It sounds like the pedestals you have are the cast iron restaurant style type, like this:
Is that correct? These peds work really well (allow for maximum leg room),
but they have to be sized correctly. The standard restaurant peds for a small diner table won't be sturdy enough. Full size poker tables are really large and
heavy, and thus they need heavy duty legs. In particular, the plate/spider that connects the top of the pedestal to the table is a key detail point. Here are good heavy duty ones:
I don't believe I have the dimensions on these anymore, but the spiders were heavy duty cast iron, so these were really solid. Not quite as solid as oak pedestals, but pretty close. If the spiders/plates on your peds look more like this:
They're lightweight and more designed for a smaller table top. You can tighten the bolts/screws to the underside of the table all you want, but if the connection from the spider/plate to the top of steel leg is flexing, I'm not sure if there's much you can do to stiffen that.