The difference between game theory and decision theory is that in game theory you need to worry about not just what is rational for you to do, you also have to consider what is rational for the other players to do.

When you play online poker, you are placing complete trust in your analysis of the trustworthiness of the 'house'. The house could cheat you, if it desires, and probably not get caught. But you analyze that cheating would be an irrational thing for the house to do an a large scale - because large scale cheating would get caught and they would lose customers.

So, what is your analysis of what they would do to a small number of their customers who violate their rules by using real-time machine assistance? They can't take those people to court. People who, if they were allowed to get away with it, would destroy the online poker business. Would it be rational for the Poker houses to try to cheat the rule-breakers?

Would they actually do that?

I used to count cards at blackjack. And when I did it in Reno, at a certain stage a new dealer would be brought to the table (outside the normal shift schedule). And from that point on, I would lose money. If I watched closely, I could see them dealing seconds.