When you’re gambling with a casino, one of you has an
advantage over the other. Usually it’s the casino which has an
advantage over you, but if you’re familiar with certain
techniques, you can get an advantage over the casino.
This page about advantage play in blackjack offers an
overview of which techniques blackjack players commonly use to
get an edge over the house.
Michael Shackleford is a gambling aficionado and a mathematician. The cost of playing 6-5 blackjack is an increase in the house edge of 1.4 percent, all other things being equal.
Before we get to that, though, we start by talking about how
a mathematical advantage works in the first place.
Mathematical Advantage Explained
This is a fundamental part of understanding advantage play,
in fact. It requires a little bit of understanding of how
probability works.
Examples are probably the easiest way to get this point
across, so we’ll provide a couple to help illustrate this
explanation.
Example 1 – Coin Toss
Let’s suppose you’re playing a casino game based on a coin
toss. You guess whether or not you’re going to get heads or
tails. Half the time you’ll win, and half the time you’ll lose,
right?
- Some Barcrest games don’t have any bonus rounds
- The first impression of this slot is that it might have
But what if you have to bet $2 every time, and you only win
$1 if you’re right?
It’s easy to see how in the long run the casino is going to
come out ahead in this example, isn’t it?
times. You win $50. But you also guess wrong 50 times, and you
lose $100 on those wrong guesses. The casino’s net profit over
those 100 coin tosses is $50.
That’s a clear example of how a casino gets an advantage over
a player.
But wait, you say. That’s a crazy example because no one
would ever take such a bet.
And yes, it is an extreme example, but it’s meant to be
illustrative. The casino is more likely to create a situation
where you have to bet $1.10 to win $1.00. They might call that
extra 10 cents an “ante” bet or something like that. When you
play blackjack in Oklahoma, you have to place a 50 cent extra
bet on every hand as an ante, so it happens.
Every casino bet works this way, though. If you place enough
bets, the math will work in the casino’s favor.
Example 2 – Roulette
Here’s a real example from a real game—roulette.
An even-money bet on black or on red seems like a 50/50
proposition until you look a little more closely at the roulette
wheel. Yeah, almost half the slots are black, and almost half of
them are read.
But two of those slots are green.
If you bet on black, the casino wins if the ball lands in a
red slot.
But it also wins if the ball lands in a green slot.
The same holds true if you bet on red. The casino wins if it
lands in black—OR if it lands in green.
There are 38 numbers on the roulette wheel. 18 of them are
red, 18 of them are black, and 2 of them are green.
If you place 38 bets in a row on black, the math says you
should win 18 of those bets and lose 20 of them. The same holds
true of 38 bets in a row on red.
Of course, in the short term, you might end such a session
winning more than you lose, but the odds are you’ll come close
to losing two of those bets.
profit.
As you place a larger number of bets, the more likely you are
to see actual results that mirror the probably results.
A casino sees hundreds of thousands of bets per month—maybe
even millions, if it has a lot of traffic. So eventually the
math results in the casino winning.
Blackjack is a more complicated game, mathematically, than
roulette, but it usually offers the house an edge of about 1%
over the player. That means you’ll lose an average of $1 for
every $100 you bet. And that’s assuming you use correct basic
strategy to make your decisions. An unskilled player might make
several bad decisions per hour, which means she’ll likely lose
2% to 4% of every bet.
But you can use certain techniques to flip that edge around
and get an advantage over the casino. Using such techniques is
called “advantage gambling”.
Casinos hate advantage gamblers.
Cheating
The first advantage gambling technique we’ll discuss is just
flat-out cheating. To be fair, most people who use the
expression “advantage gambling” or “advantage gambler” are
referring to techniques that fall outside the definition of
cheating. But it’s easy to see how you might get an edge over a
casino by cheating.
Of course, cheating is illegal in most states. In Nevada,
which is home to Las Vegas, cheating is a felony. You can find
plenty of interesting pages on the Internet about players who
have been caught cheating in Las Vegas and spent time behind
bars.
How would you cheat at blackjack?
Cheating is when you change the parameters of the game in
your favor.
Suppose you were able to change the amount you bet AFTER you
knew whether or not you’d won or lose?
This is called “past posting”. It’s all but impossible to
pull off at a blackjack table, but it’s clear to see how you
could get an advantage by doing this. You’d simply increase the
size of your bet by putting extra chips on top of your wager
after seeing that you’ve received a blackjack.
Don’t try this. You’ll get caught. Casinos will prosecute,
too.
Another cheating technique used at the blackjack table is the
marking of cards with a sharp fingernail. If you’re able to tell
what even some of the face-down cards at the table are, you can
get a mathematical edge over the casino.
This one’s less likely to get you caught, but it’s still a
bad idea—especially since there are so many legitimate ways to
get an edge over the casino in blackjack without having to
cheat.
Cheating usually involves using a machine to get an edge or
perpetrating some kind of fraud against the casino. Definitions
vary based on your jurisdiction—in some places, the state and/or
city don’t even define cheating legally. In those cases, the
definition (and enforcement) is left up to the local gambling
authorities.
Comps and Rebates
Comps and rebates are rewards offered by the casinos in order
to encourage more action from players. In order to receive these
comps and rebates, you usually need to join the players’ club or
the slots club at the property. In some cases you might be able
to get some comps from the pit boss just by playing a lot at the
tables, but most casinos prefer to track this sort of thing more
closely than they used to.
How It Works
The casino has a points system which corresponds to how much
you wager. When you’re playing their slot machines or video
poker machines, they can track exactly how much money you’ve
wagered per hour. If you’re betting $3 per spin and making 600
spins per hour, you’re putting $1800 per hour into action.
When you’re playing a table game, the casino will rate your
play. If you’re betting an average of $50 per hand on blackjack,
and you’re playing an average of 50 hands per hour, they’ll base
your comp rate on $2500 worth of action per hour.
They then offer rewards at a tiny percentage of your action.
This might be as little as 0.2% or 0.3% of how much you’ve
wagered.
In the examples above, a player would earn between $3.60 and
$5.40 per hour in comps at the slots. The example blackjack
player would earn between $5 and $7.50 per hour.
amounts on the amount of action you’re engaged in per hour, NOT
on the amount you’ve actually lose.
You could win a huge jackpot on a slot machine and still
receive a significant amount of comps based on how much you’ve
played’even though you walked away from the casino a winner for
the trip.
The casino banks on the long term expectation of the games.
They’re not interested in individual players who have individual
winning sessions—at least not when it comes to awarding comps.
The casino has done the math on these games, so they expect
you to lose a certain amount per hour. They also expect this
amount to be greater than the amount of comps you earn.
But if you can combine those comps with another strategy for
lowering the house edge, you can gamble at close to even or even
get a slight edge over the casino.
Also, casinos offer special promotional time periods where
they offer double points for your play. It’s a lot easier to
turn that tiny percentage into an advantage if it’s doubled.
You’re playing at a casino with a generous comps program.
They award 0.3% of your play in comps.
On Tuesdays from 2pm to 4pm, they offer double points. So now
you’re getting back 0.6%.
This particular casino also has really favorable blackjack
rules. The house edge on their game is only 0.5% as long as you
use perfect basic strategy.
When you take into account the 0.6% you’re getting back,
you’re actually playing with a 0.1% edge over the casino.
That’s called “comp hustling”. You can find detailed advice
on how that works in Max Rubin’s book, Comp City. It’s a little
dated now, but the advice still applies, and the math still
works the same.
When you combine comp hustling with other advantage
techniques, it increases your edge over the house.
Counting Cards
Counting cards is probably the best known advantage technique
in the casino—it’s certainly the best known advantage gambling
technique in blackjack.
But a surprising number of people don’t understand how it
works. They think you have to be some kind of mathematical
genius or idiot savant (a la Rain Man) in order to pull it off.
most people think.
That’s because you don’t have to track exactly which cards
have been played and which ones are still in the deck. You only
have to track the approximate ratio of high cards to low cards.
How Card Counting Works
A “natural” in blackjack pays off at 3 to 2. If all the aces
were eliminated from the deck, you’d be unable to ever get a
natural, which would tilt the odds further in the casino’s
favor. The same would hold true if you were out of cards ranked
10.
The reverse holds true, too, though. If you removed all the
cards in the deck except for the aces and the 10s, you’d have a
situation where you’d be MORE likely to be dealt a natural,
tilting the odds in your favor.
In a real game, though, you’ll seldom encounter a situation
where all of these cards are gone. But you an estimate the ratio
of high cards to low cards. If there are a relatively large
number of high cards compare to low cards, your odds of getting
a natural improve. Since the house edge in blackjack is low to
begin with, betting more when you have a better chance of
getting a natural gives you an edge over the casino. You would,
of course, bet less when you don’t have a favorable deck.
The easiest way to track this ratio is by assigning a value
to the high cards and a value to the low cards and keeping a
running count. It’s common for high cards (10s and aces) to be
given a value of -1 and for low cards(2s through 6s) a value of
+1. When the count is positive, there are a relatively large
number of high cards in the deck compared to low cards. When
it’s 0 or negative, the reverse is true.
The card counter raises her bet when the count is positive
and lowers her bet when it’s negative.
This gives a counter an advantage of anywhere between 0.5%
and 2% depending on the rules for that particular game and the
size of the player’s betting spread.
Multiple methods of counting cards exist, each of which
varies the values for various cards. Each of these has its
advantages and disadvantages over the other counting systems.
They all follow the same principle, though.
The Problem With Card Counting
Casinos hate card counters.
Since you’re not using a device and you’re not changing the
conditions of the game, you’re not cheating—at least not
legally. But the casinos are so opposed to the practice that
they reserve the right to ban you for life if they think you’re
counting cards.
Of course, different casinos have different policies. Some
might just ask you to stop playing blackjack there. Others might
run you off for the day. And some might ban you for life.
David Sklansky, in his book, Sklansky Talks Blackjack,
suggests only playing at a particular casino for an hour at a
time. He also suggests hitting a particular casino during
different shifts. He also suggests not playing at a particular
casino every day. These are countermeasures to help you avoid
getting caught.
Card counting is a technique that Max Rubin suggests using in
conjunction with comp hustling to maximize the amount of value
you get from your casino vacation.
Edge Sorting
You’re not allowed to do anything to mark cards. That’s
cheating.
But it’s possible for cards to develop irregularities during
regular play.
It’s also common for cards to have irregularities in the
patterns on the back of them.
advantage of them.
Players who are able to identify groups of cards which are
important—in blackjack, that would include 10s and aces—are able
to get a big edge over the casinos. The concept works in a
similar way to counting cards. If you’re able to recognize a
group of cards with lots of aces and 10s in it, you can raise
your bets to take advantage of the 3 to 2 payout.
Gambling With An Edge Blackjack Machine
Edge sorting is used to get an advantage in multiple casino
card games, including baccarat and Caribbean stud.
Hole Carding
Hole carding is an advantage play technique in which the
players get a glimpse of a card that’s supposed to be out of
sight. In blackjack, this almost always refers to the dealer’s
hole card. It should be obvious why knowing what the dealer has
in the hole offers an advantage to the player.
From a legal perspective, courts in Nevada have ruled that
hole carding is legal so long as the player is seated in the
appropriate place and isn’t using a device to help him get a
glimpse of the dealer’s hole card. Players who are able to pull
this off just look for opportunities where the dealer has gotten
sloppy.
Not all dealers offer the opportunity to get a glimpse of the
hole card. But the best spot for catching a glimpse is first
base or third base. First base is better. The reasons are simple
enough, too. Those are the spots closest to the dealer.
This sounds too good to be true, but it gets better. When
you’re counting cards, you can get an advantage of 0.5% to 1%
over the casino.
But if you can spot the dealer’s hole card, you can get an
edge of around 13% over the casino.
That’s huge.
You can also read about hole carding in Ken Uston’s Million
Dollar Blackjack.
Shuffle Tracking
For some of us, shuffle tracking is the most difficult
advantage play concept to understand. The idea is that certain
groups of cards stay more or less together when the deck is
shuffled. These groups are called zones, and if you can track
where they are in the shuffle, you can get an edge.
Shuffle tracking is often used by card counting teams in
conjunction with card counting techniques. Since players often
get to use a cut card to cut the deck, they can use this to
their advantage by making sure the deck starts off with a clump
of cards rich in aces and tens.
Summary
Various methods of getting an edge over the casino in
blackjack exist. The blanket term “advantage play in blackjack”
refers to all of them: counting cards, shuffle tracking, hole
carding, and edge sorting. Cheating, as a general rule, can get
you an edge over the casino, but most people who discuss
advantage gambling are talking about activities which aren’t
considered cheating.
Counting cards is probably the best known and perhaps the
easiest technique to use. But casinos watch for card counters
like hawks. Also, techniques like hole carding can get a greater
edge for the player.
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On This Page
Introduction
The following table shows the house edge of most casino games. For games partially of skill perfect play is assumed. See below the table for a definition of the house edge.
Gambling With An Edge Blackjack Reviews
Casino Game House Edge
| Game | Bet/Rules | House Edge | Standard Deviation |
|---|---|---|---|
| Baccarat | Banker | 1.06% | 0.93 |
| Player | 1.24% | 0.95 | |
| Tie | 14.36% | 2.64 | |
| Big Six | $1 | 11.11% | 0.99 |
| $2 | 16.67% | 1.34 | |
| $5 | 22.22% | 2.02 | |
| $10 | 18.52% | 2.88 | |
| $20 | 22.22% | 3.97 | |
| Joker/Logo | 24.07% | 5.35 | |
| Bonus Six | No insurance | 10.42% | 5.79 |
| With insurance | 23.83% | 6.51 | |
| Blackjacka | Liberal Vegas rules | 0.28% | 1.15 |
| Caribbean Stud Poker | 5.22% | 2.24 | |
| Casino War | Go to war on ties | 2.88% | 1.05 |
| Surrender on ties | 3.70% | 0.94 | |
| Bet on tie | 18.65% | 8.32 | |
| Catch a Wave | 0.50% | d | |
| Craps | Pass/Come | 1.41% | 1.00 |
| Don't pass/don't come | 1.36% | 0.99 | |
| Odds — 4 or 10 | 0.00% | 1.41 | |
| Odds — 5 or 9 | 0.00% | 1.22 | |
| Odds — 6 or 8 | 0.00% | 1.10 | |
| Field (2:1 on 12) | 5.56% | 1.08 | |
| Field (3:1 on 12) | 2.78% | 1.14 | |
| Any craps | 11.11% | 2.51 | |
| Big 6,8 | 9.09% | 1.00 | |
| Hard 4,10 | 11.11% | 2.51 | |
| Hard 6,8 | 9.09% | 2.87 | |
| Place 6,8 | 1.52% | 1.08 | |
| Place 5,9 | 4.00% | 1.18 | |
| Place 4,10 | 6.67% | 1.32 | |
| Place (to lose) 4,10 | 3.03% | 0.69 | |
| 2, 12, & all hard hops | 13.89% | 5.09 | |
| 3, 11, & all easy hops | 11.11% | 3.66 | |
| Any seven | 16.67% | 1.86 | |
| Double Down Stud | 2.67% | 2.97 | |
| Heads Up Hold 'Em | Blind pay table #1 (500-50-10-8-5) | 2.36% | 4.56 |
| Keno | 25%-29% | 1.30-46.04 | |
| Let it Ride | 3.51% | 5.17 | |
| Pai Gowc | 1.50% | 0.75 | |
| Pai Gow Pokerc | 1.46% | 0.75 | |
| Pick ’em Poker | 0% - 10% | 3.87 | |
| Red Dog | Six decks | 2.80% | 1.60 |
| Roulette | Single Zero | 2.70% | e |
| Double Zero | 5.26% | e | |
| Sic-Bo | 2.78%-33.33% | e | |
| Slot Machines | 2%-15%f | 8.74g | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | d |
| Dealer stands on soft 17 | 0.40% | d | |
| Super Fun 21 | 0.94% | d | |
| Three Card Poker | Pairplus | 7.28% | 2.85 |
| Ante & play | 3.37% | 1.64 | |
| Video Poker | Jacks or Better (Full Pay) | 0.46% | 4.42 |
| Wild Hold ’em Fold ’em | 6.86% | d |
Notes
| a | Liberal Vegas Strip rules: Dealer stands on soft 17, player may double on any two cards, player may double after splitting, resplit aces, late surrender. |
| b | Las Vegas single deck rules are dealer hits on soft 17, player may double on any two cards, player may not double after splitting, one card to split aces, no surrender. |
| c | Assuming player plays the house way, playing one on one against dealer, and half of bets made are as banker. |
| d | Yet to be determined. |
| e | Standard deviation depends on bet made. |
| f | Slot machine range is based on available returns from a major manufacturer |
| g | Slot machine standard deviation based on just one machine. While this can vary, the standard deviation on slot machines are very high. |
House Edge
The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wagered. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk.
The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.
The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Caribbean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of money lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette.
Many other sources do not count ties in the house edge calculation, especially for the Don’t Pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn’t resolved then it should be ignored. I personally opt to include ties although I respect the other definition.
Element of Risk
For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the 'element of risk.' This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.
Element of Risk
| Game | Bet | House Edge | Element of Risk |
|---|---|---|---|
| Blackjack | Atlantic City rules | 0.43% | 0.38% |
| Bonus 6 | No insurance | 10.42% | 5.41% |
| Bonus 6 | With insurance | 23.83% | 6.42% |
| Caribbean Stud Poker | 5.22% | 2.56% | |
| Casino War | Go to war on ties | 2.88% | 2.68% |
| Heads Up Hold 'Em | Pay Table #1 (500-50-10-8-5) | 2.36% | 0.64% |
| Double Down Stud | 2.67% | 2.13% | |
| Let it Ride | 3.51% | 2.85% | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | 0.65% |
| Spanish 21 | Dealer stands on soft 17 | 0.40% | 0.30% |
| Three Card Poker | Ante & play | 3.37% | 2.01% |
| Wild Hold ’em Fold ’em | 6.86% | 3.23% |
Standard Deviation
The standard deviation is a measure of how volatile your bankroll will be playing a given game. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds.
The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.
I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.
Standard Deviation
| Number | Probability |
|---|---|
| 0.25 | 0.1974 |
| 0.50 | 0.3830 |
| 0.75 | 0.5468 |
| 1.00 | 0.6826 |
| 1.25 | 0.7888 |
| 1.50 | 0.8664 |
| 1.75 | 0.9198 |
| 2.00 | 0.9546 |
| 2.25 | 0.9756 |
| 2.50 | 0.9876 |
| 2.75 | 0.9940 |
| 3.00 | 0.9974 |
| 3.25 | 0.9988 |
| 3.50 | 0.9996 |
| 3.75 | 0.9998 |
Hold
Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.
Hands per Hour, House Edge for Comp Purposes
The following table shows the average hands per hour and the house edge for comp purposes various games. The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made. This table was given to me anonymously by an executive with a major Strip casino and is used for rating players.
Hands per Hour and Average House Edge
| Games | Hands/Hour | House Edge |
|---|---|---|
| Baccarat | 72 | 1.2% |
| Blackjack | 70 | 0.75% |
| Big Six | 10 | 15.53% |
| Craps | 48 | 1.58% |
| Car. Stud | 50 | 1.46% |
| Let It Ride | 52 | 2.4% |
| Mini-Baccarat | 72 | 1.2% |
| Midi-Baccarat | 72 | 1.2% |
| Pai Gow | 30 | 1.65% |
| Pai Pow Poker | 34 | 1.96% |
| Roulette | 38 | 5.26% |
| Single 0 Roulette | 35 | 2.59% |
| Casino War | 65 | 2.87% |
| Spanish 21 | 75 | 2.2% |
| Sic Bo | 45 | 8% |
| 3 Way Action | 70 | 2.2% |
Translation
A Spanish translation of this page is available at www.eldropbox.com.
Written by: Michael Shackleford