Since both are assumed to have relatively infinite control of their bodies, and Batman’s preperations are more than likely going to at least more or less offset Superman’s abilities (x-raying the cards won’t help unless he can somehow x-ray the CARD and not the symbol ON the card, which seems unlikely… but it IS superman…) so as stated above it looks like an even playing field…
Thing is I doubt EITHER will EVER show any physical or psychological signs of bluffing, but I bet Batman’s betting strategies and playing style will be better in the long run.
<nitpick>Is it even possible to use x-ray vision to cheat at cards? Does Superman have that much control over his x-ray vision? I donno, just wondered. </nitpick>
In my ever so humble opinion, Batman is the hands-down winner here. Not only is he far more intelligent than Superman, he is the better bluffer. I have no doubt that he would be able to pass Superman’s lie-detector hearing cheat with ease. Not to mention Superman wouldn’t use his abilities to get the upper-hand. He’s just too much a wussy. Not the winning spirit there.
Batman wouldn’t have to mark the cards or cheat in any way other than use of the bluff. Now, if Batman chose to cheat, then no amount of luck would help Superman. He just isn’t that slick.
Do Superman’s enhanced senses enable him to see the fingerprints on the backs of the cards, and if so, wouldn’t that amount to a de facto marking system, if he can keep track of how Batman was holding each card before laying it down? And if so, would Superman use this capability?
Ok, let’s change it up a bit - say that Supes WILL be allowed to use his powers, but Bats is allowed to vary the rules to negate his advantage.
So they use lead cards to negate the X-ray vision. They’ll have to bring along Wonder Woman or someone with sufficient superstrength to shuffle lead cards. Can’t let Supes do it - because he could rig the deck.
Now Superman could hear any change in Batman’s pulse or breathing if Batman knew he had good cards. Superman could also use his superspeed to run around the table and take a peek when Batman looked at his cards.
So there’s only one way for Batman to play: without looking at his cards.
Superman will look at his cards and know whether he has a decent hand. If he stays in, then Bats will know that he has a good hand - or he’s bluffing. So Bats will know what to bet if at all. In addition, Bats will spend the entire time watching Supes, so he will be able to tell which goblet Superman put the iocaine powder into… whoops! Got lost there.
Of course, Superman could use his heat vision / cold breath alternatively on the sly to make Batman uncomfortable so he cannot concentrate. But Bats will prepare for this by wearing layers of bat-suit.
So in the end, it all comes down to Batman reading Superman’s body language. No contest - in a couple of hours, Wayne Enterprises would own serious drilling rights underneath a certain Fortress in Antarctica.