How many action cards can be played during a showdown?

There is no hard limit on the number of Action cards that can be played during a single showdown. Both players can play multiple Action cards throughout the duration of a showdown, provided they follow the rules for Focus and the state of the chain.

According to RiftJudge FAQ #4911 and FAQ #5451, the rules for playing Action cards during a showdown are as follows:

1. Empty Chain Requirement: Action cards can only be played when the chain is empty (an "Open" state). You cannot respond to an Action card with another Action card because playing an Action card creates a chain, which closes the window for further Action cards.
2. Focus and Priority: Players alternate opportunities to play Action cards. When a chain resolves, the state becomes "Open" again, and the player with Focus has the opportunity to start a new chain with an Action or Reaction spell.
3. Showdown Duration: The showdown continues, allowing players to alternate playing Action cards and passing, until both players pass consecutively on an empty chain.

In summary: You can play as many Action cards as you have the resources and opportunities for, as long as you only play them when you have Focus and the chain is empty. Once you play an Action card, the chain is no longer empty, and only Reaction cards may be played until that chain resolves. After it resolves, the opportunity to play another Action card returns to the player with Focus.