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Game math·beginner

Blackjack

A casino card game in which you try to build a hand that totals as close to 21 as possible, without going over, and that beats the dealer's hand.

Definition

In blackjack, number cards count at face value, face cards (jack, queen, king) count as 10, and an ace counts as either 1 or 11. Exceeding 21 is a "bust" and loses immediately, while a total of 21 on the first two cards is a "natural" or blackjack. The player acts first — choosing to hit (take a card), stand, double, or split — before the dealer plays to fixed house rules. Because these decisions influence the result, blackjack has one of the lowest house edges of any casino game when played with correct basic strategy, though the exact edge depends heavily on the specific rules in force.

Worked example

A player bets £10 and is dealt 10♥ + A♣ — a natural blackjack. Under common rules where blackjack pays 3:2, this returns £15 profit. Across a full session with liberal rules (dealer stands on soft 17, doubling and splitting allowed) and correct basic strategy, the house edge is roughly 0.5%, i.e. an expected loss of about £0.50 per £100 wagered over the long run. If the same table instead paid only 6:5 on blackjack, the house edge would rise to roughly 2% — the identical game, made about four times more expensive for the player by a single rule change.

Why it matters

Blackjack is the standard reference point for a low-house-edge game, so it is a clear teaching case for how player decisions and small rule variations — payout ratio (3:2 vs 6:5), the number of decks, whether the dealer hits or stands on soft 17, and which doubles, splits or surrenders are allowed — shift the mathematical edge. For product, game-math and compliance professionals, understanding that edge is essential for pricing tables, comparing RTP across games, and framing the game honestly as entertainment rather than a source of income.

Related

House edgeReturn to Player (RTP)Basic strategyCard countingTable gameSide bet

Note: Core rules of play are stable, but the numbers vary by operator and jurisdiction: the ~0.5% house edge assumes liberal rules plus correct basic strategy, and worsens with 6:5 payouts, more decks, dealer-hits-soft-17, or restricted doubling/splitting. Card counting is not illegal but operators may refuse or restrict play, and many online/live tables use continuous shuffling that defeats it; verify the exact paytable and rules for any specific game before quoting an edge.