opponent, the player can activate "Power Wall". In that case, when resolving the effect of "Power Wall", since the battle damage they would take is 2500, they send 5 cards from the top of their Deck to the Graveyard. (Although the effect of "Power Wall" reduces the battle damage to 0, the opponent's "Amazoness Swords Woman" is destroyed by battle and sent to the Graveyard.): If the opponent's "Amazoness Swords Woman" attacked the player's "Cyber End Dragon", can the player activate "Power Wall" during that damage calculation?

If "Performage Trapeze Magician" is in face-up Attack Position in the player's Monster Zone and is attacked by "Performapal Odd-Eyes Metal Claw", the effect of "Performage Trapeze Magician" makes any damage the player would take that is less than or equal to its current ATK of 2500 become 0. Since the battle damage they would take from the opponent’s attacking "Performapal Odd-Eyes Metal Claw" is 0 in this case, they cannot activate "Power Wall".: If "Performage Trapeze Magician" is face-up in the player's Monster Zone, can they activate "Power Wall" during that damage calculation?