- Probability Of Being Dealt A Blackjack Game
- Probability Blackjack Questions
- Probability Of Being Dealt A Blackjack Hand
- Odds Of Being Dealt A Blackjack
Blackjack strategy, applied perfectly, makes blackjack one of the most potentially lucrative games in the casino. If you play blackjack by the numbers, the House only has an edge of half a percent. That means if you spend $100 at a blackjack table in an hour, and you play using perfect basic strategy, you only stand to lose about 50 cents. The low house edge makes blackjack a truly cheap form of entertainment.
Blackjack rules give the game a certain purity of probability, a statistical beauty that statisticians and math nerds have exploited over the years to come up with blackjack strategy. Odds and probabilities are a huge part of winning at blackjack, so if you want to win big money at the casino, you have to understand the game’s odds and probabilities.
Probability Of Being Dealt A Blackjack Game
Aug 28, 2008 The probability of being dealt a full house in poker is 3744/2,598,960 or 1 in 694. The probability of moving up from a full house in poker is 4/47. In the game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. A winning 'blackjack' hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. The two cards can be in any order. Find the probability of being dealt a.
Blackjack Math
Blackjack strategy cards are sold at every casino gift shop in Vegas. These cards range from simple “if ___ happens, do ___” suggestions all the way up to cards with multiple rule change options on strategy. Casinos sell these cards because most people are more interested in playing a game and making big gambles than methodically picking apart the House using blackjack math and a little plastic card.
Blackjack math gives players an informed opinion about what move to make next. Rather than taking a random gamble, blackjack strategy uses odds and probabilities to tell you the move most likely to end in you beating the House. Blackjack strategy tips are more than educated guesses, they have hard math to back them up.
Here are some blackjack math basics: any deck of 52 cards contains a certain number of cards worth 10 points and a certain number of cards worth their face value. The odds of pulling a single face value card, like a 7 or a 9, is 4 out of 52. or 7.69%.
There are 16 cards in a standard deck with a value of 10 points: four 10s, four Jacks, four Queens, and four Kings. That means the odds of drawing a 10-point card are 16 out of 52, or 30.8%.
Players are four times more likely to draw a card worth ten than any other card value. 10 point cards outnumber all others, so most blackjack strategy is built around figuring out the probability of the player or the dealer drawing those high point value cards.
Using Blackjack Odds & Probabilities
The math behind the game of blackjack has a direct effect on proper blackjack strategy. We just saw how much more likely a blackjack player is to draw a 10 point card than any other card, but how does that effect blackjack strategy? At the most basic level, knowing that you’re more likely to draw a card worth ten points makes a point total of 12 or more an anxious game decision.
Another example of how blackjack odds play a big part in player strategy is what blackjack experts call bust probability. Bust probability is a number that indicates how often a certain point total will lead to a bust. Since the blackjack dealer doesn’t have free will, and must stand at 17 in most casinos, his bust likelihood is higher when his point total is 16, because dealers have to hit at 16. This rule also affects early dealer point totals—imagine a dealer with an upcard of 6. He has to hit, and we already know how much more likely you are to draw a ten point card than any other, putting him in great danger of drawing a 16 and being forced to hit into a bust.
Other Blackjack Odds & Probabilities
Blackjack math is straightforward, since each card in the deck has its own consistent point value and there’s a clear line drawn between winner and loser. Applying a little bit of math, blackjack experts have figured out the odds of being dealt different types of blackjack hands. Your chance of drawing a natural 21, and winning instantly, is 4.8%. Play 100 hands of blackjack and you’re likely to only be dealt a natural blackjack 5 times.
That makes blackjack sound like a hard game to beat, but the truth couldn’t be more different. Those same odds show that the most common hand dealt in blackjack is the decision hand, any point total between 1 and 16. These hands are dealt 38.7% of the time, meaning that out of every 100 hands you play, you’ll have to make a decision only about 40 times. In the other 60 hands, the decision will be made for you.
If you play with basic strategy, and make the right play according to that strategy for each of those decision hands, you can minimize the house edge.
A final trick to using blackjack odds to beat the House is considering two crucial statistics at once. We’ve already talked about dealer bust probability and player edge against the House. Just combine the two statistics for an idea of when you have the best chance to beat the blackjack dealer.
For each dealer upcard, mathematicians have figured out their likelihood of drawing to a bust. For example, if a dealer’s upcard is a 2, his bust probability is 38%. Factor in the player’s advantage gained by using basic strategy against each upcard, and you get a good look at when you have your best shot at beating the House.
The House is in the most danger of busting or losing to basic strategy when the dealer’s upcard is a 5 or 6. When the dealer shows a 5 upcard, his bust probability is 42.89%. Since players have a 23.2% advantage against that upcard if they play with perfect strategy, it’s clear that when a dealer shows a 5, players are more likely to beat the dealer.
Using blackjack math and odds to your advantage against the casino is called basic blackjack strategy. Make sure and pick up a blackjack strategy chart next time you hit the casino, and work on memorizing the proper play for different game situations. Following the lead of smarter blackjack players who have gone before you is important if you like making money on the gambling floor.
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Probability Blackjack Questions
Odds are everywhere you look. Seriously. Odds are in a casino, your workplace, your day-to-day live and habits, your marriage and where in the world you live.
Don’t believe me? Take a look for yourself:
- Odds of having twins (21st century) – 3 in 100 or 3%
- Odds of getting a divorce – 40 to 50%
- Odds of being stuck by lightning – 1 in 5,000 or 1 in 700,000 in any given year
- Odds of being audited by the IRS – .4% if you make less than $200,000 / year
- Odds of being dealt a blackjack – About 4.83%
Odds are just the likelihood that something will happen. As a blackjack player you deal with this all the time.
Lets look at a couple real examples to show you what I mean.
Here are the odds of you busting your hand, depending on what you were dealt:
- 21 – 100%
- 20 – 92%
- 19 – 85%
- 18 – 77%
- 17 – 69%
- 16 – 62%
- 15 – 58%
- 14 – 56%
- 13 – 39%
- 12 – 31%
- <11 – 0%
Probability Of Being Dealt A Blackjack Hand
Odds of Being Dealt Specific Hands
Here are the probabilities for being dealt a specific hand:
- Blackjack – 4.8%
- Standing Hand (17-20) – 30%
- Decision Hand – (1-16) – 38.7%
- No Bust – 26.5%
Here are the odds for the final hands that the dealer will make:
- Natural 21 – 4.82%
- 21 (3+ cards) – 7.36%
- 20 – 17.58%
- 19 – 13.48%
- 18 – 13.81%
- 17 – 14.58%
- 16 – 28.36%
Dealer vs. Player Odds
Finally, here are the odds of the dealer busting based on their up card:
- 2 – 35.30%
- 3 – 37.56%
- 4 – 40.28%
- 5 – 42.89%
- 6 – 42.08%
- 7 – 25.99%
- 8 – 23.86%
- 9 – 23.34%
- J,Q,K – 21.43%
- A – 11.65%
Of these examples, this is the most useful. Notice what hands the dealer is most likely to bust with. The dealer will most often bust with 4, 5 or 6, followed by 2 and 3.
The odds above are static. There’s nothing you can do to change them. However, you can find ways to improve your odds so that you lose fewer hands and less money. And the less money you lose, the more you can keep to play more blackjack.
Here’s what you can do to improve your odds in blackjack:
- Use basic blackjack strategy. Without basic strategy you’re playing at an 8% disadvantage. With strategy, however, the odds increase significantly. You’ll be playing at only .5 to 1.5% disadvantage.
- Find the best games. The rules make all the difference. For example, if you play a 6:5 blackjack game you’re adding a 1.39% disadvantage. If the dealer hits soft 17 that’s another .18%. However, it’s possible to find games where the player is paid 3:2 for blackjacks and the dealer stands on soft 17. So find those games. Also be careful about which blackjack variation you play. The best games to play are blackjack, Spanish 21, Vegas Strip BJ and Blackjack Switch.
- Avoid side bets. Side bets look exciting, because for a nominal amount you could possibly win a huge jackpot — worth hundreds or even thousands of dollars. The problem is that the odds against winning can be anywhere from 2-40%.
- Avoid wives tales. There are a lot of bad strategies like never busting (never hit a 12+), mimicking the dealer and assume that the dealer has a 10 in the whole (with ace up). The problem with using any of these strategies is that they increase the house edge from 3 to 10 percent.
Odds Of Being Dealt A Blackjack
You can do other things, too, like count cards or read books (usually a mix of basic strategy, card counting and general how-to’s for casino blackjack). However, you’ll improve your odds at winning at blackjack just by following my suggestions above.
Understanding the Long Run – Sample Size and Variance
I wanted to finish up this article with a brief explanation of odds, and how they work over the long run. You see, I think a lot of people will see the numbers above and get confused when they don’t match their own stats. In other words, someone might go to the casino play 500 hands of blackjack, and wonder why they didn’t get 24 natural blackjacks, or the other way around, why they got 42.
The thing is, odds and statistics are all about the long run. Long run usually meaning sample size, or the total number of hands (or games) played.
What that means is that over a significant sample size, hundreds of thousands or even millions of hands, the number of times you’ll receive a blackjack is about 4.82%. The more hands you play the truer this will become.
The reason why odds don’t match up in smaller sessions, say over 500 hands, is because of variance. There’s a technical term and definition for variance, but I’ll just give you my version; variance is the ups and downs you experience on your way to the long term (expected) results.
Mike Caro, a poker player and author, puts it this way:
A measure of the spread of statistical distribution about its mean or centre.
That means in a short time frame, it’s possible to experience more drastic odds. You might win or lose more than you’re supposed to. It also explains why people can go into a casino, not use basic strategy and win 3x as much as what they walked in with. The cards ran in their favor — they experienced a positive streak of variance.
So that’s the gist of it. So the next time you walk into the casino and have a wild swing one way or another, you know that that’s not normal, and that in the long run you’ll be closer to break-even so long as you stick to basic strategy — the plan with the best odds.