Tamiyo, Compleated Sage

two generic mana one green mana one green mana, one blue mana, or 2 life Legendary Planeswalker — TamiyoLoyalty5

Compleated ( one green mana, one blue mana, or 2 life can be paid with , , or 2 life. If life was paid, this planeswalker enters with two fewer loyalty counters.)

: Tap up to one target artifact or creature. It doesn't untap during its controller's next untap step.

: Exile target nonland permanent card with mana value X from your graveyard. Create a token that's a copy of that card.

: Create Tamiyo's Notebook, a legendary colorless Book artifact token with "Spells you cast cost two generic mana less to cast" and " tap this permanent : Draw a card."

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Tamiyo, Compleated Sage rulings

2022-02-18
A hybrid Phyrexian mana symbol is counted the same way as a normal mana symbol when determining the mana value of a card. Specifically, Tamiyo’s mana value is always 5, even if you pay and 2 life to cast her.
2022-02-18
Phyrexian is not a color nor a type of mana, and players cannot add Phyrexian mana. It’s just a symbol that gives you another way to pay for a spell or ability.
2022-02-18
Compleated is a replacement effect, and it applies only to a permanent that is entering the battlefield with loyalty counters. Any other replacement effect that would apply to the number of loyalty counters it enters the battlefield with will apply as normal.
2022-02-18
The compleated ability looks only at whether a player chose to pay 2 life for a Phyrexian mana symbol as they were casting the spell. If a player paid life for some other reason while casting the spell, that will not reduce the number of loyalty counters the planeswalker enters the battlefield with.

Tamiyo, Compleated Sage keyword rules

Compleated Rule 702.150

Compleated is a static ability found on some planeswalker cards. Compleated means “If this permanent would enter with one or more loyalty counters on it and the player who cast it chose to pay life for any part of its cost represented by Phyrexian mana symbols, it instead enters the battlefield with that many loyalty counters minus two for each of those mana symbols.”