A Sting?
A poster on another message thread said he thought it was unlikely that Flower and Stone's game would have improved so dramatically in just a few weeks, expert tuition or not. But the way it struck me in the film (I haven't read the book - perhaps it's clarified there?) is that the two old men were already expert players, conducting a sting operation. They go to Atlantic City, lose a lot of money deliberately to a greedy card sharp, and lure him back to their house a few weeks later (where he'll be expecting to make another killing), then when he lets his guard down they start playing properly and clean him out. A couple of things made me think this: first, when showing Pozzi and Nashe around the City of the World, they made a couple of heavy hints about wondering who they were going to get to build their wall, and exchanged knowing glances, implying they already had the plan in mind (even though this was before the game had begun). Second, the fact that for the first hour of the game they were playing just as badly as in the Atlantic City game, then turned things around at will just when Pozzi began to overreach himself and made a huge bet. Pozzi blamed Nashe for going away and taking his "luck" with him, but it seemed pretty clear to me the two old men had only been letting him win for precisely as long as they wanted to.
Why would they do it? They clearly don't need the money. I assume it was just a case of a couple of bored rich sadists wanting some entertainment and deciding they could get it by making somebody suffer (hence also later the sudden presentation of the ludicrously inflated food bill, just at the point where Pozzi and Nashe seemed about to regain their freedom, and consequently when it would have the maximum crushing impact on their morale).
Anyway, that's how it struck me - did anyone else see it that way?