Blackjack Strategy: Basic Strategy & Card Counting

Q: What is the best blackjack strategy?

Perfect basic strategy: the mathematically correct hit, stand, double, and split for every hand against every dealer upcard. It cuts the house edge to about 0.5% (roughly 0.4% to 0.6% depending on the rules), the lowest of any bet on the floor. Blackjack paying 3:2 and the dealer standing on soft 17 are the friendliest rules.

Q: Is card counting illegal?

No. Counting cards in your head is just mental arithmetic and is not illegal. But casinos are private property and can shuffle early, cut the deck deep, lower your limits, or bar you. Using a counting device or app, however, is a crime in most jurisdictions.

Q: How does the Hi-Lo card counting system work?

In Hi-Lo you add +1 for each 2 through 6 dealt, 0 for each 7 through 9, and −1 for each 10, face card, or ace. Divide that running count by the decks remaining to get the true count. A high true count means the shoe is rich in tens and aces, which favors the player.

Q: Can you actually win at blackjack by counting cards?

The math allows a positive edge of roughly 0.5% to 1.5% with perfect basic strategy, an accurate count, and a large bet spread. But the edge is tiny, the variance is enormous, it demands a big bankroll and flawless discipline, and casinos will limit or eject you. For almost everyone it is a grind, not easy money.

By Alex Thornton · author of the MIT-licensed teachersbettextbook library · Last reviewed 24 July 2026

Blackjack is the one casino game a disciplined player can beat with arithmetic alone. Perfect basic strategy shaves the house edge to a rounding error; card counting can flip the sign. The catch is everything it takes to collect.

Part of the house edge, game by game. Blackjack is the exception.

How to read this game

Every casino bet has a price: the house edge, the casino’s average take per dollar wagered, straight out of expected value:

\mathrm{EV} = \sum_i p_i \cdot (\text{payoff}_i), \qquad \text{house edge} = -\,\mathrm{EV}

For most games that number is fixed and negative forever. Blackjack differs twice: how you play changes the edge, and which cards remain changes it too. Master both and, for brief stretches, the sign flips.

Basic strategy: getting to the floor

Basic strategy is the solved answer to every blackjack decision: the exact hit, stand, double, or split for your hand against the dealer’s upcard. Four Army statisticians computed it in 1956; it hasn’t changed.^[1] Memorize the chart and the game is played as well as it can be played.

Worked example: what perfect play buys you

\text{house edge (basic strategy)} \approx 0.5\% \quad (\text{ranges } 0.4\%\text{–}0.6\%\text{ by rules})

\text{best rules: blackjack pays } 3\!:\!2, \quad \text{dealer stands on soft } 17

A 3:2 natural pays $3 per $2 staked; the 6:5 tables quietly triple the house edge. Dealer standing on soft 17 helps too. The game is only beatable from the 0.5% floor, never from a 6:5 table.

Half a percent is the best price in the building: better than the craps pass line, far better than roulette or slots. Still negative. Basic strategy makes you a cheap customer, not a winner.

The twist: blackjack has memory

Roulette forgets. Every spin is independent and the 5.26% edge is fixed. Blackjack deals from a shrinking shoe that isn’t reshuffled every hand, so the cards already played tell you about the cards to come.

When the low cards are gone and the shoe runs rich in tens and aces, the player is favored: more $3\!:\!2$ naturals, more dealer busts on stiff hands, more tens under your double-downs. Card counting just tracks that balance.

Card counting: the Hi-Lo system

The standard count is Hi-Lo, public since 1966.^[2] Tag every card as it leaves the shoe and keep a running total:

Worked example: the Hi-Lo tags

\underbrace{2,3,4,5,6}_{\text{low}} \to +1, \qquad \underbrace{7,8,9}_{\text{neutral}} \to 0, \qquad \underbrace{10,\text{J},\text{Q},\text{K},\text{A}}_{\text{high}} \to -1

Low cards leaving help you: count up. High cards leaving hurt: count down. A positive running count means the tens and aces are still to come.

But a running count of $+10$ means different things with six decks left versus one. Divide by the decks still in the shoe to get the true count:

Worked example: running count to true count

\text{true count} = \frac{\text{running count}}{\text{decks remaining}}

\frac{+10}{5\text{ decks}} = +2, \qquad \frac{+10}{2\text{ decks}} = +5

Same running count, wildly different shoes: ten extra high cards packed into two decks is far richer than ten spread across five. The true count is what maps to an edge.

What the count is worth

Each point of true count adds roughly half a percent of edge to the basic-strategy start.^[3]

\text{edge} \approx -0.5\% + \big(0.5\% \times \text{true count}\big)

Run the line:

Worked example: the edge at three counts

\text{TC } 0: \quad -0.5\% + 0.5\%(0) = -0.5\% \;\;(\text{house edge})

\text{TC } +1: \quad -0.5\% + 0.5\%(1) = 0\% \;\;(\text{break-even})

\text{TC } +4: \quad -0.5\% + 0.5\%(4) = +1.5\% \;\;(\textbf{player edge})

The sign flips near a true count of

+1

; by

+4

the player is up about

+1.5\%

. That peak is thinner than the vig on a single sports bet, and it shows up only on the minority of hands when the shoe runs rich.

The strategy: it’s all in the bet spread

The count barely changes how you play. Basic strategy handles that, minus a few deviations at extreme counts. What the count changes is how much you bet: table minimum when it’s low or negative, big when it’s high. That spread is the entire edge. Flat-bet a perfect count and you win exactly nothing.

Sizing a thin, noisy edge against big variance is a Kelly criterion problem. Treat a high-count hand as roughly even money:

Worked example: sizing a high count with Kelly

\text{at TC }+4,\ \text{edge} \approx 1.5\%, \quad \text{even-money } (b \approx 1)

f^{*} \approx \text{edge} = 1.5\%\text{ of bankroll (full Kelly)}

\tfrac14\text{-Kelly}: \quad 0.25 \times 1.5\% \approx 0.375\%\text{ of bankroll}

On a $20,000 bankroll, quarter-Kelly is about $75 at the best counts and the table minimum the rest of the time. Overbet that 1.5% edge (the temptation when a big count finally hits) and one ordinary cold streak wipes you out. See the Kelly article for why full Kelly on a noisy edge is a loaded gun.

Read this part: the catch

Card counting is real, legal, and mathematically positive. It is also, for almost everyone, a bad idea:

Tiny edge, savage variance. A ~1% edge on a fraction of hands means the swings dwarf the signal. You can count flawlessly for a hundred hours and still be down. That’s the math, not bad luck. Surviving takes a large bankroll and iron discipline.
The casino is not a fair opponent. Counting in your head isn’t illegal, but casinos are private property: they can shuffle early, cut the deck deep, drop your limits, or bar you. The bet spread is exactly the tell they watch for. A counting device or app, though, is a crime in most jurisdictions.
“Easy money” is the tell of a losing gambler. The reality is a grinding, low-margin job under surveillance by a house trying to fire you. Most who try are worse than they think at both the count and the discipline.

The edge is real; collecting it is a job with a hostile employer.

The scoreboard (house edge, typical)

\begin{array}{ll} \text{Blackjack, counted (skilled)} & \approx +0.5\%\text{ to }+1.5\% \;(\textbf{player edge}) \\ \text{Blackjack, basic strategy} & \approx -0.5\% \\ \text{Blackjack, 6:5 table, basic strategy} & \approx -1.5\% \\ \text{Craps, pass line} & \approx -1.41\% \\ \text{American roulette} & \approx -5.26\% \\ \text{Slots} & \approx -3\%\text{ to }-12\% \end{array}

One line is positive. It belongs to a skilled, funded, disciplined player the casino is trying to remove, and only when the count runs high. At a 6:5 table even that hope is gone. That is the whole lesson.

The short version

Basic strategy: ~0.5% house edge, the best price on the floor, still a price. Hi-Lo turns a rich shoe into a player edge of up to ~1.5%. The edge lives entirely in the bet spread, sized by Kelly. The catch: tiny edge, brutal variance, big bankroll, perfect discipline, hostile house.

The same expected-value and Kelly math runs the sports side of the house. Try the free Kelly calculator, read how expected value finds an edge, or open it in the live app.

Watch the edge compound (the idealized case)

Six flawless counters, flat-betting a +1% edge 1,000 hands each. The line climbs. Slowly, and only because nobody here miscounts or gets barred. That’s the fantasy; the catch above is the reality.

Want more math?the Nerd Corner

Nerd Corner

Advanced material. Nothing above depends on it.

Where these numbers come from

Blackjack has a genuine academic paper trail. The originals:

Baldwin, R. R., Cantey, W. E., Maisel, H. & McDermott, J. P. (1956). “The Optimum Strategy in Blackjack.” Journal of the American Statistical Association 51(275), 429–439. The first complete basic strategy, computed at the Army’s Aberdeen Proving Ground.
Thorp, E. O. (1962). Beat the Dealer: A Winning Strategy for the Game of Twenty-One. Random House; rev. ed. 1966. Card counting made public: the Ten-Count in 1962, the Hi-Lo (High-Low) count in the 1966 edition.
Griffin, P. A. (1979). The Theory of Blackjack: The Compleat Card Counter’s Guide to the Casino Game of 21. Huntington Press. The standard mathematical treatment of what a count is actually worth.

Frequently asked questions

What is the best blackjack strategy?

Perfect basic strategy: the correct hit, stand, double, and split for every hand against every dealer upcard. It cuts the house edge to about 0.5% (0.4%–0.6% by rules), the lowest on the floor. Friendliest rules: blackjack pays 3:2, dealer stands on soft 17.

Is card counting illegal?

No. Counting in your head is mental arithmetic, not a crime. But casinos are private property and can shuffle early, cut the deck deep, lower your limits, or bar you. A counting device or app, however, is a crime in most jurisdictions.

How does the Hi-Lo card counting system work?

Add +1 for each 2–6 dealt, 0 for 7–9, and −1 for each 10, face card, or ace. Divide the running count by the decks remaining to get the true count. A high true count means the shoe is rich in tens and aces, which favors the player.

Can you actually win at blackjack by counting cards?

The math allows roughly +0.5% to +1.5% with perfect basic strategy, an accurate count, and a large bet spread. But the edge is tiny, the variance enormous, it demands a big bankroll and flawless discipline, and casinos will limit or eject you. A grind, not easy money.