A new email is waiting for you from Gil.
After completing Helping Havarl's Scientists or Stage a Rescue and returning to the Tempest, speak to Gil Brodie. Once Ryder has spoken to Gil about poker, Gil will send Ryder an email inviting Ryder to a game.
Read Email From Gil Edit
Meet Gil At The Vortex Edit
If Ryder accepts, Ryder will end Gil's winning streak. If Ryder declines, Gil thrashes Ryder handily.
Either way, Gil tells Ryder more about his friend Jill.
If Ryder wins by cheating and then confesses, Gil just laughs it off.
The mission is complete once the conversation is over.