Blackjack Odds & Probability — House Edge Calculator
Blackjack is a math game disguised as a card game. Every decision — hit, stand, double, split — has a calculable expected value. Understanding the probabilities behind each scenario transforms you from a gut-feel player into someone who knows exactly what they are giving up (or gaining) with every action.
Baseline House Edge: Where It Comes From
The house edge in blackjack exists for one fundamental reason: the player acts first. If both you and the dealer bust on the same hand, you still lose — your money was already collected when you busted. This “double bust” scenario is the entire foundation of the casino's advantage.
In a hypothetical game where you mirror the dealer's strategy (hit to 17, stand on 17+), the house edge would be approximately 8% because both sides bust about 28% of the time, and those simultaneous busts all go to the house. Basic strategy recovers most of this by making mathematically optimal decisions — doubling when you have the edge, splitting to exploit weak dealer upcards, and surrendering when the math says to cut your losses.
With perfect basic strategy, you claw back roughly 7.5% of that 8% disadvantage, leaving the house with only 0.4-0.6% depending on the specific rules.
House Edge by Rule Variation
Not all blackjack games are created equal. Each rule change shifts the house edge by a specific, measurable amount. Here is the complete breakdown for the most common rule variations you will encounter online.
| Rule | Player-Favorable | House-Favorable | Edge Difference |
|---|---|---|---|
| Natural payout | 3:2 | 6:5 | 1.39% |
| Dealer soft 17 | Stands (S17) | Hits (H17) | 0.22% |
| Double after split | Allowed (DAS) | Not allowed | 0.14% |
| Late surrender | Allowed | Not allowed | 0.08% |
| Re-split aces | Allowed | Not allowed | 0.08% |
| Number of decks | 1 deck | 8 decks | 0.59% |
| Doubling restriction | Any two cards | 9-11 only | 0.09% |
When evaluating an online blackjack game, stack these rule effects. A 6-deck, S17, DAS, 3:2 game with late surrender has roughly a 0.40% house edge. Change that to 8-deck, H17, no DAS, 6:5 with no surrender and you are looking at 2.0%+ — five times worse. The game name might be identical; the math is radically different.
Bust Probabilities by Hand Total
The probability of busting on the next card is the single most important factor in hit/stand decisions. These numbers assume a fresh 6-deck shoe and represent the chance of exceeding 21 if you take exactly one more card.
| Hand Total | Bust Probability | Basic Strategy Implication |
|---|---|---|
| 11 or less | 0% | Always hit or double — no risk of busting |
| 12 | 31% | Hit vs dealer 2-3, stand vs 4-6, hit vs 7+ |
| 13 | 39% | Stand vs dealer 2-6, hit vs 7+ |
| 14 | 56% | Stand vs dealer 2-6, hit vs 7+ |
| 15 | 58% | Stand vs 2-6, surrender vs 10/A, else hit |
| 16 | 62% | Stand vs 2-6, surrender vs 9/10/A, else hit |
| 17 | 69% | Always stand on hard 17 |
| 18 | 77% | Always stand |
| 19–20 | 85–92% | Always stand |
Notice the critical zone: hands of 12-16 are where every important decision happens. Below 12 you always take a card. Above 16 you always stand. The strategic complexity of blackjack lives entirely in the 12-16 range, where bust risk must be weighed against the probability of the dealer making a strong hand.
Dealer Outcome Probabilities
Understanding what the dealer is likely to end up with — based solely on their upcard — is essential for making correct basic strategy decisions. Here are the dealer final outcome probabilities for a 6-deck, S17 game.
| Upcard | Bust % | 17 | 18 | 19 | 20 | 21 |
|---|---|---|---|---|---|---|
| 2 | 35.3% | 14.0% | 13.4% | 13.0% | 12.4% | 11.9% |
| 3 | 37.6% | 13.5% | 13.1% | 12.5% | 12.0% | 11.3% |
| 4 | 40.3% | 13.1% | 12.6% | 12.0% | 11.4% | 10.6% |
| 5 | 42.9% | 12.2% | 12.0% | 11.7% | 10.9% | 10.3% |
| 6 | 42.1% | 16.6% | 10.6% | 10.7% | 10.1% | 9.9% |
| 7 | 26.2% | 36.9% | 13.8% | 7.9% | 7.9% | 7.3% |
| 8 | 24.4% | 12.9% | 36.0% | 12.9% | 6.9% | 6.9% |
| 9 | 23.3% | 12.0% | 12.0% | 35.1% | 12.0% | 5.6% |
| 10 | 21.4% | 11.2% | 11.2% | 11.2% | 34.0% | 11.0% |
| A | 11.7% | 13.1% | 13.1% | 13.1% | 13.0% | 36.0% |
The key insight from this table: dealer upcards of 2-6 are “stiff” cards with bust rates of 35-43%. This is why basic strategy tells you to stand on lower totals against these cards — let the dealer take the bust risk. Dealer upcards of 7-A are strong cards with bust rates below 27%, which is why you need to be more aggressive and try to improve your hand against them.
The dealer's 6 upcard deserves special attention: it has a 42.1% bust rate, the second highest. Combined with a forced stand on 17 (S17 rules), the 6 is the weakest dealer upcard overall. When the dealer shows a 6, you double more hands and split more aggressively than against any other card.
Expected Value of Key Decisions
Every basic strategy decision is based on expected value (EV) — the average amount you win or lose per dollar wagered on that specific play. Understanding the EV behind the most commonly misplayed hands helps you trust the math when your gut says otherwise.
Hard 16 vs. Dealer 10
Stand EV: -0.540 | Hit EV: -0.507 | Surrender EV: -0.500
Surrender is the best play, saving 4 cents per dollar compared to hitting and 4 more vs. standing. If surrender is unavailable, hit — you lose less despite the 62% bust risk because standing against a 10 is even worse.
11 vs. Dealer 6
Hit EV: +0.235 | Double EV: +0.397
Doubling here is one of the most profitable plays in blackjack. You expect to win 39.7 cents per dollar doubled. This is one of the rare situations where you are a mathematical favorite — make sure you double every time.
8,8 vs. Dealer 10
Stand EV: -0.540 | Hit EV: -0.507 | Split EV: -0.476
Splitting eights against a 10 is one of the most counterintuitive plays. You are turning one bad hand into two hands that are still underdogs. But the math is clear: splitting loses 47.6 cents per dollar vs. 50.7 for hitting or 54.0 for standing.
12 vs. Dealer 3
Stand EV: -0.232 | Hit EV: -0.233
This is the closest decision in blackjack — a virtual coin flip. Basic strategy says hit because the EV is microscopically better (-0.233 vs. -0.232, with rounding making them appear equal). In practice, the difference is so small that either play is defensible.
For every hand combination and the complete decision matrix, see our blackjack basic strategy guide.
The Real Cost of Playing Blackjack Online
Knowing the house edge lets you calculate exactly what blackjack costs you per hour. The formula is simple: House Edge x Average Bet x Hands Per Hour = Expected Hourly Loss.
| Scenario | Bet Size | Hands/Hr | House Edge | Hourly Cost |
|---|---|---|---|---|
| RNG, basic strategy | $1 | 200 | 0.46% | $0.92 |
| RNG, no strategy | $1 | 200 | 3.0% | $6.00 |
| Live dealer, basic strategy | $5 | 55 | 0.50% | $1.38 |
| RNG 6:5, basic strategy | $5 | 200 | 1.85% | $18.50 |
| RNG 3:2, basic strategy | $10 | 200 | 0.46% | $9.20 |
Context matters: a $0.92/hour entertainment cost is less than virtually any other paid activity. Even at $10 per hand with basic strategy, your expected hourly cost of $9.20 is less than a movie ticket. The players who get into trouble are those playing without strategy at higher stakes on 6:5 games — their hourly cost can exceed $50 without them realizing it.
Frequently Asked Questions
What are the odds of getting a natural blackjack?+
In a standard 6-deck shoe, the probability of being dealt a natural blackjack (ace + 10-value card) is approximately 4.75%, or about 1 in every 21 hands. This holds for both the player and the dealer. The probability decreases marginally with more decks (4.77% single-deck, 4.75% six-deck).
What is the house edge in blackjack?+
The house edge ranges from about 0.28% (single-deck, best rules) to over 2% (8-deck, 6:5 payout, H17). A typical 6-deck game with 3:2 naturals, S17, DAS, and late surrender has roughly a 0.40% house edge with perfect basic strategy. Without basic strategy, the effective edge jumps to 2-4%.
What is the probability of busting on a hit?+
It depends entirely on your hand total. At 11 or below: 0% bust chance. At 12: 31%. At 13: 39%. At 14: 56%. At 15: 58%. At 16: 62%. At 17-20: 69-92%. These probabilities drive basic strategy decisions — you never hit hard 17+ because the bust risk exceeds the potential gain.
Does the number of decks affect blackjack odds?+
Yes, but less than most players think. Going from 1 deck to 6 decks increases the house edge by about 0.48%, assuming all other rules are identical. However, single-deck games almost always compensate with worse rules (6:5 payouts), which more than offsets the deck advantage.
Is blackjack beatable in the long run?+
For the vast majority of players, no. Basic strategy minimizes the house edge but does not eliminate it. Card counting can create a theoretical edge of 0.5-1.5% in physical casinos with favorable conditions, but online RNG blackjack is mathematically unbeatable. Live dealer online games have conditions too unfavorable for practical counting.
How much does 6:5 vs 3:2 really matter?+
It is the single biggest rule difference in blackjack. A 6:5 payout on naturals increases the house edge by 1.39% compared to 3:2. On a $10 game over 200 hands, that costs you an extra $27.80 in expected value. Always check the payout table before playing — 6:5 games should be avoided.