Ethersworn Sphinx

seven generic mana one white mana one blue mana Artifact Creature — SphinxPower and toughness4/4

Affinity for artifacts (This spell costs one generic mana less to cast for each artifact you control.)

Flying

Cascade (When you cast this spell, exile cards from the top of your library until you exile a nonland card with lesser mana value. You may cast it without paying its mana cost. Put the exiled cards on the bottom in a random order.)

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Ethersworn Sphinx rulings

2021-06-18
Affinity can reduce only the generic mana in a spell's total cost. It can't reduce colored mana requirements.
2021-06-18
The cost reduction is set before you pay any of the spell's costs. Specifically, you could lock in a discount for an artifact you control and then sacrifice that artifact to activate a mana ability.
2021-06-18
If there are any additional costs or cost increases that would apply to Ethersworn Sphinx, apply those before applying any cost reductions.
2021-06-18
A spell's mana value is determined only by its mana cost. Ignore any alternative costs, additional costs, cost increases, or cost reductions.
2021-06-18
Cascade triggers when you cast the spell, meaning that it resolves before that spell. If you end up casting the exiled card, it will go on the stack above the spell with cascade.
2021-06-18
When the cascade ability resolves, you must exile cards. The only optional part of the ability is whether or not you cast the last card exiled.
2021-06-18
If a spell with cascade is countered, the cascade ability will still resolve normally.
2021-06-18
You exile the cards face up. All players will be able to see them.
2021-06-18
If you cast a card "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, you must pay those to cast the card.
2021-06-18
If the card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
2021-06-18
Due to a 2021 rules change to cascade, not only do you stop exiling cards if you exile a nonland card with lesser mana value than the spell with cascade, but the resulting spell you cast must also have lesser mana value. Previously, in cases where a card's mana value differed from the resulting spell, such as with some modal double-faced cards or cards with an Adventure, you could cast a spell with a higher mana value than the exiled card.
2021-06-18
The mana value of a split card is determined by the combined mana cost of its two halves. If cascade allows you to cast a split card, you may cast either half but not both halves.

Ethersworn Sphinx keyword rules

Cascade Rule 702.85

Cascade is a triggered ability that functions only while the spell with cascade is on the stack. “Cascade” means “When you cast this spell, exile cards from the top of your library until you exile a nonland card whose mana value is less than this spell’s mana value. You may cast that card without paying its mana cost if the resulting spell’s mana value is less than this spell’s mana value. Then put all cards exiled this way that weren’t cast on the bottom of your library in a random order.”

If an effect allows a player to take an action with one or more of the exiled cards “as you cascade,” the player may take that action after they have finished exiling cards due to the cascade ability. This action is taken before choosing whether to cast the last exiled card or, if no appropriate card was exiled, before putting the exiled cards on the bottom of their library in a random order.

If a spell has multiple instances of cascade, each triggers separately.

Flying Rule 702.9

Flying is an evasion ability.

A creature with flying can’t be blocked except by creatures with flying and/or reach. A creature with flying can block a creature with or without flying. (See rule , “Declare Blockers Step,” and rule , “Reach.”)

Multiple instances of flying on the same creature are redundant.

Affinity Rule 702.41

Affinity is a static ability that functions while the spell with affinity is on the stack. “Affinity for [text]” means “This spell costs you {1} less to cast for each [text] you control.”

If a spell has multiple instances of affinity, each of them applies.