Blackjack Calculator

How the Blackjack Calculator Works

The blackjack calculator determines the mathematically optimal play for any hand combination using basic strategy — the complete set of rules derived by analyzing all possible outcomes for each hand against each dealer upcard. Basic strategy is computed by exhaustively simulating every possible hand sequence, determining which action (hit, stand, double down, split, or surrender) produces the highest expected value.

The goal of blackjack is to beat the dealer by getting closer to 21 without going over. Your hand value: number cards = face value; face cards (J, Q, K) = 10; Ace = 1 or 11 (whichever is more favorable). A "blackjack" (natural) = an ace plus a 10-value card on the first two cards — pays 3:2 (or 6:5 at worse tables).

Blackjack Basic Strategy — Key Rules

Basic strategy reduces the house edge to approximately 0.5% in a standard 6-deck game — the lowest of any casino table game. Core decision rules:

• Always stand on hard 17+: Never hit when you have 17 or higher in a hard hand.
• Always hit on hard 8 or less: No bust risk; always take another card.
• Hard 9: Double down vs. dealer 3–6 (dealer "bust cards"); otherwise hit.
• Hard 10 or 11: Double down if your total exceeds the dealer's upcard; hit otherwise.
• Hard 12: Stand vs. dealer 4–6; hit vs. 2, 3, or 7+.
• Hard 13–16: Stand vs. dealer 2–6; hit vs. 7–Ace.
• Soft 17 (Ace + 6): Always hit or double; never stand. (Even though "17" sounds good, the Ace means no bust risk.)
• Soft 18 (Ace + 7): Double vs. dealer 3–6; stand vs. 2, 7, or 8; hit vs. 9–Ace.
• Soft 19+: Always stand.

Blackjack Odds — Probability of Winning Each Hand

With perfect basic strategy in a standard 6-deck game (dealer stands soft 17):

• Player win probability: ~42.2%
• Dealer win probability: ~49.1%
• Push (tie) probability: ~8.5%
• House edge: Approximately 0.46–0.65% (varies by specific rules)
• Blackjack probability (first two cards): 4.75% (roughly 1 in 21 hands)
• Dealer bust probability: 28.4% overall; varies dramatically by upcard

Dealer bust probability by upcard: 2 → 35.3%; 3 → 37.6%; 4 → 40.3%; 5 → 42.9%; 6 → 42.1%; 7 → 26.2%; 8 → 23.9%; 9 → 23.3%; 10/Face → 21.4%; Ace → 11.7%. This is why basic strategy stands against dealer bust cards (2–6) and hits aggressively against dealer strong cards (7–Ace).

When to Split Pairs

Pair splitting rules under standard basic strategy:

• Always split Aces: Two separate chances to hit 21
• Always split 8s: Hard 16 is the worst hand; splitting gives two chances to improve
• Never split 10s or face cards: 20 is an excellent hand; splitting is always negative expected value
• Never split 5s: Two 5s = 10, which is excellent for doubling; splitting loses this advantage
• Split 9s vs. dealer 2–6, 8–9; stand vs. 7 (your 18 beats dealer 7), stand vs. 10/Ace
• Split 7s vs. dealer 2–7; hit vs. 8–Ace
• Split 6s vs. dealer 2–6; hit vs. 7–Ace
• Split 4s vs. dealer 5–6 (when doubling after split is allowed); otherwise hit
• Split 2s or 3s vs. dealer 2–7; hit vs. 8–Ace

House Edge by Rule Variation

Blackjack rules vary by casino and table. These rule variations affect house edge:

• Blackjack pays 3:2 (standard): baseline 0.5% house edge
• Blackjack pays 6:5 (common at single-deck tables): adds +1.4% to house edge — major player disadvantage
• Dealer hits soft 17 (H17): adds +0.22% house edge vs. dealer stands soft 17 (S17)
• Double down allowed on any two cards: reduces house edge ~0.25%
• Double after split (DAS) allowed: reduces house edge ~0.14%
• Late surrender option: reduces house edge ~0.08%
• More decks used: adds house edge (single deck ~0.17% lower than 6-deck game)

Frequently Asked Questions

What is blackjack basic strategy?

Basic strategy is the complete set of mathematically optimal decisions for every possible player hand and dealer upcard combination, computed by analyzing millions of simulated hands. Following basic strategy reduces the house edge to its minimum possible value (~0.5% in standard rules). It does not guarantee winning individual sessions but maximizes your statistical chances over time. Basic strategy charts are freely available and can be consulted at most live casino tables.

When should you double down in blackjack?

Double down by placing an additional bet equal to your initial bet and receiving exactly one more card. Optimal doubling situations: always double hard 11 vs. dealer 2–10; double hard 10 vs. dealer 2–9; double hard 9 vs. dealer 3–6; double soft 13–18 in specific situations vs. dealer 4–6. The key principle: double when you have a strong position and the dealer shows a bust card (2–6), maximizing expected value when conditions favor the player.

Does card counting work in blackjack?

Yes — card counting is a legitimate strategy that shifts the mathematical edge to the player by tracking the ratio of high to low cards remaining in the shoe. When many high cards (10s, aces) remain, players bet more; when low cards remain, they bet less. The most common system (Hi-Lo) assigns values: 2–6 = +1; 7–9 = 0; 10–Ace = -1. A skilled card counter can gain an edge of 0.5–1.5% over the casino. However, casinos actively counter card counting through reshuffling, multiple decks, and banning suspected counters. Card counting is legal but results in exclusion from casinos if detected.

What is the best blackjack bet for beginners?

Start at a $10 minimum table that pays 3:2 for blackjack (avoid 6:5 tables). Use basic strategy consistently — print or memorize the chart. Bet the table minimum while learning. Avoid side bets (Perfect Pairs, Lucky Ladies, insurance) — all carry house edges of 4–25%, far worse than the main game. Once comfortable with basic strategy, bankroll management (never betting more than 2–5% of your session bankroll on a single hand) is the most important skill to develop.