Currently in MTGA Arena, part of Dead Man's Chest ability affects the mana cost of all cards in your hand and all future draws.
You may cast nonland cards from among them for as long as they remain exiled, and you may spend mana as though it were mana of any type to cast those spells.
That later half is the part that is bugged.
Before triggering Dead Man's Chest
Effect Persists even after the taken cards have been played
Example of abuse, casting a red cost card using all swamps
I've repro'd this in back to back games. Once the effect is triggered, it affects the cost of all cards that you ever draw. This includes cards that were in your deck when the effect triggered.
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