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Nonbasic lands don't untap during their controllers' untap steps.

Urza, Lord High Artificer

When Urza, Lord High Artificer enters the battlefield, create a 0/0 colorless Construct artifact creature token with "This creature gets +1/+1 for each artifact you control."
Tap an untapped artifact you control: Add {U}.
{5}: Shuffle your library, then exile the top card. Until end of turn, you may play that card without paying its mana cost.

Reality Shift

Exile target creature. Its controller manifests the top card of their library. (That player puts the top card of their library onto the battlefield face down as a 2/2 creature. If it's a creature card, it can be turned face up any time for its mana cost.)

Torrential Gearhulk

Flash
When Torrential Gearhulk enters the battlefield, you may cast target instant card from your graveyard without paying its mana cost. If that spell would be put into your graveyard, exile it instead.

Brainstorm

Draw three cards, then put two cards from your hand on top of your library in any order.

Geier Reach Sanitarium

{T}: Add {C}.
{2}, {T}: Each player draws a card, then discards a card.

Peregrine Drake

Flying
When Peregrine Drake enters the battlefield, untap up to five lands.

Ponder

Look at the top three cards of your library, then put them back in any order. You may shuffle.
Draw a card.

High Tide

Until end of turn, whenever a player taps an Island for mana, that player adds an additional {U}.

Impulse

Look at the top four cards of your library. Put one of them into your hand and the rest on the bottom of your library in any order.

Timetwister

Each player shuffles their hand and graveyard into their library, then draws seven cards. (Then put Timetwister into its owner's graveyard.)

Chrome Mox

Imprint — When Chrome Mox enters the battlefield, you may exile a nonartifact, nonland card from your hand.
{T}: Add one mana of any of the exiled card's colors.

Flusterstorm

Counter target instant or sorcery spell unless its controller pays {1}.
Storm (When you cast this spell, copy it for each spell cast before it this turn. You may choose new targets for the copies.)

Sol Ring

Howling Mine

At the beginning of each player's draw step, if Howling Mine is untapped, that player draws an additional card.

Mulldrifter

Flying
When Mulldrifter enters the battlefield, draw two cards.
Evoke {2}{U} (You may cast this spell for its evoke cost. If you do, it's sacrificed when it enters the battlefield.)

Snapcaster Mage

Flash
When Snapcaster Mage enters the battlefield, target instant or sorcery card in your graveyard gains flashback until end of turn. The flashback cost is equal to its mana cost. (You may cast that card from your graveyard for its flashback cost. Then exile it.)

Pact of Negation

Counter target spell.
At the beginning of your next upkeep, pay {3}{U}{U}. If you don't, you lose the game.

Force of Will

You may pay 1 life and exile a blue card from your hand rather than pay this spell's mana cost.
Counter target spell.

Frantic Search

Draw two cards, then discard two cards. Untap up to three lands.

Kozilek, Butcher of Truth

When you cast this spell, draw four cards.
Annihilator 4 (Whenever this creature attacks, defending player sacrifices four permanents.)
When Kozilek, Butcher of Truth is put into a graveyard from anywhere, its owner shuffles their graveyard into their library.

Archaeomancer

When Archaeomancer enters the battlefield, return target instant or sorcery card from your graveyard to your hand.

Logic Knot

Delve (Each card you exile from your graveyard while casting this spell pays for {1}.)
Counter target spell unless its controller pays {X}.

Cryptic Command

Choose two —
• Counter target spell.
• Return target permanent to its owner's hand.
• Tap all creatures your opponents control.
• Draw a card.

Force of Negation

If it's not your turn, you may exile a blue card from your hand rather than pay this spell's mana cost.
Counter target noncreature spell. If that spell is countered this way, exile it instead of putting it into its owner's graveyard.

Hurkyl's Recall

Return all artifacts target player owns to their hand.

Lion's Eye Diamond

Discard your hand, Sacrifice Lion's Eye Diamond: Add three mana of any one color. Activate only as an instant.

Ghostly Flicker

Exile two target artifacts, creatures, and/or lands you control, then return those cards to the battlefield under your control.

Emrakul, the Promised End

This spell costs {1} less to cast for each card type among cards in your graveyard.
When you cast this spell, you gain control of target opponent during that player's next turn. After that turn, that player takes an extra turn.
Flying, trample, protection from instants

Jeweled Lotus

{T}, Sacrifice Jeweled Lotus: Add three mana of any one color. Spend this mana only to cast your commander.

Mox Amber

{T}: Add one mana of any color among legendary creatures and planeswalkers you control.

Scalding Tarn

{T}, Pay 1 life, Sacrifice Scalding Tarn: Search your library for an Island or Mountain card, put it onto the battlefield, then shuffle.

Polluted Delta

{T}, Pay 1 life, Sacrifice Polluted Delta: Search your library for an Island or Swamp card, put it onto the battlefield, then shuffle.

Ulamog, the Ceaseless Hunger

When you cast this spell, exile two target permanents.
Indestructible
Whenever Ulamog, the Ceaseless Hunger attacks, defending player exiles the top twenty cards of their library.

Grim Monolith

Grim Monolith doesn't untap during your untap step.
{T}: Add {C}{C}{C}.
{4}: Untap Grim Monolith.

Fact or Fiction

Reveal the top five cards of your library. An opponent separates those cards into two piles. Put one pile into your hand and the other into your graveyard.

Treachery

Enchant creature
When Treachery enters the battlefield, untap up to five lands.
You control enchanted creature.

Negate

Sensei's Divining Top

{1}: Look at the top three cards of your library, then put them back in any order.
{T}: Draw a card, then put Sensei's Divining Top on top of its owner's library.

Paradoxical Outcome

Return any number of target nonland, nontoken permanents you control to their owners' hands. Draw a card for each card returned to your hand this way.

Mox Opal

Metalcraft — {T}: Add one mana of any color. Activate only if you control three or more artifacts.

Mana Drain

Counter target spell. At the beginning of your next main phase, add an amount of {C} equal to that spell's mana value.

Turnabout

Choose artifact, creature, or land. Tap all untapped permanents of the chosen type target player controls, or untap all tapped permanents of that type that player controls.

Narset, Parter of Veils

Each opponent can't draw more than one card each turn.
−2: Look at the top four cards of your library. You may reveal a noncreature, nonland card from among them and put it into your hand. Put the rest on the bottom of your library in a random order.

Mind's Desire

Shuffle your library. Then exile the top card of your library. Until end of turn, you may play that card without paying its mana cost.
Storm (When you cast this spell, copy it for each spell cast before it this turn.)

Solemn Simulacrum

When Solemn Simulacrum enters the battlefield, you may search your library for a basic land card, put that card onto the battlefield tapped, then shuffle.
When Solemn Simulacrum dies, you may draw a card.

Ulamog, the Infinite Gyre

When you cast this spell, destroy target permanent.
Indestructible
Annihilator 4 (Whenever this creature attacks, defending player sacrifices four permanents.)
When Ulamog, the Infinite Gyre is put into a graveyard from anywhere, its owner shuffles their graveyard into their library.

Mana Vault

Mana Vault doesn't untap during your untap step.
At the beginning of your upkeep, you may pay {4}. If you do, untap Mana Vault.
At the beginning of your draw step, if Mana Vault is tapped, it deals 1 damage to you.
{T}: Add {C}{C}{C}.

Island

Mystical Tutor

Search your library for an instant or sorcery card, reveal it, then shuffle and put that card on top.

Tezzeret the Seeker

+1: Untap up to two target artifacts.
−X: Search your library for an artifact card with mana value X or less, put it onto the battlefield, then shuffle.
−5: Artifacts you control become artifact creatures with base power and toughness 5/5 until end of turn.

Time Warp

Target player takes an extra turn after this one.

Propaganda

Creatures can't attack you unless their controller pays {2} for each creature they control that's attacking you.

Disallow

Counter target spell, activated ability, or triggered ability. (Mana abilities can't be targeted.)

Misty Rainforest

{T}, Pay 1 life, Sacrifice Misty Rainforest: Search your library for a Forest or Island card, put it onto the battlefield, then shuffle.

Deadeye Navigator

Soulbond (You may pair this creature with another unpaired creature when either enters the battlefield. They remain paired for as long as you control both of them.)
As long as Deadeye Navigator is paired with another creature, each of those creatures has "{1}{U}: Exile this creature, then return it to the battlefield under your control."

Preordain

Scry 2, then draw a card. (To scry 2, look at the top two cards of your library, then put any number of them on the bottom and the rest on top in any order.)

Mikokoro, Center of the Sea

{T}: Add {C}.
{2}, {T}: Each player draws a card.

Mox Diamond

If Mox Diamond would enter the battlefield, you may discard a land card instead. If you do, put Mox Diamond onto the battlefield. If you don't, put it into its owner's graveyard.
{T}: Add one mana of any color.

Aetherflux Reservoir

Whenever you cast a spell, you gain 1 life for each spell you've cast this turn.
Pay 50 life: Aetherflux Reservoir deals 50 damage to any target.

Rhystic Study

Whenever an opponent casts a spell, you may draw a card unless that player pays {1}.

Walking Ballista

Walking Ballista enters the battlefield with X +1/+1 counters on it.
{4}: Put a +1/+1 counter on Walking Ballista.
Remove a +1/+1 counter from Walking Ballista: It deals 1 damage to any target.

Gilded Drake

Flying
When Gilded Drake enters the battlefield, exchange control of Gilded Drake and up to one target creature an opponent controls. If you don't or can't make an exchange, sacrifice Gilded Drake. This ability still resolves if its target becomes illegal.

Serum Visions

Thassa's Oracle

When Thassa's Oracle enters the battlefield, look at the top X cards of your library, where X is your devotion to blue. Put up to one of them on top of your library and the rest on the bottom of your library in a random order. If X is greater than or equal to the number of cards in your library, you win the game. (Each {U} in the mana costs of permanents you control counts toward your devotion to blue.)

Basalt Monolith

Basalt Monolith doesn't untap during your untap step.
{T}: Add {C}{C}{C}.
{3}: Untap Basalt Monolith.

Enter the Infinite

Draw cards equal to the number of cards in your library, then put a card from your hand on top of your library. You have no maximum hand size until your next turn.

Kami of the Crescent Moon

At the beginning of each player's draw step, that player draws an additional card.

Time Spiral

Exile Time Spiral. Each player shuffles their hand and graveyard into their library, then draws seven cards. You untap up to six lands.