I think it's worth addressing your question on two levels, the practical level and the philosophical/ethical level (which by itself also has some bearing on the practical level).
On the practical level, it sounds like both the options of mentioning or not mentioning your poker occupation carry some risk. It cannot be denied that some people may perceive your choice of making a living from a card game as a negative, or at least not a positive, thing, whether this is justified or not. On the other hand, an unexplained 4-year gap on your CV would also very likely be perceived as a negative thing, perhaps by an even larger number of people than in the case of poker.
More positively however, if you were successful enough as a poker player to be able to make a living out of it for several years, that can say several good things about you that may impress even some people who tend to disapprove of poker. For example, if you want my personal opinion, I would infer that you are intelligent and have strong analytical skills, while at the same time not exactly getting the impression that you have strong altruistic tendencies or are especially passionate about using your talents for the good of society; of course, if I found out that you also volunteered at a homeless shelter or donated half of your poker proceeds to charity, my impressions on such things can change. If you are considering mentioning the poker, it may be a good idea to mention specific achievements in this area (e.g., which/how many tournaments you won).
Now, to address the more philosophical aspect of the question, I think as a matter of principle there's something to be said for being honest about what you have been doing with your life (as long as it's a legal activity), even though it may be a somewhat controversial activity that risks bothering or offending some people. More to the point, as I said this philosophical argument maps to the practical level, in the sense that if I were reading your application I would be somewhat impressed by the fact that you chose to mention it despite the obvious risks, independently of anything else, and would see that as evidence of a certain amount of character (at least if you didn't mention it in a way that seemed very cavalier or arrogant). Now, whether that positive impression would be enough to counterbalance the negative impression I would get if I were the sort of person who strongly disapproves of card games, is hard to say; probably for some such people the answer is no. For my case specifically, while I have a mild disapproval of someone with obvious talents taking up a form of employment that has essentially zero societal impact (whether it's poker or many other less controversial types of employment with the same characteristic), I do think the positive effect of seeing you take ownership of your lifestyle decisions in an honest way could actually make me see you in overall a quite positive light.
So should you mention it or not? I don't know. Only you can decide that, and given how critical of a decision this is, it would be irresponsible of me to give you any definite advice, even if I had a strong feeling about what the correct choice is, which I don't. I hope this analysis can still be a bit helpful though. In any case, good luck.