- By way of comparison, Stanford Wong, in his book Professional Blackjack (page 203) says the variance is 1.28 and the covariance 0.47 for his Benchmark Rules, which are six decks, dealer stands on soft 17, no double after split, no re-splitting aces, no surrender.
- Then the Blackjack 6-7-8 software takes each 2-card combination (for 16, for example, the 2-card combinations are 10-6, 9-7, and 8-8) and plays blackjack against the various dealer upcards. For one cycle, the program will stand each time.
- Can I get a chart for Hi-Lo 6 Deck H17 playing deviations for the following? LS 17 vs A 16 vs 7 16 vs A 15 vs 7 15 vs 8 15 vs A 14 vs A 13 vs 10 88 vs A The charts should look like this and show how the advantage changes with the count. I want to see a chart and not just index numbers.
Mar 26, 2014
While poker requires people reading skills to win and roulette just requires a hell of a lot of luck, blackjack on the other hand boasts one of the lowest houses edges in the casino, making it the game to place your bets on, but how can you use mathematics to your advantage?
It doesn't take long to learn perfect basic blackjack strategy, and if you know what you're doing you can even get as far as lowering the house edge to 0.5%.
Standard deviation and its effect on blackjack If you account for all the blackjack rules and basic strategy of blackjack, the standard deviation of the game falls at the value of 1.14, in general. This means that in a game with a 0.5% house edge, the standard deviation marks the odds to win and lose on both sides of the bell curve.
The house edge alone is not a determining factor in whether you win or lose, since the unexpected always happens in cards, which is why it's called gambling in the first place, but there is a mathematical area for deviation that can give you an insight into your winning and losses.
The secret behind blackjack lies in the mathematics behind statistics, in the variance and its standard deviation.
Deviating from the standard
When you use strategy to lower the house edge down to 0.5%, theoretically this means that after playing a certain amount of time, you'll lose 0.5% of your money, which goes back to the casino.
Some basic blackjack strategy tips:
• Always hit a hard 4 to 8
• Always stand on a hard 17 and on any combination above 18
• Surrender a 16 versus 10
• Double a hard 10 or 11 if more than the dealer
However, real life is not as simple as that, since there is always room for a variation, which mathematically is deemed as the 'variance', which is calculated by measuring the standard deviation.
Blackjack Apprenticeship Deviations Chart
In statistics, probability is not an act of chaos with no pattern, but rather follows a bell curve, where the middle corresponds with the average, and the distribution shows all the possible outcomes and their probabilities.
The standard deviation is essentially the number marking the number of units falling to each side of the average, which means that 68% of the outcomes will fall within the standard deviation of the average.
Mathematically, this also means that 95% and 99.7% of the outcomes will fall within 2 and 3 standard deviations, respectively.
Standard deviation and its effect on blackjack
If you account for all the blackjack rules and basic strategy of blackjack, the standard deviation of the game falls at the value of 1.14, in general.
This means that in a game with a 0.5% house edge, the standard deviation marks the odds to win and lose on both sides of the bell curve. This means that 68% of the time you'd either win or lose 1.14 units, and 95% of the time win or lose 2.28 units.
But again, statistics also shifts depending on how many hands you play, and the more hands you do play mean that you get closer to the average. Thereby by including the variable of your dealt hands, you can predict your winning and losing likelihood by a fixed number.
To calculate the amount you win or lose, you basically take the square root of the number of hands played and multiply by 1.14.
So that means for 100 hands of blackjack, yields a standard deviation of 11.4 in this case. So betting, say, $1 per hand would yield an expected loss of 50cents, since the house edge is 0.5% (for 200 hands, this would go up to $1).
If you play 100 hands, then there is a 68% chance you could win or lose $11.4, for example. While there is room for manoeuvre, you can use standard deviation to budget your losses.
Show me the money
Let's take a more concrete example. Let's see how often you would lose $50 in a game of blackjack using the above examples.
To calculate this you need to factor in the expected loss (50cents for 100 hands) and measure the difference from the actual loss ($50 in this case). So the difference applied here is $49.5.
You then need to apply the standard deviation for your set of hands, so for 100 hands this is 11.4, as seen before, and divide this difference so 49.5/11.4 = 4.34.
This means losing $50 is over 3 standard deviations, so the chances of winning or losing the amount is in the margin of around 0.3% of time.
Using standard deviation can help you to optimize and minimize your risk. Playing 100 hands of blackjack and betting $1, with setting your maximum loss at $50, means that you're only likely to lose that amount 0.3% of the time.
To maximize your blackjack game, you simply need a smart strategy and a bit of statistics know-how.
Playing with standard deviation means you can leave your card counting system at home for once, and not get yourself banned from a casino.
Tags: blackjack strategy, card counting system, smart strategy, Standard deviation, Variance
Related posts:
- The Mathematics of Card Counting and Advantage Play in Blackjack
A look into mathematical strategies behind card counting and advantage play.. - Banned for Good: Blacklisted Blackjack Counters
Blacklisted blackjack counters are always polarizing, with some seeing them as heroes and others as.. - How the Wolf of Wall Street Can Help You Become a Professional Blackjack Player
If you want to be a professional blackjack player watch The Wolf of Wall Street;.. - How to Get Caught Using a Card Counting System
Getting caught using a card counting system will get you the boot from any casino,.. - How You Can Knockout the Casino Using the K-O Card Counting System
If you're looking for an alternative to the usual Hi-Lo card counting system, then try..
Card counting systems grew in popularity significantly over the past years and this is the reason why a great number of strategies of this kind have been developed and improved in order to meet every player's needs. In general, these systems are considered to be more advanced as they require more concentration, efforts and time.
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They can be extremely beneficial only on the condition that they are applied correctly throughout the course of the game but sometimes this can be a very challenging task as the casinos are full of distractions. It is no secret that card counting systems work best in combination with the basic strategy which is the reason why players shouldn't learn any of them if they lack the needed knowledge.
Importance of Altering the Basic Strategy
The basic strategy provides players with the opportunity to make the best possible bets and moves in a particular situation, taking into account the dealer's up card and their hand's total. Card counting gives players valuable information about the ratio between the high and low value cards which in some cases requires altering the basic strategy as its suggested moves aren't the most beneficial ones.
This is the reasons why they should be ready to make changes of it according to the true count of their chosen system as this is the only way they will be able to take advantage of the its accuracy and efficiency.
Blackjack Deviations Chart
In this sense, if players were to alter their decisions for their bets and moves at the time of playing, they still need to be prepared beforehand for these possible changes. It is true that to be able to recall the basic strategy and keep track of the cards at once is a really challenging task and remembering any additional variations of it can make the matters worse.
However, players need to understand that it is compulsory for them to be flexible and adjust their bets according to the particular situation as this is the only way they can make the most of it. This is the reason why the term index number was created as it shows which move is the best in a particular case from mathematical point of view.
Blackjack Deviation Chart Printable
Basic Strategy Chart | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Players' Hand | Dealer's Up Card | |||||||||
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
8 | H | H | H | D | D | H | H | H | H | H |
9 | H | D | D | D | D | H | H | H | H | H |
10 | D | D | D | D | D | D | D | D | H | H |
11 | D | D | D | D | D | D | D | D | D | D |
12 | H | H | S | S | S | H | H | H | H | H |
13 | S | S | S | S | S | H | H | H | H | H |
14 | S | S | S | S | S | H | H | H | H | H |
15 | S | S | S | S | S | H | H | H | H | H |
16 | S | S | S | S | S | H | H | H | H | H |
A-2 | H | H | H | D | D | H | H | H | H | H |
A-3 | H | H | D | D | D | H | H | H | H | H |
A-4 | H | H | D | D | D | H | H | H | H | H |
A-5 | D | H | D | D | D | H | H | H | H | H |
A-6 | H | D | D | D | D | H | H | H | H | H |
A-7 | S | D | D | D | D | S | S | H | H | H |
A-8 | S | S | S | S | D | S | S | S | S | S |
A-9 | S | S | S | S | S | S | S | S | S | S |
Ace-Ace | SP | SP | SP | SP | SP | SP | SP | SP | SP | SP |
2-2 | SP | SP | SP | SP | SP | SP | H | H | H | H |
3-3 | SP | SP | SP | SP | SP | SP | H | H | H | H |
4-4 | H | H | H | SP | SP | H | H | H | H | H |
5-5 | D | D | D | D | D | D | D | D | H | H |
6-6 | SP | SP | SP | SP | SP | H | H | H | H | H |
7-7 | SP | SP | SP | SP | SP | SP | H | H | S | H |
8-8 | SP | SP | SP | SP | SP | SP | SP | SP | SP | SP |
9-9 | SP | SP | SP | SP | SP | S | SP | SP | S | S |
What is the Illustrious 18
Card counters need to take into account a few important things, if they want to make the best possible move and bet in every situation. It is essential to know the chosen system besides the basic strategy backwards and forwards so that they will be able to apply them when needed. Also, players should be able to understand how to use the true count as it gives them valuable information regarding their bets – whether it's better to increase or decrease them.
Hi-Opt Systems
Zen Count System
Wong Halves System
The Illustrious 18
Single-deck Card Counting
Poker face emoji ascii generator. However, as already mentioned there are some situations in which the best move is based on the true count as well as on the index number. The Illustrious 18 are eighteen extremely efficient variations of the basic strategy which were invented by Don Schlesinger.
The reason why they become so popular is that thanks to them, players can make the most of every hand by altering the basic strategy accordingly and taking into account the valuable information the card counting system provides them with. The index numbers of his chart play a crucial role and if players want to be able to take advantage of these variations, they need to fully understand them.
How the Illustrious 18 works
The Illustrious 18 was developed in order to improve the expected return of money depending on the moves players make. Just like any other strategy, in order to apply it correctly, they need to take their time to memorise the index numbers, the suggested by the chart moves and of course the particular situation they should be used in. Even though these variations are more information to remember on top of everything else, they give players a really good chance of winning and making a profit.
This way they will be able to make the most of every system and apply the valuable information it provides them with in the best possible way. Players need to understand that every little subtlety can make the difference between winning and losing a particular hand. One very important thing that should be taken into account as well is the number of decks involved in the game as they also require altering the players' strategy to some extent.
Blackjack Basic Strategy Deviations Chart
‘Illustrious 18' Hi-Lo Card Counting Indices | |||
---|---|---|---|
Rank | Hand | Index | Decision |
1 | Insurance | 3 | Take |
2 | 16 vs. T | 0 | Hit/Stand |
3 | 15 vs. T | 4 | Hit/Stand |
4 | T-T vs. 5 | 5 | Stand/Split |
5 | T-T vs. 6 | 4 | Stand/Split |
6 | 10 vs. T | 4 | Hit/Double |
7 | 12 vs. 3 | 2 | Hit/Stand |
8 | 12 vs. 4 | 3 | Hit/Stand |
9 | 11 vs. A | 1 | Hit/Double |
10 | 9 vs. 2 | 1 | Hit/Double |
11 | 10 vs. A | 4 | Hit/Double |
12 | 9 vs. 7 | 3 | Hit/Double |
13 | 16 vs. 9 | 5 | Hit/Stand |
14 | 13 vs. 2 | -1 | Hit/Stand |
15 | 12 vs. 4 | 0 | Hit/Stand |
16 | 12 vs. 5 | -2 | Hit/Stand |
17 | 12 vs. 6 | -1 | Hit/Stand |
18 | 13 vs. 3 | -2 | Hit/Stand |
About the Creator of the Illustrious 18
The secret behind blackjack lies in the mathematics behind statistics, in the variance and its standard deviation.
Deviating from the standard
When you use strategy to lower the house edge down to 0.5%, theoretically this means that after playing a certain amount of time, you'll lose 0.5% of your money, which goes back to the casino.
Some basic blackjack strategy tips:
• Always hit a hard 4 to 8
• Always stand on a hard 17 and on any combination above 18
• Surrender a 16 versus 10
• Double a hard 10 or 11 if more than the dealer
However, real life is not as simple as that, since there is always room for a variation, which mathematically is deemed as the 'variance', which is calculated by measuring the standard deviation.
Blackjack Apprenticeship Deviations Chart
In statistics, probability is not an act of chaos with no pattern, but rather follows a bell curve, where the middle corresponds with the average, and the distribution shows all the possible outcomes and their probabilities.
The standard deviation is essentially the number marking the number of units falling to each side of the average, which means that 68% of the outcomes will fall within the standard deviation of the average.
Mathematically, this also means that 95% and 99.7% of the outcomes will fall within 2 and 3 standard deviations, respectively.
Standard deviation and its effect on blackjack
If you account for all the blackjack rules and basic strategy of blackjack, the standard deviation of the game falls at the value of 1.14, in general.
This means that in a game with a 0.5% house edge, the standard deviation marks the odds to win and lose on both sides of the bell curve. This means that 68% of the time you'd either win or lose 1.14 units, and 95% of the time win or lose 2.28 units.
But again, statistics also shifts depending on how many hands you play, and the more hands you do play mean that you get closer to the average. Thereby by including the variable of your dealt hands, you can predict your winning and losing likelihood by a fixed number.
To calculate the amount you win or lose, you basically take the square root of the number of hands played and multiply by 1.14.
So that means for 100 hands of blackjack, yields a standard deviation of 11.4 in this case. So betting, say, $1 per hand would yield an expected loss of 50cents, since the house edge is 0.5% (for 200 hands, this would go up to $1).
If you play 100 hands, then there is a 68% chance you could win or lose $11.4, for example. While there is room for manoeuvre, you can use standard deviation to budget your losses.
Show me the money
Let's take a more concrete example. Let's see how often you would lose $50 in a game of blackjack using the above examples.
To calculate this you need to factor in the expected loss (50cents for 100 hands) and measure the difference from the actual loss ($50 in this case). So the difference applied here is $49.5.
You then need to apply the standard deviation for your set of hands, so for 100 hands this is 11.4, as seen before, and divide this difference so 49.5/11.4 = 4.34.
This means losing $50 is over 3 standard deviations, so the chances of winning or losing the amount is in the margin of around 0.3% of time.
Using standard deviation can help you to optimize and minimize your risk. Playing 100 hands of blackjack and betting $1, with setting your maximum loss at $50, means that you're only likely to lose that amount 0.3% of the time.
To maximize your blackjack game, you simply need a smart strategy and a bit of statistics know-how.
Playing with standard deviation means you can leave your card counting system at home for once, and not get yourself banned from a casino.
Tags: blackjack strategy, card counting system, smart strategy, Standard deviation, Variance
Related posts:
- The Mathematics of Card Counting and Advantage Play in Blackjack
A look into mathematical strategies behind card counting and advantage play.. - Banned for Good: Blacklisted Blackjack Counters
Blacklisted blackjack counters are always polarizing, with some seeing them as heroes and others as.. - How the Wolf of Wall Street Can Help You Become a Professional Blackjack Player
If you want to be a professional blackjack player watch The Wolf of Wall Street;.. - How to Get Caught Using a Card Counting System
Getting caught using a card counting system will get you the boot from any casino,.. - How You Can Knockout the Casino Using the K-O Card Counting System
If you're looking for an alternative to the usual Hi-Lo card counting system, then try..
Card counting systems grew in popularity significantly over the past years and this is the reason why a great number of strategies of this kind have been developed and improved in order to meet every player's needs. In general, these systems are considered to be more advanced as they require more concentration, efforts and time.
Holdem Starting Hands Odds Calculator a bonus offer of same value (14-day expiry). Total of four (4) Deposit bonuses + bonus spins offers available. 35x real money cash wagering of bonus offer amount must be met (30 days from deposit) on eligible casino games. The world's most trusted Texas hold'em poker odds calculator. Improve your poker or find out just how bad that bad beat was. Ignition Casino 100% up to $1,000 Black Chip Poker 100% up to. How the poker calculator works. The Grosvenor Casinos Poker Calculator works by using what's known as a 'Monte Carlo' algorithm. This algorithm estimates the percentage of making a hand in Texas Hold'em by simulating what would or could happen had the hand been played out multiple times. Casino holdem odds calculator yahoo.
They can be extremely beneficial only on the condition that they are applied correctly throughout the course of the game but sometimes this can be a very challenging task as the casinos are full of distractions. It is no secret that card counting systems work best in combination with the basic strategy which is the reason why players shouldn't learn any of them if they lack the needed knowledge.
Importance of Altering the Basic Strategy
The basic strategy provides players with the opportunity to make the best possible bets and moves in a particular situation, taking into account the dealer's up card and their hand's total. Card counting gives players valuable information about the ratio between the high and low value cards which in some cases requires altering the basic strategy as its suggested moves aren't the most beneficial ones.
This is the reasons why they should be ready to make changes of it according to the true count of their chosen system as this is the only way they will be able to take advantage of the its accuracy and efficiency.
Blackjack Deviations Chart
In this sense, if players were to alter their decisions for their bets and moves at the time of playing, they still need to be prepared beforehand for these possible changes. It is true that to be able to recall the basic strategy and keep track of the cards at once is a really challenging task and remembering any additional variations of it can make the matters worse.
However, players need to understand that it is compulsory for them to be flexible and adjust their bets according to the particular situation as this is the only way they can make the most of it. This is the reason why the term index number was created as it shows which move is the best in a particular case from mathematical point of view.
Blackjack Deviation Chart Printable
Basic Strategy Chart | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Players' Hand | Dealer's Up Card | |||||||||
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
8 | H | H | H | D | D | H | H | H | H | H |
9 | H | D | D | D | D | H | H | H | H | H |
10 | D | D | D | D | D | D | D | D | H | H |
11 | D | D | D | D | D | D | D | D | D | D |
12 | H | H | S | S | S | H | H | H | H | H |
13 | S | S | S | S | S | H | H | H | H | H |
14 | S | S | S | S | S | H | H | H | H | H |
15 | S | S | S | S | S | H | H | H | H | H |
16 | S | S | S | S | S | H | H | H | H | H |
A-2 | H | H | H | D | D | H | H | H | H | H |
A-3 | H | H | D | D | D | H | H | H | H | H |
A-4 | H | H | D | D | D | H | H | H | H | H |
A-5 | D | H | D | D | D | H | H | H | H | H |
A-6 | H | D | D | D | D | H | H | H | H | H |
A-7 | S | D | D | D | D | S | S | H | H | H |
A-8 | S | S | S | S | D | S | S | S | S | S |
A-9 | S | S | S | S | S | S | S | S | S | S |
Ace-Ace | SP | SP | SP | SP | SP | SP | SP | SP | SP | SP |
2-2 | SP | SP | SP | SP | SP | SP | H | H | H | H |
3-3 | SP | SP | SP | SP | SP | SP | H | H | H | H |
4-4 | H | H | H | SP | SP | H | H | H | H | H |
5-5 | D | D | D | D | D | D | D | D | H | H |
6-6 | SP | SP | SP | SP | SP | H | H | H | H | H |
7-7 | SP | SP | SP | SP | SP | SP | H | H | S | H |
8-8 | SP | SP | SP | SP | SP | SP | SP | SP | SP | SP |
9-9 | SP | SP | SP | SP | SP | S | SP | SP | S | S |
What is the Illustrious 18
Card counters need to take into account a few important things, if they want to make the best possible move and bet in every situation. It is essential to know the chosen system besides the basic strategy backwards and forwards so that they will be able to apply them when needed. Also, players should be able to understand how to use the true count as it gives them valuable information regarding their bets – whether it's better to increase or decrease them.
Hi-Opt Systems
Zen Count System
Wong Halves System
The Illustrious 18
Single-deck Card Counting
Poker face emoji ascii generator. However, as already mentioned there are some situations in which the best move is based on the true count as well as on the index number. The Illustrious 18 are eighteen extremely efficient variations of the basic strategy which were invented by Don Schlesinger.
The reason why they become so popular is that thanks to them, players can make the most of every hand by altering the basic strategy accordingly and taking into account the valuable information the card counting system provides them with. The index numbers of his chart play a crucial role and if players want to be able to take advantage of these variations, they need to fully understand them.
How the Illustrious 18 works
The Illustrious 18 was developed in order to improve the expected return of money depending on the moves players make. Just like any other strategy, in order to apply it correctly, they need to take their time to memorise the index numbers, the suggested by the chart moves and of course the particular situation they should be used in. Even though these variations are more information to remember on top of everything else, they give players a really good chance of winning and making a profit.
This way they will be able to make the most of every system and apply the valuable information it provides them with in the best possible way. Players need to understand that every little subtlety can make the difference between winning and losing a particular hand. One very important thing that should be taken into account as well is the number of decks involved in the game as they also require altering the players' strategy to some extent.
Blackjack Basic Strategy Deviations Chart
‘Illustrious 18' Hi-Lo Card Counting Indices | |||
---|---|---|---|
Rank | Hand | Index | Decision |
1 | Insurance | 3 | Take |
2 | 16 vs. T | 0 | Hit/Stand |
3 | 15 vs. T | 4 | Hit/Stand |
4 | T-T vs. 5 | 5 | Stand/Split |
5 | T-T vs. 6 | 4 | Stand/Split |
6 | 10 vs. T | 4 | Hit/Double |
7 | 12 vs. 3 | 2 | Hit/Stand |
8 | 12 vs. 4 | 3 | Hit/Stand |
9 | 11 vs. A | 1 | Hit/Double |
10 | 9 vs. 2 | 1 | Hit/Double |
11 | 10 vs. A | 4 | Hit/Double |
12 | 9 vs. 7 | 3 | Hit/Double |
13 | 16 vs. 9 | 5 | Hit/Stand |
14 | 13 vs. 2 | -1 | Hit/Stand |
15 | 12 vs. 4 | 0 | Hit/Stand |
16 | 12 vs. 5 | -2 | Hit/Stand |
17 | 12 vs. 6 | -1 | Hit/Stand |
18 | 13 vs. 3 | -2 | Hit/Stand |
About the Creator of the Illustrious 18
Donald Schlesinger is a very successful author as well as prominent mathematician who is a member of the Blackjack Hall of Fame. His works are read by many players worldwide as they have proven to be extremely beneficial and interesting.
One of his best books is Blackjack Attack – Playing the Pros' Way as it includes both theory and its practical application and his observations are worth reading. Mr. Schlesinger is most well-known for establishing the Illustrious 18 as these play variations become inseparable part of every card counters strategy.
Conclusion
Card counting systems are famous for their accuracy and efficiency and this is the reason why many advanced players reply on them. If applied along with the basic strategy, they can be extremely beneficial and give players the opportunity to gain advantage over the casino.
However, there are a number of other factors which should be taken into account as they also play crucial role for the players' performance. It is true that both strategies work very well together, however the card counting provides gamblers with valuable information about the upcoming cards which can be used to make even better decisions about their bets and moves.
The basic strategy suggested turns are based on the condition that players don't know what the upcoming cards will be. The card counting systems are especially designed to provide such information and this is the reason why the basic strategy should be adjusted accordingly as this way, their edge will be significantly increased. Also, if players want to succeed in winning, they need to be very disciplined and organised in order to manage to apply the systems in a casino setting.