Rain Man made card counting look like a feat of photographic memory. The truth is plainer and harder. A counter tracks one thing only: the ratio of high cards to low cards left in the shoe. In the Hi-Lo system, twos through sixes count as plus one, tens, face cards, and aces as minus one, and sevens through nines as zero. This episode explains why a deck rich in tens and aces favors the player, and why the dealer’s fixed rules are the weakness that makes it work.

The math is easy at home and grueling on a casino floor. A player must convert the running count into a true count, size bets by the Kelly Criterion, and endure brutal swings for an edge of about 1 percent. From there the story becomes a contest of tactics: Stanford Wong’s back counting, the spotter and big player teams pioneered by Al Francesco and Ken Uston, and the surveillance systems casinos built in reply. Counting with your brain is legal, but the house can still show you the door.

• Edward O. Thorp used room-sized IBM 704 computers in the early 1960s to simulate millions of hands and measure how removing each card shifts the odds.
• Even with flawless play on a six-deck shoe, the count is positive only about 10 to 35 percent of the time, and professionals keep a bankroll of 100 times their maximum bet.
• In team play, spotters grind minimum bets and secretly signal a big player, who swoops in at table maximum, a method that cleared millions for groups like the MIT Blackjack Team.
• Casinos answered with RFID chips, software such as Bloodhound and Protec 21, continuous shuffling machines, and the face databases of Griffin Investigations.
• After Ken Uston’s 1979 lawsuit, the New Jersey Supreme Court ruled Atlantic City casinos cannot ban skilled players, so they shuffle early or cap bets instead.