This was just a side project on my part, a chance to learn something about renpy that I'm not currently using myself. I only shared it because it turned out to be a bit simpler in renpy than I initially thought and I thought it might help you out.
Whether having the poker be interactive adds anything to the story...? Definitely not my call.
One thing to note is that the majority of my diagram is in the VN.
Zack's flawless victory is 44,43,42,41,40
Braden's flawless is 44,34,24,14,04
The nail-biter is 44,43,33,32,22,21,11, 10 or 01
Not there: hands 23,13,12,31 strip 30,20,03,02
So of the 24 nodes, 16 were represented in the VN.
And you have almost all the image assets already done and in the game. The only noticeable miss is Zack watching with just his shirt off (I think there are a couple of 'no shoes' needed as well).
And of course all of the poker game's branching doesn't matter, because everything should flow back to the scene where Braden towels up, declares he's 'done playing' and heads off to shower.
Anyway, good luck with however you do it.