## Counting Systems Übersetzungen und Beispiele

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This strategy helps players determine how to approach each situation that ensues on the blackjack table as it is based on mathematical probabilities in the respective situation.

In most cases the basic strategy is presented in the form of a chart which indicates when players should stand, hit, double or split a pair, depending on the hand of the dealer but memorizing the scheme is a better idea as most casinos don't allow players to bring the chart in and use it on the table.

Skilled and experienced blackjack players don't have to resort to using the basic strategy chart.

More so because their main objective is not gaining experience or playing recreationally but winning against the house and thus benefiting financially from the blackjack game.

Such players employ other techniques which allow them to gain advantage over the house. Such methods are known as advantage play and are perfectly legal and safe as long as the player does not gain a considerable advantage over the house's edge.

Otherwise the player may be added to the casino's blacklist and a complete ban from the casino is also a possible outcome.

However, their behavior and gestures while at the blackjack table may also be indicative of whether or not the player is using an advanced play strategy.

Basically the term advantage play refers to a number of practices the player can use to increase the mathematical probability of collecting a good hand and thus winning against the house.

The most common technique, employed by advanced players is card counting but it requires a good amount of time and concentration to master.

As the dealer exposes cards from the shoe which have already been dealt, card counting makes it possible for the player to infer what are the remaining cards, left to be dealt and decide upon their further course of action.

Thus, the player is able to determine whether or not he or she has an advantage over the dealer and act accordingly, for example by placing a larger bet.

Keeping track of dealt cards is by no means illegal as it is based chiefly on statistics and mathematical probability.

After each round there are fewer cards left in the remaining deck and a correct count allows players to determine the value of the cards that remain to be dealt.

On the other hand, the greater the number of players participating in the game, the more difficult it is to keep track of the dealt cards.

An experienced player should be able to pay close attention to the cards dealt to other participants in the game as well, which further increases the complexity of this strategy.

Furthermore, card counting may be essential for skilled blackjack players as their chances of winning greatly depend on the value of the cards obviously.

Face cards such as kings, queens and jacks are of a point value; the Ace, on the other hand, is a special case as its value can be either 1 or 11, so respectively the Ace can also be a high-value card.

What makes the Ace special is that players are allowed to determine its value , depending on the situation — they can either use it as a 1 or For instance, if the player has been dealt an Ace, a 6 and a 10, they should count the Ace as 1 because otherwise the total value of the hand will go over 21, resulting in a loss for the player.

This is important as being dealt higher-value cards, increases players' chance of winning while lower-value cards are more beneficial for the dealer as they decrease the chance of pulling out a face card and going over Even though card counting is not considered illegal, most dealers are wary of the practice and a problem might ensue.

Because of this keeping an accurate track of dealt cards is only one aspect of the card counting strategy , what's also important is to do it as inconspicuously as possible.

This requires practice and above all composure. Choosing suitable blackjack counting systems largely depends on the degree of skill and experience of the players.

There are simpler counting systems that are more suitable for beginners , as well as more complex ones that can be employed effectively only by expert players.

The following systems of counting cards are arranged in accordance with their level of complexity , starting from the more simpler ones and proceeding with those that are more elaborate.

Let's start from the very beginning. The first card counting system ever, was introduced in the sixties when blackjack gained more popularity.

The man behind it is Edward Thorp, a professor of mathematics with the Massachusetts Institute of Technology.

Thorp systematized the so-called Ten Count system in his book Beat the Dealer. Today, his system is used in specific cases as it was originally created for a single-deck blackjack games while at the present moment most casinos employ more than one deck to decrease the probability of players counting the cards correctly.

However, it's suitable for beginners who wish to practice and improve their skills. The cards are counted throughout the game and special attention is paid to their value.

This helps players decide when to bet and how high their stakes should be. The higher the total sum of the dealt cards is, the more value cards have remained in the deck.

This situation is favorable for players so they might opt for placing a higher bet. Let's say the player has kept track of the following cards in the course of a game: 5, 2, Ace, Queen, 3, 4, 8, 9, 7, King.

This means the cards should be counted as follows 4, 4, 4, -9, 4, 4, 4, 4, 4, It helps neutralize, though only partially, the advantage the house has over players.

At the beginning of the first deck, starting from 0, add the number 1 for each dealt 5-value card you notice. When an Ace is dealt, subtract 1 from the sum.

If the final result is equal to two or surpasses it, you can double the amount you've bet. Note that when it's equal to one or lower, avoid placing high bets.

As this system takes into consideration only two card values, it's much easier to keep track of. It's most effective when the dealer doesn't frequently reshuffle the remaining cards in the shoe.

With this method, it's best to double your bet only after a win to make your card counting less conspicuous. Inexperienced card counters can use it to develop their skills before they switch to more elaborate options like the Hi-Lo.

The strategy is suitable for beginners as well as for intermediate players. In fact, it's one of the most frequently used blackjack counting systems in the world because it's relatively simple and easy to memorize.

This kind of board was good for doing quick computations, but it did not provide a good way to keep a permanent recording of quantities or computations.

For this purpose, they used the quipu. The quipu is a collection of cords with knots in them. These cords and knots are carefully arranged so that the position and type of cord or knot gives specific information on how to decipher the cord.

A quipu is made up of a main cord which has other cords branches tied to it. See pictures to the right. Locke called the branches H cords.

They are attached to the main cord. B cords, in turn, were attached to the H cords. Most of these cords would have knots on them.

Rarely are knots found on the main cord, however, and tend to be mainly on the H and B cords. Locke points out that there are three types of knots, each representing a different value, depending on the kind of knot used and its position on the cord.

The Incas, like us, had a decimal base-ten system, so each kind of knot had a specific decimal value. They would be on the upper levels of the H cords.

Sometimes long knots were used to represents tens and hundreds. Note that the long knot has several turns in it…the number of turns indicates which integer is being represented.

The units ones were placed closest to the bottom of the cord, then tens right above them, then the hundreds, and so on. In order to make reading these pictures easier, we will adopt a convention that is consistent.

For the long knot with turns in it representing the numbers 2 through 9 , we will use the following notation:.

The four horizontal bars represent four turns and the curved arc on the right links the four turns together. This would represent the number 4.

What numbers are represented on each of the four cords hanging from the main cord? The colors of the cords had meaning and could distinguish one object from another.

One color could represent llamas, while a different color might represent sheep, for example. When all the colors available were exhausted, they would have to be re-used.

Because of this, the ability to read the quipu became a complicated task and specially trained individuals did this job. They were called Quipucamayoc, which means keeper of the quipus.

They would build, guard, and decipher quipus. There were various purposes for the quipu. Some believe that they were used to keep an account of their traditions and history, using knots to record history rather than some other formal system of writing.

One writer has even suggested that the quipu replaced writing as it formed a role in the Incan postal system.

Yet another proposed use of the quipu was to record numbers related to magic and astronomy, although this is not a widely accepted interpretation.

The mysteries of the quipu have not been fully explored yet. We are so used to seeing the symbols 1, 2, 3, 4, etc.

Unfortunately, as we proceed through our mathematical education in grade and high school, we receive very little information about the wide range of number systems that have existed and which still exist all over the world.

The fact that it has survived for hundreds of years and shows no sign of going away any time soon suggests that we may have finally found a system that works well and may not need further improvement, but only time will tell that whether or not that conjecture is valid or not.

We now turn to a brief historical look at how our current system developed over history. This is a base-ten decimal system since place values increase by powers of ten.

Furthermore, this system is positional, which means that the position of a symbol has bearing on the value of that symbol within the number.

For example, the position of the symbol 3 in the number , gives it a value much greater than the value of the symbol 8 in that same number.

The development of these ten symbols and their use in a positional system comes to us primarily from India.

However, the history of these numbers and their development goes back hundreds of years. One important source of information on this topic is the writer al-Biruni, whose picture is shown in figure When we look at the origins of the numbers that al-Biruni encountered, we have to go back to the third century BCE to explore their origins.

It is then that the Brahmi numerals were being used. The Brahmi numerals were more complicated than those used in our own modern system.

They had separate symbols for the numbers 1 through 9, as well as distinct symbols for 10, , ,…, also for 20, 30, 40,…, and others for , , , …, The Brahmi symbols for 1, 2, and 3 are shown below.

For example, in the first century CE, one particular set of Brahmi numerals took on the following form: [14]. One of those paths led to our current numeral system, and went through what are called the Gupta numerals.

They have the following form: [15]. How the numbers got to their Gupta form is open to considerable debate. Many possible hypotheses have been offered, most of which boil down to two basic types.

This is not uncommon. The second type of hypothesis states that they were derived from some earlier number system. However, there are other hypotheses that are offered, one of which is by the researcher Ifrah.

His theory is that there were originally nine numerals, each represented by a corresponding number of vertical lines.

One possibility is this: [17]. Because these symbols would have taken a lot of time to write, they eventually evolved into cursive symbols that could be written more quickly.

For zero to fulfil its potential in mathematics, it is necessary for each number up to the base figure to have its own symbol. This seems to have been achieved first in India.

The digits now used internationally make their appearance gradually from about the 3rd century BC, when some of them feature in the inscriptions of Asoka.

The Indians use a dot or small circle when the place in a number has no value, and they give this dot a Sanskrit name - sunya , meaning 'empty'.

The system has fully evolved by about AD , when it is adopted also in Baghdad. The Arabs use the same 'empty' symbol of dot or circle, and they give it the equivalent Arabic name, sifr.

About two centuries later the Indian digits reach Europe in Arabic manuscripts, becoming known as Arabic numerals. And the Arabic sifr is transformed into the 'zero' of modern European languages.

But several more centuries must pass before the ten Arabic numerals gradually replace the system inherited in Europe from the Roman empire.

In practical arithmetic the merchants have been far ahead of the scribes, for the idea of zero is in use in the market place long before its adoption in written systems.

It is an essential element in humanity's most basic counting machine, the Abacus. This method of calculation - originally simple furrows drawn on the ground, in which pebbles can be placed - is believed to have been used by Babylonians and Phoenicians from perhaps as early as BC.

In a later and more convenient form, still seen in many parts of the world today, the abacus consists of a frame in which the pebbles are kept in clear rows by being threaded on rods.

Zero is represented by any row with no pebble at the active end of the rod. Roman numerals: from the 3rd century BC. The completed decimal system is so effective that it becomes, eventually, the first example of a fully international method of communication.

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