Whiting estimates the number of successful advantage players to be in the hundreds. Cumulatively, they rake in large profits from games that were designed to be unbeatable: While some bettors might get lucky and win in the short run, over time they are supposed to lose and the casinos are expected to win, statistically speaking. In recent years, however, Whiting says the ranks of advantage players have swelled. Several factors are responsible. One is the ease with which gamblers can find each other online and share tactics. Grosjean has a blog called Beyond Numbers, for example. Another is the proliferation of books like Grosjean’s “Beyond Counting,” which he published in 2000 and updated in 2009 as a self-published edition (though he claims that if he doesn’t know who you are, he won’t sell you a copy). And because regulated casino gambling now takes place in at least 40 states, casinos compete for customers in part by introducing new games, some of which turn out to be vulnerable.

Common advantage-play techniques include “hole carding,” in which sharp-eyed players profit from careless dealers who unwittingly reveal tiny portions of the cards; “shuffle tracking,” or memorizing strings of cards in order to predict when specific cards will be dealt after they are next shuffled; and counting systems that monitor already dealt cards in order to estimate the value of those that remain in the deck. Richard Munchkin, a professional gambler who is the author of “Gambling Wizards” and a co-host of the radio show “Gambling With an Edge,” claims to have mastered all of these techniques. “I think every game can be beaten,” he says. (Munchkin, whose real first name is Richard, chose his professional surname because of the fact that he stands slightly taller than five feet.) “For example, certain slot machines must pay off their jackpots once they have accumulated $30,000. At $28,000, a slot machine might be a play” — gambling argot for something that can be bet on advantageously — “and there are slot teams that specialize in this. I know people who clock roulette wheels and others who can control a single die at craps.”

Among the most susceptible games these days are blackjack and poker variations like Ultimate Texas Hold ’Em, in which play is against the house rather than other gamblers. Teams of advantage players — which usually require one person to bet and another to spot dealers’ hole cards (those turned down and not supposed to be seen), track shuffles or count cards — have become so prevalent that they often find themselves in the same casino, at the same time, targeting the same game. “We had a blackjack game in Atlantic City with a weak dealer,” recalls Bobby Sanchez, known as the Bullet, a frequent playing partner of Grosjean’s. “We had our key seats locked up when players from two other crews tried jumping into the game. Elbows were thrown and there was a lot of jostling around the table. An older civilian accidentally got in the middle of it. His son thought I had hit him, and the son jumped on my back.” Things ultimately calmed down and an agreement was reached via surreptitious cellphone conversations: Members from the other teams would be able to sit and play at the table and use information from Sanchez’s spotter, but their betting would be capped at $800 per hand. “Meanwhile I bet three hands of $3,000 each,” Sanchez says. “Unfortunately, the dealer got pulled out after about 90 minutes. Following all the tumult, the table was being watched and somebody figured out what was going on. Still, we managed to win around $100,000 that night.”

One Friday night I accompanied the slimly built Grosjean, who wore baggy jeans, a red polo shirt and a hat with its bill riding low, as he strolled across the carpeted mezzanine of the Potawatomi Indian tribe’s Grand Casino Hotel and Resort in Shawnee. As I walked beside him, I tried to appear casual, with the tail of my untucked shirt covering the notepad in the back pocket of my slacks.

Grosjean passed an escalator and headed down a back staircase. To experienced surveillance people, he is a known advantage player; at any time he could be spotted, matched to his picture in a database of such players and asked to leave a casino. If that happens, the security guard could also read him the trespass act, meaning Grosjean would risk arrest if he tried to return. Getting away, on the other hand, would give him an opportunity to come back on some future day and perhaps go unnoticed. So if security was waiting for him at the bottom, Grosjean needed to be able to run back up in the opposite direction with the hope of avoiding a confrontation. He couldn’t do that on an escalator.

Down below on the gaming floor, ringed by wall-mounted TV monitors silently showing a sporting event, slot machines chirped and crowded blackjack tables buzzed with action. Grosjean sidestepped a cocktail waitress and approached the casino’s only craps game, the one in which cards are used instead of dice.

Grosjean had explained earlier the reason for this quirk: The Grand happens to be located in a jurisdiction where it is illegal for dice to determine financial outcomes in games of chance. Two sets of six playing cards, numbered one through six, one set with red backs, the other with blue backs, serve as de facto dice. A player rolls a giant numbered cube, apparently made from plastic foam. The cube determines which cards are turned over. It is a way to make the game feel like craps without dice directly producing a monetary outcome.