Blackjack Crash Course: How Card Counting Actually Works
Card counting is not a trick of memory and it is not illegal. It is a way of tracking one number, the composition of the cards that are left, and betting more when that number favours you. Here is what it actually does, in numbers.
Why the deck has a memory
Roulette has no memory: every spin starts from the same 37 pockets. Blackjack is different, because cards that have been dealt are gone until the shuffle. If a lot of small cards have come out, the cards that remain are rich in tens and aces, and that changes the odds of the next hand.
A deck rich in tens and aces helps the player for three reasons:
- More blackjacks. Player and dealer get blackjack equally often, but the player's is paid 3:2 and the dealer's only costs the player their bet.
- The dealer busts more. The dealer must hit stiff hands (12 to 16); the player may stand on them.
- Doubling pays off more. A double down on 10 or 11 is worth more when the next card is likely to be a ten.
Edward Thorp worked this out on an IBM 704 and published it in Beat the Dealer in 1962. Every counting system since is a simplification of the same idea.
The Hi-Lo count
The most widely taught system, Hi-Lo, gives every card a tag:
| Cards | Tag | Why |
|---|---|---|
| 2, 3, 4, 5, 6 | +1 | Small cards leaving the shoe help the player |
| 7, 8, 9 | 0 | Roughly neutral |
| 10, J, Q, K, A | −1 | Big cards leaving the shoe hurt the player |
A full deck sums to zero: twenty +1 cards, twenty −1 cards and twelve zeros. You start at zero after the shuffle and add each card's tag as it is dealt. That total is the running count.
From running count to true count
A running count of +6 means something different with one deck left than with five. So counters divide by the number of decks still to be dealt:
True count = running count ÷ decks remaining
Running count +6 with 3 decks left → true count +2.
Running count +6 with 1.5 decks left → true count +4.
A common rule of thumb is that each +1 of true count moves the player's expectation by about half a percent. A game that costs a basic-strategy player 0.5% at a true count of 0 is roughly break-even at +1 and a small player edge at +2 and above.
Betting is where the money is
Counting changes nothing if you bet the same amount every hand. The edge comes from the bet spread: a minimum bet when the count is neutral or negative, and larger bets when it is high. Most of the time the count is close to zero, so most hands are still played at a slight disadvantage. The profit comes from the relatively few hands played at a high count with a large bet.
We simulated this on ten million hands of a common six-deck game (dealer stands on soft 17, blackjack pays 3:2, double after split allowed, 75% of the shoe dealt). The full code and method are in our simulation write-up.
| Strategy | Result per unit bet | Units per 100 hands |
|---|---|---|
| Basic strategy, flat 1-unit bet | −0.52% | −0.52 |
| Hi-Lo, spread 1 to 12 units | +0.33% | +0.50 |
That is the honest size of it: half a betting unit per hundred hands, with a standard deviation of about 2.5 units on every single hand. It takes enormous volume before the edge reliably shows. We work through how much in variance and risk of ruin.
Playing deviations
Counters also change a few basic-strategy decisions when the count is high or low. The best known:
- Insurance: basic strategy says never take it. At a true count of about +3 or higher, insurance becomes a positive bet, because more than a third of the remaining cards are tens.
- 16 against a dealer 10: stand instead of hitting when the true count is above zero.
- 12 against a dealer 3: stand instead of hitting at a true count of about +2 or more.
These deviations add a little, but most of a counter's advantage comes from the bet spread, not from playing hands differently.
What casinos do about it
Counting in your head is legal in most jurisdictions. Casinos are still private businesses, and they counter it: more decks, earlier shuffles (lower penetration), continuous shuffling machines, 6:5 blackjack payouts, flat-bet limits, or simply asking a suspected counter to stop playing blackjack. A 6:5 payout alone adds about 1.4% to the house edge, which wipes out everything in the table above.
The takeaway
Card counting is one of the few cases in a casino where the maths can favour the player. It is also a slow, high-variance grind that pays about half a unit per hundred hands under good conditions. As a probability lesson it is excellent: it shows how removing items from a finite population changes the odds of what comes next.
- Edward O. Thorp and Beat the Dealer, Wikipedia
- Introduction to the High-Low card counting strategy, Wizard of Odds
- Blackjack basic strategy calculator, Wizard of Odds
- Card counting, Wikipedia