Tie Rate = 9.5%. Loss Rate = 49.1%. Our win rate is far lower than the loss rate of the game. It would have been much better if we just tossed a coin. The biggest difference is that the dealer wins if both the player and the dealer gets burst. If you remove that single condition, here are the win/loss rate. Win Rate = 41.4%. Unlike a player bust, the dealer often wins when she busts, because players who act first and bust automatically lose (this is how the house has a built-in edge in blackjack). The 28 percent is an average over all possible dealer upcards. A survey conducted by the RAIN Group Center for Sales Research found respondents had an average win rate of 47%. The survey involved 472 companies with sales team that range from ten reps to over 5000 reps.

Allstar Gambling USA / Guides / Best Blackjack Betting Strategies

Do you want to learn the fundamentals of blackjack strategy from an expert? Learn Blackjack and Counting Cards to learn how to play blackjack in any casino and maximize your average win rate. Blackjack basics for players and dealers. The basic rules of blackjack are simple. Players try to score as close to 21 as possible without exceeding 21. So if you bet $10 on every hand and average 80 hands per hour you will have made a total of $800 worth of bets. The casino expects to earn 0.5% of the $800 or $4.00. Of course, the more likely result is that you'll win or lose much more than $4 after an hour of play. But on average you can expect over time to lose at the rate of $4 per hour.

Allstar GamblingJuly 3, 2019TwitterFacebookWhatsApp

For centuries, the strategic potential of blackjack has defied the chances and reduced the house edge to the point of complete elimination. The advanced card counting strategies were fought off by the casino operators through a gradual increase of the card decks inside the shoe.

Nowadays, it is next to impossible to find a live blackjack variant played with 1, 2, or even 4 decks; instead, 6 and 8-deck blackjack games are dominating the market, thwarting the beginner-level card counters. This, along with the RNG (Random Number Generator) blackjack, has created the need for alternative solutions, and a number of players resorted to blackjack betting strategies that exploit the winning and losing streaks, focusing on money management rather than trying to predict the next card. At the same time, these are much easier to master than some of the advanced blackjack techniques, such as Shuffle Tracking, Zen, or Omega 2.

Where to Start – The Most Popular Blackjack Betting Strategies

The complexity and dedication are not the only reasons people shy away from card counting techniques. Casino operators frown upon any skill that will give you an unfair advantage over other players (and the house), which is why advanced budget management methods are your safest resorts. They can also be arranged according to the difficulty level, starting with the simplest form of betting (flat) and gradually advancing to the complex patterns used by experienced players (Labouchere):

• Flat Betting
• Martingale
• 1-3-2-6 System
• Paroli
• D’ Alembert
• Oscar’s Grind
• Labouchere

Apart from the complexity level, each of the systems can also be classified according to the risk degree and the type of progression it entails – negative or positive.

Flat betting

Flat betting is somewhat of an exception, and many do not even consider it a strategy at all. The only requirement of this “system” is to remain in the game by constantly submitting the same size bet. Ideally, the player needs to establish a budget and divide it into equal portions of up to 5% of the total balance. Clearly, flat betting will not make you rich, but the strategy is deemed successful if you manage to generate around 10-20% profit.

Advantages and Disadvantages of Flat Betting

Apart from the extreme simplicity, the strongest suit of flat betting is the damage control it delivers. The fixed stakes will prevent you from suffering a sudden, substantial loss that some of the other methods are prone to.

On the other hand, the results that flat betting can produce are modest and rest on the assumption that you will win more than 50% of the time. This is why most players outgrow this strategy fairly quickly. The monotony makes it quite easy to abandon this process and move onto potentially more profitable (and riskier) blackjack betting strategies described below.

Risk Rate: Low

Positive Progressive Betting Systems – Definition and Popular Variants

Positive progressive betting systems are designed to get the most of the players’ winning streak, commanding a bet increase every time you score a winning blackjack hand. The stakes are raised systematically and lowered after the first losing hand. The most popular representatives of positive progressive strategies are Paroli and Oscar’s Grind.

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Paroli

Paroli is often defined as a reversed Martingale system, prompting the players to top the stake after every winning hand. Every next bet should be doubled and re-set after three consecutive winning rounds. For example, if we are to start our betting session with a $1 stake, the next two stakes should be increased by 2:

$1 > $2 > $4

For the sake of illustration, let us assume that you have placed a $10 bet and your hand trumped the dealer’s, resulting in an even money payout. Your next bet should, therefore, be $20, which is your base bet + $10 that you have won in the previous round. If you manage to win that hand as well, the follow-up stake should amount to $40 – again, the $10 base stake, plus the winnings from the previous rounds. The third win will result in an $80 bet, after which you will need to go back to the initial $10 bet, regardless of the outcome. Looking at the starting point, we can easily deduce that a $10 starting bet generated a total of $160.

Advantages and Disadvantages of Introducing Paroli Betting System to Your Gameplay

As you can see, the Reversed Martingale is very easy to use, as it requires the player to press the bet only 3 times and revert to the original wager in two cases – after a loss or when a series of three winning hands in a row is completed.

An added value of Paroli is that you do not need to have a substantial budget to implement this strategy, which is the main drawback of some other progressive betting patterns.

On the downside, three linked winning hands are not that easy to land, and the players may find themselves operating at a loss before long.

Risk Rate: Medium

Oscars Grind

A medium complexity system with a low-risk rate, Oscars Grind (aka Hoyle’s Press) starts off with a single unit bet and aims at generating an equivalent profit amount. The losing hands will follow the flat betting pattern whereas the winning hands will be followed by the bet increase – but only if it will result in the desired profit of one unit. Otherwise, the bet size is decreased to assure that the accurate amount is acquired, as shown in the table below:

Bet	Outcome	Return	Your next move
$1	Loss	-1	No change in bet
$1	Loss	-2	No change in bet
$1	Loss	-3	No change in bet
$1	Loss	-4	No change in bet
$1	Loss	-5	No change in bet
$1	Win	-4	Next bet increases by 1 unit
$2	Loss	-6	Bet remains the same (2 units)
$2	Win	-4	Next bet increased to 3 units
$3	Win	-1	Next bet adjusted to 2 units needed for a single unit profit
$2	Win	1	Round completed

The desired result is a single unit win on every session as well as the increased damage control during the losing streaks.

Pros and Cons of Oscars Grind

The method is not aggressive which means that you will be able to sustain longer losing streaks without suffering irreparable damage to your finances. The proceeds, although modest, will gradually accumulate, recuperating the losses incurred across ten rounds in no more than 4 wins.

At the same time, you may find the system frustrating as it requires a lot of self-discipline and restraint.

Risk Rate: Low

What Are Negative Progressive Betting Systems?

As opposed to the progressive betting methods, the negative strategies demand that the bets are increased during the losing streaks; the idea is to recover all that you have previously lost and to gain a profit. By default, negative progressions are more aggressive than their counterparts and they carry a somewhat higher risk rate. The representatives of this methodology are Martingale, D’Alembert, and Laboucher systems.

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Martingale Betting System

When you first come across to Martingale, it may seem like a heaven-sent system that simply cannot fail. You will soon discover that not all share your initial enthusiasm; there will be those who might urge you to avoid this strategy, especially if your gambling budget is limited.

As a negative progression system, Martingale mandates that you double the stake after every losing hand and go back to flat betting after a win. In the perfect world, this should generate a series of cumulative winnings and recuperate the losses in a course of a single losing streak.

But what happens if the streak prolongs and you budget dries out? Even if you start wagering with the betting minimum, you are running a risk of leaving the table empty-handed. To illustrate, let us assume that you begin the session with a $5 wager and start losing. To get back on the track, you will now need to double every next wager, which means that it will take no more than 8 consecutive losses to find yourself short of $1,275:

Bet	Outcome	Total in Losses
$5	Loss	$5
$10	Loss	$10
$20	Loss	$35
$40	Loss	$75
$80	Loss	$155
$160	Loss	$315
$320	Loss	$635
$640	Loss	$1,275

If the trend keeps up, you can soon end up with a considerable debt, which is probably not what you have signed up for when joining the blackjack table and introducing a betting structure to your game. High rollers will, of course, be able to disregard the elevated risk rate of the Martingale system, but average online or land-based casino visitors will probably need to adjust their strategy to the amount of money they can afford to lose. For most of them, this means that Martingale is off the limits.

The benefit of using Martingale is that it can produce excellent results in a relatively short time span.

Pros:

• Can be effective in short-term sessions
• Simple to use

Cons:

• Uncomfortably risky
• More suitable for high rollers
• Possibility of the stake amount exceeding the payout rate
• Table limits can easily stop the progression

As you can see, the cons, in this case, outweigh the pros, which means that you may want to leave the strategy to those with more money to waste.

Risk Rate: Extremely High

D’Alembert

D’Alembert is a great alternative to Martingale, since it offers a reduced risk rate but has the same complexity level, which makes it suitable for beginners. The system has an alternating pattern, urging the players to increase the stakes by a single unit after a loss or deduct one unit from the follow-up wager after a win. So, if you should happen to lose $5 bet, the next amount that you need to wager is $10 and the one after that $15 (as $5 is considered a single unit). Should the $15 result in a win, the subsequent bet should be re-set to $10. Example:

Bet	Outcome	The follow-up bet	Total Balance
$1	Loss	$2	$99
$2	Loss	$3	$97
$3	Win	$2	$100
$2	Loss	$3	$98
$3	Loss	$4	$95
$4	Win	$3	$99
$3	Win	$2	$102

Pros of D’Alembert Betting System

The entire scheme is very easy to follow through – all you need to do is remember your previous bet and act accordingly. Also, since the increase is moderate, you will not risk losing a large portion of your budget. Last but not least, thanks to the controlled variations in bet size, you are less likely to hit the table limits.

Cons of D’Alembert

The main defect of this system is that it’ll take forever to recover the lost bets, not to mention the perils of the long losing streaks that are likely to severely affect your balance.

Risk Rate: Medium High

Labouchere Betting System

In Laboucher, the players start with any sequence of numbers, where the first and the last number in the chain determine the bet total. Let’s say that you select the following string:

2 – 3 – 4 – 6 – 9

When you add up the first and the last number, you will get a total of 11, which should be the initial bet. If you happen to win, the relevant numbers should be eliminated from the sequence, leaving you with 3 – 4 – 6.

Assuming that you win again, the remaining number (4) should be doubled.

If, on the other hand, you lose the initial bet, the total must be added to the chain:

2 – 3 – 4 – 6 – 9 – 11

The bet will now amount to $13 (2 + 11), adding the number $13 to the string if the player loses again, or removing both 2 and 11 if the outcome is favorable.

The sequence total will depend on the target amount, which means that the players whose objective is to make a profit of $20 will create any sequence that can add up to that sum.

Pros of Laboucher

The increased control of both the budget and the progression of your bets is the main perk of Laboucher, but the players should make sure to use it at high limit tables.

Cons of Laboucher

Just like Martingale, this system threatens to hit the table limits, although, not as fast.

Risk Rate: Medium

The “In-Between” Split System: 1-3-2-6 Blackjack Betting System

Seemingly complicated, the 1-3-2-6 blackjack betting strategy is actually much simpler than it looks at first glance. After deciding on the betting unit, the players will just need to make sure that the system is executed correctly, in accordance with the 1-3-2-6 sequence. On a $5 unit bet, the process would look like this:

• Step 1: bet the single $5 unit. If you lose, repeat. If you win, proceed to Step 2.
• Step 2: bet 3 units ($15). If you lose, start over. If you win, proceed to Step 3
• Step 3: bet 2 units ($10). If you lose, start over. If you win, proceed to Step 4
• Step 4: bet 6 units ($30)

Pros of 1-3-2-6 System

The upside of this betting pattern is that you will have no difficulties mastering it – the formula is in the name itself, so it does not get any easier than that. The losses will not be severe, and you will be quite happy with the results this system provides in the short-run.

Cons of 1-3-2-6 System

You might not need a huge bankroll to execute the 1-3-2-6 betting scheme but bear in mind that the system’s “expiration date” is just around the corner. While the maneuver is efficient enough to be included in the list of the best blackjack betting strategies, it will not eliminate the house edge and provide lasting results.

Risk Rate: Low to Medium

Conclusion on the most successful Blackjack betting strategies

Adding some structure and limitation to your gambling routine might be just what you need to handle your money more efficiently. Still, you will need to remember that these systems are flawed, especially in the long run. As they have zero effect on the house edge, the end results they produce will be modest, but some of the low-risk systems mentioned above will prove quite handy in cutting down the unwanted losses.

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One of the most interesting aspects of blackjack is the
probability math involved. It’s more complicated than other
games. In fact, it’s easier for computer programs to calculate
blackjack probability by running billions of simulated hands
than it is to calculate the massive number of possible outcomes.

This page takes a look at how blackjack probability works. It
also includes sections on the odds in various blackjack
situations you might encounter.

An Introduction to Probability

Probability is the branch of mathematics that deals with the
likelihood of events. When a meteorologist estimates a 50%
chance of rain on Tuesday, there’s more than meteorology at
work. There’s also math.

Probability is also the branch of math that governs gambling.
After all, what is gambling besides placing bets on various
events? When you can analyze the payoff of the bet in relation
to the odds of winning, you can determine whether or not a bet
is a long term winner or loser.

The Probability Formula

The basic formula for probability is simple. You divide the
number of ways something can happen by the total possible number
of events.

Here are three examples.

Example 1:

You want to determine the probability of getting heads when
you flip a coin. You only have one way of getting heads, but
there are two possible outcomes—heads or tails. So the
probability of getting heads is 1/2.

Example 2:

You want to determine the probability of rolling a 6 on a
standard die. You have one possible way of rolling a six, but
there are six possible results. Your probability of rolling a
six is 1/6.

Example 3:

You want to determine the probability of drawing the ace of
spades out of a deck of cards. There’s only one ace of spades in
a deck of cards, but there are 52 cards total. Your probability
of drawing the ace of spades is 1/52.

A probability is always a number between 0 and 1. An event
with a probability of 0 will never happen. An event with a
probability of 1 will always happen.

Here are three more examples.

Example 4:

You want to know the probability of rolling a seven on a
single die. There is no seven, so there are zero ways for this
to happen out of six possible results. 0/6 = 0.

Example 5:

You want to know the probability of drawing a joker out of a
deck of cards with no joker in it. There are zero jokers and 52
possible cards to draw. 0/52 = 0.

Example 6:

You have a two headed coin. Your probability of getting heads
is 100%. You have two possible outcomes, and both of them are
heads, which is 2/2 = 1.

A fraction is just one way of expressing a probability,
though. You can also express fractions as a decimal or a
percentage. So 1/2 is the same as 0.5 and 50%.

You probably remember how to convert a fraction into a
decimal or a percentage from junior high school math, though.

Expressing a Probability in Odds Format

The more interesting and useful way to express probability is
in odds format. When you’re expressing a probability as odds,
you compare the number of ways it can’t happen with the number
of ways it can happen.

Here are a couple of examples of this.

Example 1:

You want to express your chances of rolling a six on a six
sided die in odds format. There are five ways to get something
other than a six, and only one way to get a six, so the odds are
5 to 1.

Example 2:

You want to express the odds of drawing an ace of spades out
a deck of cards. 51 of those cards are something else, but one
of those cards is the ace, so the odds are 51 to 1.

Odds become useful when you compare them with payouts on
bets. True odds are when a bet pays off at the same rate as its
probability.

Here’s an example of true odds:

You and your buddy are playing a simple gambling game you
made up. He bets a dollar on every roll of a single die, and he
gets to guess a number. If he’s right, you pay him $5. If he’s
wrong, he pays you $1.

Since the odds of him winning are 5 to 1, and the payoff is
also 5 to 1, you’re playing a game with true odds. In the long
run, you’ll both break even. In the short run, of course,
anything can happen.

Probability and Expected Value

One of the truisms about probability is that the greater the
number of trials, the closer you’ll get to the expected results.

If you changed the equation slightly, you could play this
game at a profit. Suppose you only paid him $4 every time he
won. You’d have him at an advantage, wouldn’t you?

• He’d win an average of $4 once every six rolls
• But he’d lose an average of $5 on every six rolls
• This gives him a net loss of $1 for every six rolls.

You can reduce that to how much he expects to lose on every
single roll by dividing $1 by 6. You’ll get 16.67 cents.

On the other hand, if you paid him $7 every time he won, he’d
have an advantage over you. He’d still lose more often than he’d
win. But his winnings would be large enough to compensate for
those 5 losses and then some.

The difference between the payout odds on a bet and the true
odds is where every casino in the world makes its money. The
only bet in the casino which offers a true odds payout is the
odds bet in craps, and you have to make a bet at a disadvantage
before you can place that bet.

Here’s an actual example of how odds work in a casino. A
roulette wheel has 38 numbers on it. Your odds of picking the
correct number are therefore 37 to 1. A bet on a single number
in roulette only pays off at 35 to 1.

You can also look at the odds of multiple events occurring.
The operative words in these situations are “and” and “or”.

• If you want to know the probability of A happening AND
  of B happening, you multiply the probabilities.
• If you want to know the probability of A happening OR of
  B happening, you add the probabilities together.

Here are some examples of how that works.

Example 1:

You want to know the probability that you’ll draw an ace of
spades AND then draw the jack of spades. The probability of
drawing the ace of spades is 1/52. The probability of then
drawing the jack of spades is 1/51. (That’s not a typo—you
already drew the ace of spades, so you only have 51 cards left
in the deck.)

The probability of drawing those 2 cards in that order is
1/52 X 1/51, or 1/2652.

Example 2:

You want to know the probability that you’ll get a blackjack.
That’s easily calculated, but it varies based on how many decks
are being used. For this example, we’ll use one deck.

To get a blackjack, you need either an ace-ten combination,
or a ten-ace combination. Order doesn’t matter, because either
will have the same chance of happening.

Your probability of getting an ace on your first card is
4/52. You have four aces in the deck, and you have 52 total
cards. That reduces down to 1/13.

Your probability of getting a ten on your second card is
16/51. There are 16 cards in the deck with a value of ten; four
each of a jack, queen, king, and ten.

So your probability of being dealt an ace and then a 10 is
1/13 X 16/51, or 16/663.

The probability of being dealt a 10 and then an ace is also
16/663.

You want to know if one or the other is going to happen, so
you add the two probabilities together.

16/663 + 16/663 = 32/663.

That translates to approximately 0.0483, or 4.83%. That’s
about 5%, which is about 1 in 20.

Example 3:

You’re playing in a single deck blackjack game, and you’ve
seen 4 hands against the dealer. In all 4 of those hands, no ace
or 10 has appeared. You’ve seen a total of 24 cards.

What is your probability of getting a blackjack now?

Your probability of getting an ace is now 4/28, or 1/7.
(There are only 28 cards left in the deck.)

Your probability of getting a 10 is now 16/27.

Your probability of getting an ace and then a 10 is 1/7 X
16/27, or 16/189.

Again, you could get a blackjack by getting an ace and a ten
or by getting a ten and then an ace, so you add the two
probabilities together.

16/189 + 16/189 = 32/189

Blackjack Average Win Rate Today

Your chance of getting a blackjack is now 16.9%.

This last example demonstrates why counting cards works. The
deck has a memory of sorts. If you track the ratio of aces and
tens to the low cards in the deck, you can tell when you’re more
likely to be dealt a blackjack.

Since that hand pays out at 3 to 2 instead of even money,
you’ll raise your bet in these situations.

The House Edge

The house edge is a related concept. It’s a calculation of
your expected value in relation to the amount of your bet.

Here’s an example.

Expected value is just the average amount of money you’ll win
or lose on a bet over a huge number of trials.

Using a simple example from earlier, let’s suppose you are a
12 year old entrepreneur, and you open a small casino on the
street corner. You allow your customers to roll a six sided die
and guess which result they’ll get. They have to bet a dollar,
and they get a $4 win if they’re right with their guess.

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.

The expected value of that $1 bet, for the customer, is about
84 cents. The expected value of each of those bets–for you–is
$1.16.

That’s how the casino does the math on all its casino games,
and the casino makes sure that the house edge is always in their
favor.

With blackjack, calculating this house edge is harder. After
all, you have to keep up with the expected value for every
situation and then add those together. Luckily, this is easy
enough to do with a computer. We’d hate to have to work it out
with a pencil and paper, though.

What does the house edge for blackjack amount to, then?

It depends on the game and the rules variations in place. It
also depends on the quality of your decisions. If you play
perfectly in every situation—making the move with the highest
possible expected value—then the house edge is usually between
0.5% and 1%.

If you just guess at what the correct play is in every
situation, you can add between 2% and 4% to that number. Even
for the gambler who ignores basic strategy, blackjack is one of
the best games in the casino.

Expected Hourly Loss and/or Win

You can use this information to estimate how much money
you’re liable to lose or win per hour in the casino. Of course,
this expected hourly win or loss rate is an average over a long
period of time. Over any small number of sessions, your results
will vary wildly from the expectation.

Here’s an example of how that calculation works.

• You are a perfect basic strategy player in a game with a
  0.5% house edge.
• You’re playing for $100 per hand, and you’re averaging
  50 hands per hour.
• You’re putting $5,000 into action each hour ($100 x 50).
• 0.5% of $5,000 is $25.
• You’re expected (mathematically) to lose $25 per hour.

Here’s another example that assumes you’re a skilled card
counter.

• You’re able to count cards well enough to get a 1% edge
  over the casino.
• You’re playing the same 50 hands per hour at $100 per
  hand.
• Again, you’re putting $5,000 into action each hour ($100
  x $50).
• 1% of $5,000 is $50.
• Now, instead of losing $25/hour, you’re winning $50 per
  hour.

Effects of Different Rules on the House Edge

The conditions under which you play blackjack affect the
house edge. For example, the more decks in play, the higher the
house edge. If the dealer hits a soft 17 instead of standing,
the house edge goes up. Getting paid 6 to 5 instead of 3 to 2
for a blackjack also increases the house edge.

Luckily, we know the effect each of these changes has on the
house edge. Using this information, we can make educated
decisions about which games to play and which games to avoid.

Here’s a table with some of the effects of various rule
conditions.

Rules Variation	Effect on House Edge
6 to 5 payout on a natural instead of the stand 3 to 2 payout	+1.3%
Not having the option to surrender	+0.08%
8 decks instead of 1 deck	+0.61%
Dealer hits a soft 17 instead of standing	+0.21%
Player is not allowed to double after splitting	+0.14%
Player is only allowed to double with a total of 10 or 11	+0.18%
Player isn’t allowed to re-split aces	+0.07%
Player isn’t allow to hit split aces	+0.18%

These are just some examples. There are multiple rules
variations you can find, some of which are so dramatic that the
game gets a different name entirely. Examples include Spanish 21
and Double Exposure.

The composition of the deck affects the house edge, too. We
touched on this earlier when discussing how card counting works.
But we can go into more detail here.

Every card that is removed from the deck moves the house edge
up or down on the subsequent hands. This might not make sense
initially, but think about it. If you removed all the aces from
the deck, it would be impossible to get a 3 to 2 payout on a
blackjack. That would increase the house edge significantly,
wouldn’t it?

Here’s the effect on the house edge when you remove a card of
a certain rank from the deck.

Card Rank	Effect on House Edge When Removed
2	-0.40%
3	-0.43%
4	-0.52%
5	-0.67%
6	-0.45%
7	-0.30%
8	-0.01%
9	+0.15%
10	+0.51%
A	+0.59%

These percentages are based on a single deck. If you’re
playing in a game with multiple decks, the effect of the removal
of each card is diluted by the number of decks in play.

Looking at these numbers is telling, especially when you
compare these percentages with the values given to the cards
when counting. The low cards (2-6) have the most dramatic effect
on the house edge. That’s why almost all counting systems assign
a value to each of them. The middle cards (7-9) have a much
smaller effect. Then the high cards, aces and tens, also have a
large effect.

The most important cards are the aces and the fives. Each of
those cards is worth over 0.5% to the house edge. That’s why the
simplest card counting system, the ace-five count, only tracks
those two ranks. They’re that powerful.

You can also look at the probability that a dealer will bust
based on her up card. This provides some insight into how basic
strategy decisions work.

Blackjack Average Win Rate Calculator

Dealer’s Up Card	Percentage Chance Dealer Will Bust
2	35.30%
3	37.56%
4	40.28%
5	42.89%
6	42.08%
7	25.99%
8	23.86%
9	23.34%
10	21.43%
A	11.65%

Perceptive readers will notice a big jump in the probability
of a dealer busting between the numbers six and seven. They’ll
also notice a similar division on most basic strategy charts.
Players generally stand more often when the dealer has a six or
lower showing. That’s because the dealer has a significantly
greater chance of going bust.

Blackjack Average Win Rates

Summary and Further Reading

Odds and probability in blackjack is a subject with endless
ramifications. The most important concepts to understand are how
to calculate probability, how to understand expected value, and
how to quantify the house edge. Understanding the underlying
probabilities in the game makes learning basic strategy and card
counting techniques easier.