Blackjack occupies an unusual position among casino games: for every combination of a player’s hand and a dealer’s upcard, there is one mathematically correct decision, and it has been known for the better part of seventy years. The chart that encodes those decisions, sold in casino gift shops and tolerated at the tables, is not folklore. It is the published solution to a solved problem.
Four soldiers and a desk calculator
The solution arrived from an unlikely quarter. In the mid-1950s four US Army mathematicians stationed at the Aberdeen Proving Ground in Maryland, Roger Baldwin, Wilbert Cantey, Herbert Maisel and James McDermott, spent their off-duty hours grinding through blackjack’s combinatorics on desk calculators. Their paper, The Optimum Strategy in Blackjack, appeared in the Journal of the American Statistical Association in September 1956. It was the first rigorous demonstration that the game’s house edge, then casually assumed to be several per cent, could be cut to a fraction of one per cent by pure decision-making, with no memory of previous cards required.
The work reached a young MIT mathematician named Edward Thorp, who refined the calculations on an IBM 704 mainframe and went further, showing that the composition of the remaining deck shifts the odds enough to be exploited by counting cards. His 1962 book Beat the Dealer became a bestseller, forced casinos to change their rules and shuffling procedures, and incidentally spread basic strategy to a mass audience. Later refinements by computer analysts, most notably IBM’s Julian Braun, polished the numbers to their modern precision.
What the strategy actually says
Basic strategy is simply the answer, for each situation, to one question: which available action loses the least, or wins the most, on average? Some answers match intuition, such as standing on 20. Others feel wrong and are still correct. Hitting 16 against a dealer’s 10 loses money on average, but standing loses slightly more, so hitting is right. Doubling down on 11, splitting eights, and never taking insurance all fall out of the same expected-value arithmetic. The strategy varies at the margins with the rules in play, chiefly the number of decks, whether the dealer hits or stands on soft 17, and when doubling is permitted, which is why printed charts specify the rule set they were computed for.
What it does and does not achieve
Played perfectly under favourable rules, basic strategy reduces the house edge to roughly 0.5 per cent, among the lowest figures on any casino floor, and lower still under liberal rule sets. It does not make blackjack beatable. The remaining half a per cent belongs to the house because the player must act first and loses immediately on busting, even if the dealer later busts too. Rule changes can move the number sharply in the other direction: paying blackjacks at 6:5 instead of the traditional 3:2, now widespread on the Las Vegas Strip, adds about 1.4 percentage points to the edge and swamps everything a strategy chart saves. Only card counting, a legal but unwelcome extension of Thorp’s work, historically pushed expectation past zero, and modern countermeasures such as continuous shuffling machines have largely closed that door.
Casual players give back far more than the theoretical minimum. Industry analyses consistently find that average blackjack tables hold around 1.5 to 2 per cent or more, the gap between solved mathematics and human play. Online blackjack enforces the same underlying probabilities through certified random number generators, as outlined in this magazine’s explainer on how online casinos work, and the broader family of table games is surveyed on the main casino section.
Frequently Asked Questions
Does basic strategy guarantee winning at blackjack?
No. It minimises the house edge to roughly half a per cent under good rules, which means the casino still holds a small long-term advantage over every basic-strategy player.
Is using a basic strategy chart allowed in casinos?
Generally yes. Most casinos permit players to consult a strategy card at the table, because the game remains profitable for the house even against perfect basic strategy.