You could make Poker a knowledge skill rather than an Active skill. You could link it to Logic (if the player is brute-force calculating probabilities) or Intuition.
I wouldn't add Edge directly into the dice pool. If anything, I'd use it as teamwork dice. In fact, there are several things which could go into the teamwork bucket: Edge, Perception, Judge Intentions, etc. Teamwork dice are only going to convert into hits on a 9:1 basis, so you can have a fairly generous teamwork pool without massively skewing the end results.
After that, it depends on how much dice rolling you enjoy and how abstract you want things to be. I probably wouldn't roll for each hand, unless you really like rolling, but perhaps for each circuit around the table. Maybe each net hit changes your chip stack +/- 5%.