Where Basic Strategy Came From, and What 6:5 Costs You

Four US Army mathematicians with desk calculators solved optimal blackjack strategy in 1956, proving that a 3-to-2 payout on natural blackjacks lets a disciplined player hold the house edge under 0.5%. When a modern casino changes that payout stamp to 6 to 5, it adds 1.36 percentage points to the house edge and more than triples the cost of playing the exact same strategy.

Before the 1950s, casino twenty-one was played by hunches and folklore. Card-room guides told players to stand on 15 or 16 no matter what card the dealer showed, never split pairs of 8s, and treat the dealer’s fixed rule—hit 16 or less, stand on 17 through 21—as if both sides had the same options.

1. Desk calculators at Aberdeen Proving Ground (Baldwin et al., 1956)

In September 1956, four young Army mathematicians stationed at Aberdeen Proving Ground in Maryland—Roger R. Baldwin, Wilbert E. Cantey, Herbert Maisel, and James P. McDermott—published a ten-page paper in the Journal of the American Statistical Association titled “The Optimum Strategy in Blackjack.”

Working on mechanical desk calculators during off-duty hours, the “Four Horsemen of Aberdeen” realized that because the dealer has no choices, you can calculate the exact chance that each dealer upcard (2 through Ace) finishes at 17, 18, 19, 20, 21, or busts. Once you know the dealer’s odds, every player decision has a single right answer:

• Stand or Hit: Hit hard 12 through 16 when the dealer shows 7 through Ace, but stand on hard 12 through 16 when the dealer shows a bust card (4, 5, or 6).
• Double Down: Double your bet when one extra card leaves you favored—such as hard 11 against a dealer 2 through 10, or hard 10 against 2 through 9.
• Split Pairs: Always split Aces and 8s; never split 10s or 5s.

Their calculations showed that playing every hand by the numbers cut the casino’s advantage to 0.62%, making blackjack the closest game in the pit to a fair coin toss.

2. IBM mainframes and finite-deck math (Thorp, 1962; Griffin, 1999)

After reading the 1956 paper, mathematician Edward O. Thorp programmed an IBM 704 mainframe at MIT to calculate exact finite-deck probabilities. In Beat the Dealer (1962), Thorp refined basic strategy for single- and multi-deck games and proved that because cards are dealt without replacement between shuffles, dealing out small cards (2 through 6) tilts the remaining pack toward the player while dealing out tens and Aces tilts it toward the house.

Mathematician Peter A. Griffin later expanded the exact combinatorics in The Theory of Blackjack (1979; 6th ed. 1999), measuring the effect of removing each rank and establishing the per-hand standard deviation of basic strategy at roughly 1.15 units per wager.

3. Why the 3:2 natural bonus holds basic strategy together

Why does a basic-strategy player lose less than half a percent when the player wins only about 42.5% of hands, pushes 8.5%, and loses 49.0%?

Because the player acts first. When both you and the dealer bust on the same round, you lose your bet immediately before the dealer turns over the hole card. That double-bust rule gives the casino a huge head start of nearly 8%. Basic strategy wins almost all of that ground back in two ways: doubling and splitting when the dealer is weak, and collecting a 3-to-2 (+1.5×) bonus on every natural two-card 21 while a dealer natural wins only 1 to 1.

4. What 6:5 does to your hourly cost

On a standard 6-deck shoe where the dealer hits soft 17 and double after split is allowed, a 3:2 table has a basic-strategy house edge of 0.62% (or 0.40% when the dealer stands on soft 17; Shackleford, Wizard of Odds).

Change the felt stamp to Blackjack pays 6 to 5 and the house edge on that same shoe jumps from 0.62% to 1.98%. At $25 a hand and 70 hands an hour, your expected cost rises from $10.85 an hour at a 3:2 table to $34.65 an hour at a 6:5 table right beside it. Practice every decision in our Free Blackjack Game & Strategy Trainer and compare rule combinations in the Blackjack House Edge Calculator.

Sources

• 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. https://doi.org/10.1080/01621459.1956.10501334
• Thorp, E. O. (1962; 2nd ed. 1966). Beat the Dealer: A Winning Strategy for the Game of Twenty-One. Random House / Vintage Books. ISBN 978-0-394-70310-7.
• Griffin, P. A. (1979; 6th ed. 1999). The Theory of Blackjack: The Compleat Card Counter’s Guide to the Casino Game of 21. Huntington Press. ISBN 978-0-929712-13-0.
• Shackleford, M. Blackjack house edge calculator and rule variations. Wizard of Odds. https://wizardofodds.com/games/blackjack/rule-variations/