Being scientifically minded, I am very skeptical about psychic abilities. However, having been a professional poker player in a former career, I know what Doyle Brunson (Texas Dolly) is talking about...
I would not call it extrasensory, but rather how the unconscious (subconscious mind) processes information. When you are sitting around a poker table there is ample time to study other players and the situation to glean obscure, incidental information. After counting the cards and calculating the probabilities becomes second nature from constant practice, the mind has time to observe tells, interpret body language and draw conclusions. It's like machine learning or AI, except that the intelligence isn't a computer algorithm but a poker player's brain reckoning how to maximize winnings.
I can't make the experience something concrete that anyone can understand and duplicate. All I know is that when I was in good mental zone, I had a better than average ability to predict the hand my opponent was on. Unfortunately, I did not think to record my predictions and results in a scientific study. Being scientific is not a profitable persona at a poker table;)
One time, I even faced Doyle Brunson over a poker table at The Mint in downtown Las Vegas. I remember it rather well though it was 37 years ago. At the showdown (after the betting), Doyle showed jacks and 10s, but I won the hand with queens and 8s. Beating Texas Dolly by a narrow margin in a hand of poker doesn't prove much of anything, but it is sincerely a cherished memory of my experience with the great legend of Poker.
RE: Psychic Poker - do cardplayers use ESP to gain an advantage? Part 1