If you have the time then...

Rather than having a camcorder next to each player: Cut holes in the table 4" (10cm) x 10" (25cm) in front of each of the players. Fit this with a piece of glass (preferably non-reflective) such that the players lay their cards face down on this glass. You might want to put a "modesty board" about 2-3 iches high in front of this so that the other players have no chance at all of seeing the cards. Place the cameras (all ten of them, wow, you really do have a budget) under the table. That way the "technology" isn't so in-yer-face and the players won't constantly feel that someone's looking over their shoulder.

Quick & Dirty lighting? A Chinese lantern suspended over the middle of the table.

With a bit of effort you'll get the table and faces lit well with the background dark. This way the camera crews moving about won't be a distraction on screen or to the players.

If you want to know how to light it so that it'll look grrrrrreat, then spending a bit on a Lighting Director is a good investment!