- This article details the numbers behind blackjack including the probability of events occurring, positive and negative EV, and expected payouts.
LAS VEGAS – Everyone can jump on a blackjack table and begin playing without much knowledge of the game and that is one of the beautiful things about the game. But for those more serious, knowing the mathematics behind blackjack can put bettors well ahead of the game by limiting their risk and remaining vigilant of their bankroll versus expected outcomes.
Probability Of Being Dealt Blackjack
The odds of getting a blackjack depend on the game you are playing, as single deck blackjack holds the advantage over two-deck or multi-deck. While the difference may only be .07%, this creates more of an edge to make up.
What Is The Probability Of The Dealer Busting In Blackjack?
Assuming the dealer hits on a soft 17, their up card is the determining factor for their busting probability. If their up card sits at 4-6, their probability of busting is about 5/12 - the best situation for the player.
| Dealer Up Card | Single Deck | Two Decks | Six Decks |
|---|---|---|---|
| A | 0.114% | 0.118% | 0.122% |
| 2 | 0.357% | 0.367% | 0.380% |
| 3 | 0.378% | 0.396% | 0.415% |
| 4 | 0.411% | 0.429% | 0.448% |
| 5 | 0.425% | 0.448% | 0.466% |
| 6 | 0.426% | 0.446% | 0.464% |
| 7 | 0.288% | 0.297% | 0.305% |
| 8 | 0.253% | 0.259% | 0.265% |
| 9 | 0.159% | 0.165% | 0.169% |
| 10 | 0.307% | 0.317% | 0.326% |
The Math Behind 6:5 vs 3:2 Tables
If you’re unfamiliar, blackjack casinos that offer 6:5 vs 3:2 payouts should you receive blackjack are the tables you want to stay away from. Always make sure you are playing at a 3:2 table and here’s why.
While it doesn’t seem like much of a difference, let’s apply it to the averages over a large number of hands scenario. In most cases, you’ll hit blackjack 4.8% of the time, win in other ways 44.4% of the time, and lose 50.8% of the time.
| Table Type | Blackjack % | Other Win % | Lose % | Expected Value |
|---|---|---|---|---|
| 3:2 | 0.048 x $15 | 0.444 x $10 | 0.508 x -$10 | $0.72 |
| 6:5 | 0.048 x $12 | 0.444 x $10 | 0.508 x -$10 | -$0.24 |
If we take the payouts in these $10 bet situations, you can see how 3:2 offers an EV that is positive compared to the negative 6:5 table. Despite hitting blackjack and winning at the same rate, the $3 difference in payout really means a lot when offsetting losses.
Calculations For Card Counting
There is no true equation for card counting and its edge because of so many factors. But, the main way to follow along with card counting is to know the true count. That is the running count divided by the number of decks remaining. Higher true counts (high cards remaining) open players for more aggressive bets while low true counts incentivize playing by the book.
*For more information on how to count cards, visit our Blackjack Card Counting page
Are Side Bets Worth It?
In order to see if side bets are worth it mathematically in blackjack, it’s important to break it down depending on the side bet. Even in the best case though, you have less than a 1% chance to hit a flush or another side bet in blackjack.
This means that a flush is probable to occur once every roughly 100 hands. Since the payout for blackjack side bets on a flush is often closer to five times your money, the casino has a massive edge here. But, you’re often looking for the jackpot, which means you’re hoping for the 100x payout for hitting a suited three of a kind. Even still, you can expect to hit a suited three of a kind approximately 0.23 times in 100 hands of blackjack, meaning you’d have to play roughly 4350 hands to complete the probability cycle.
Is Blackjack The Best Casino Game By House Edge?
Blackjack is certainly one of the best games to play if you’re looking to beat the house edge. In most cases, the house edge for blackjack falls between 0.5 and 2%. This means over time, you should only lose about 50 cents to $2 for every $100 wagered. Compare that to other casino games and you’ll see why legal blackjack online has tables that are always full.
Blackjack Edge Compared To Casino Games
| Game | Edge |
|---|---|
| Blackjack | 0.43%-2% |
| Baccarat | 1.06%-1.24% |
| Craps | 1.36%-1.41% |
| Pai Gow Poker | 2.84% |
| American Roulette | 5.3% |