I see now the possibly for 2 separate types of “intuition” that might be useful division we aren't otherwise aware of. The first is alluded to in my writing on deception and religion in poker which is effectively that natural selection, or random chance, is going to provide players that have religious beliefs on how to player poker which are conducive to success, but without that those players actually understanding the game.
So there is a type of (artificial) intuition here in which you could ask such a player who accidentally and naturally makes the correct play, “What is your underlying reasoning?” and their honest response is “I don't really have any.”
We could mistake that for, or call that, intuition.
Furthermore, I think that in regard to our limited way of representing experiences, and the possibility of outgrowing such functions I think it might be shown that what we call “intuition” is rather related to one's ability to correctly act (directly) off of one's “core beliefs” or “fundamental rule-sets”.
In other words it might be that the rule sets are so perfectly concise AND representative of the implied strategy that the action/response seems to fire (near) simultaneously with their stimulus (or at least fast enough to call it intuition rather than a reasoned response).
This is without suggesting that the player really understandings what they are doing or not (that is to say in this latter definition a player may or may not understand the game well, whereas the former speaks to players that certainly don't).
Of course this is more a re-solution of what COULD be seen as otherwise two types of intuition, and the re-solution is such that we can see the danger of putting our scientific faith into the possibility of intuition as a trainable and intelligent response or a skill to be honed.