Nov 01, 2010 But of course, each hand at blackjack is not independent, particularly when counting cards. Playing more than one hand seems to better help exploit a card counting strategy, no? I'm not a counter but from what I've read two hands in blackjack have are slightly correlated for winning and losing. Over every six trials, the probability is that you’ll win five bets and lose one bet. You win $5 and lose $4 for a net win of $1 for every 6 bets. A good example of this practice is roulette, in which a wager on a single number pays 35 to 1 even though the odds of winning are 1 in 37. What are the odds of winning blackjack. Blackjack, however, foils the computation of odds based on random events because there are a number of influences that prevent it from being completely random—most significantly the player’s choices during the course of the game. In such cases, the odds are set to turn a reasonable profit from the average player.
Blackjack offers some of the best odds in the casino. Everyone knows that already. But what does it mean to say that one casino games offers better odds than another casino game? This page goes into some detail about how to measure the odds of a casino game. Then it continues with an examination of the specifics related to the game of blackjack.
Odds and Probability Explained
Probability is the branch of math that covers how likely it is to achieve a certain result. Any possible result can be measured as a number between 0 and 1, with a 0 meaning that it will never happen and a 1 meaning that it will always happen. It’s probably easier to think of this number as a percentage, so something with a 0% chance of happening will never happen, while something that will always happen has a probability of 100%.
If you add the probability of something happening with the probability of something not happening, you will always get a total of 100%. So it’s always possible to calculate that number backwards. For example, if you know that there is an 80% chance of something not happening, you also know that there is a 20% chance of it happening, and vice versa.
Probabilities are sometimes explained as odds. This is just a way of expressing a probability as the number of possibilities of it failing versus the number of possibilities of it succeeding. For example, if you want to express the odds of getting an ace with the next card you draw out of a fresh deck of playing cards, then you know that the odds are 12 to 1. (For every ace in the deck, there are 12 cards that are NOT aces.) How much money needed to play poker casino.
Casinos make their money by paying out wagers at odds that are less than their odds of happening. For example, on a single number bet in roulette, the odds of winning are 37 to 1. (There are 38 different numbers, and you only bet on 1 of them in this example.) But that bet only pays out at 35 to 1.
In a mathematically perfect set of spins, you’d win once and lose 37 times. If you’re betting $1 per spin, then you’ve lost $37, but you’ve won $35 the one time you got a winning spin. The casino gets the other $2, and that’s how they stay in business.
All casino games, including blackjack, work on this seemingly-simple principle. In fact, it’s relatively easy to determine a percentage of each bet that you make that the casino can expect to receive over time. This percentage is called the house edge.
In the roulette example above, the house edge is 5.26%. That’s the amount of each bet that will be lost over an infinite number of trials. Of course, in the short term, anything can (and often will) happen, but as you get closer to an infinite number of trials, the closer the results become to the mathematical expectation.
The house edge can be as high as 25% on slot machines in Nevada, or as low as 0.5% on blackjack in the same state. But achieving that 0.5% number requires a certain amount of skill and strategy. Players who just use “common sense” or who “play their hunches” face a house edge of closer to 2-4%.
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Basic Strategy Is the Key to the Best Blackjack Odds
The key to maintaining the lowest possible house edge on blackjack is to use basic strategy every time you play. By doing so, you maximize your expectation and minimize the casino’s expectation. Basic strategy is the mathematically perfect play in every possible blackjack situation.
This might seem like an unearthly number of scenarios to memorize, but it’s actually easier than you think. The dealer’s upcard is limited to 10 possibilities. Your hand is limited to 20 different totals. Since many hands will be played with the same strategy as many others, memorizing basic strategy is far easier than you’d think.
Many websites and almost all blackjack books offer basic strategy charts which can help visual learners memorize the correct strategy. The conditions and house rules can affect a handful of strategy decisions, but even then, it’s a tiny percentage of the potential situations you might face. Learning one basic strategy is better than learning no basic strategy at all. In other words, don’t get hung up on making the occasional error because of local playing conditions.
Playing Conditions and Rules Variations
The other key to getting the best odds in blackjack is to make intelligent choices about which blackjack games you’ll play. The biggest variation that you need to watch out for is the payout on a natural 21. At most casinos, a natural 21 pays out at 3 to 2 odds, but you’ll often find games that pay out at 6 to 5 odds instead.
The difference in that single rules variation is tremendous. In fact, it gives the casino an additional edge of 1.39%. In most blackjack games, this doubles or even triples the house’s edge. The easiest way to avoid that additional “tax” on your game is to just say no to any blackjack game that doesn’t pay out at least 3 to 2 for a natural.
Other variations in the rules can actually improve the player’s odds. For example, a single deck blackjack game versus a game with two decks or more gives 0.48% back to the player. That’s not nearly as significant as the 1.39%, so don’t fall for the trap of playing a single deck game with a 6 to 5 payout on a natural blackjack.
Most other rules variations have smaller effects on the house edge, but they can add up quickly when combined. For example, if the dealer hits on soft 17 (instead of standing), the house gains 0.22%. But if the player is also limited to only being able to double down on 10 or 11, the house gains another 0.18%, for a total gain to the house of 0.4%.
The Effects of Card Counting on the Odds
Entire books have been written about counting cards and how it affects the player’s odds in the game of blackjack, but for the purposes of this page, I just want to explain how card counters get an edge over the casino. Suppose you found a way to get another 1-2% edge on the casino by raising your bets when you have better odds and lowering your bets when you have worse odds?
For example, if you had a deck with nothing but aces and tens in it, your chances of getting a natural (and the corresponding 3 to 2 payout) would be much greater, wouldn’t it? So it would make sense to bet more in that situation.
On the other hand, if all the aces in the deck have already been dealt, it’s impossible to get a natural, which means you should lower your bet.
It turns out that each card that’s dealt out of a blackjack show affects the odds by a certain amount. By tracking the ratio of high cards versus low cards that have already been dealt, a card counter can raise or lower her bets in order to take advantage of favorable situations.
By doing so, the counter can actually gain an edge over the casino. This is mostly the result of putting more money into action when the odds are good, but some card counters also make strategy adjustments based on their count, too.
Summary
This page provides an introduction to blackjack odds. Many other pages on this site go into more details about the rules variations that increase or decrease the odds in the players and the casinos’ favor. The most important things to remember are that you should always play using basic strategy, in order to minimize the house’s edge, and also to avoid playing 6:5 blackjack games.
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.
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.
Odds Of Winning A Blackjack Hand
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.
Odds Of A Blackjack
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.
Blackjack Odds Of Runs
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.