Bluffing isn't hard to code, especially if you are using some kind of AI argoithm. You may not even code it directly, you will just notice that it's actually bluffing at the end, mimicking humans What is "bluffing" from an algorithm development perspective? It's just one of optimization parameters of the system. It's much harder to code emotions, than such ideas with binary/measurable outputs and outcomes. Taking into account that these robots came from the real world, they may got accustomed to bluffing when playing against human players. And, when you will finally make them play with each other, there is no reason for them to change their behavior.
If programmed open-ended enough and could get away with it, then certainly. If learning from human game history only without other directions, it could actually be a starting point for making bad bets, err bots. The best playing bots would probably be something like Alpha Zero. They'd probably bluff too, at least at the start, somewhere in the middle, and before the end.
The poker bot should play to maximize expect winnings. Whether it is a person or a bot their are many situations where the math indicates a bluff is prudent. It really boils down to simple math.
I remember reading about Kasparov vs big blue and Kasparov was loosing several games and was kinda desperate(accordingly to the story). Then he made a mistake by accident. He made completely counter intuitive move. This completely threw the algo off and he found a way to beat it. Of course developers went back and adjusted the algo to take such cases into account and the rest is history.
Those who compare human vs AI often forget about human+AI combination Imagine Big Blue against Kasparov+Bigger Blue
IIRC game theory defines bluffing as "an action that is designed to induces sub-optimal actions in the other participants" and by that definition it very hard to code.
I see it just as a set of tests with various input parameters which isn't that complex. "Designed to induce" doesn't mean that we need to code sub-optimal actions. We just need to perform some experiments, recording and analyzing their outcomes. The black box.
In that case it's not bluffing, it's just rational actions under uncertainty. A perfectly rational player would make all decisions based on known states, i.e. cards that have crossed the table, possibly betting by the other players etc. depending on the game. In bluffing, you are making an assumption that the other player(s) is(are) not rational. So you end up trying to somehow convince him that your position is either stronger or weaker than what should be expected based on the known state(s).