Is PSYqualia real? The short answer is no. But the longer and more complicated answer is...kinda?
In essence, PSYqualia is the mystical ability used by a few characters in the Cardfight Vanguard Anime and Manga which gives them a connection to their cards and allows them to manipulate the outcome of the game they are playing to an extent.
Now Cardfight isn't by any means the only series to use this type of mechanic in their show, with the most famous being arguably the "Heart of the Cards" from Yu-Gi-Oh!
This type of PSYqualia is not real, it is just a mechanic to make the media advertising the card game more interesting, but it's still fun to pretend some times that you can use the "Heart of the Cards" to get a good top-deck. drive check or shield trigger.
Now, the more complicated answer is regarding what PSYqualia is meant to represent. Whilst not really explained in the Anime (yet) the Manga explains that whilst PSYqualia does allow you to connect with your units and allows the units to affect your deck to give you a good draw, but it mostly relies on the user's natural skill and instinct, or in other words, it represents the user being able to follow the flow of their deck and the current game in effect.
What do I mean by the flow of the deck or game? Well, if you have enough experience in any game, and have used a certain deck (or at least the barebones of a deck) enough times then you begin to notice trends, and how the opponent plays their cards and what that can mean for how they would react.
Was that confusing? Well here's a personal anecdote as an example!
I was at TFNation 2018 (a Transformers convention) and a couple of friends were playing a standard game. Royal Paladin vs Kagero. I don't remember the field, but they had King of Knights Alfred and Dragonic Waterfall as the Vanguards, and it was the Kagero player's turn. He attacked with his Vanguard first and his opponent placed shields that required two triggers to pass. His first drive check was a critical trigger so he was considering his options, and asked for my opinion (it was just a friendly match, so it's not a rule violation) and I said he should give the power to his Vanguard, but the critical to the Rear Guard, just in case. He decided to just give everything to the Rear Guard, and his next check was another critical trigger.
If he had taken my advice he would have won, as he would have still dealt two damage to his opponent in the late game, despite giving the first trigger effect to another unit.
Now, how did I know to do this? Did I use PSYqualia to know that he was likely to get a second trigger? Nope. I just watched their match and kept a loose track of how many triggers and of what types had already passed through each of their hands and knew he had a high chance of getting another trigger.
So, all in all, PSYqualia, in it's essence IS real, but to in the magical sense. It is real in that experienced players do tend to see patterns and trends with their decks, especially if they are built in a balanced manner.
It also helps to use Oracle Think Tank and literally stack the deck in the middle of the game without cheating :D
