🖐 GitHub - jfdegner/BlackJack: In which I turn some functions I wrote to understand blackjack strategy and card counting into a dynamic statistical comparison in R (dscr).

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This table lists all blackjack card counting systems that are listed in The Encyclopedia of Blackjack (Twenty-One).


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GitHub - jfdegner/BlackJack: In which I turn some functions I wrote to understand blackjack strategy and card counting into a dynamic statistical comparison in R (dscr).
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Feb 28, 2015 at 1:14PM With the rapid expansion of land-based casino gaming across the U.
And with the great advancements in gambling knowledge and game strategy over this time period, more gamblers — millennials in particular — are more sophisticated and more knowledgeable about gambling than at any point in the history of mankind.
The casino is losing its mystique, and the product of gambling is maturing.
As a consequence, the tastes of the modern gambler are changing, such that there is an increasing demand for gaming activity that is more social in nature, and an increasing demand for gaming activity at least partially based on skill.
But what does that really mean for the next wave of casino games?
Basing payouts on Pong The first and most prominent interpretation of this trend thus far has been to develop video slot games designed to appeal to a video game generation.
About a decade ago at the 2004 Global Gaming Expo G2EBally Technologies acquired by Scientific Games Corporation last year introduced a slot game based on Pong, the landmark Atari game released in 1972.
Bally's slot adaptation — by Nevada gaming regulators in 2007 — included a bonus feature in which the player would play a 45-second round of Pong, and the player's performance affected the payout; the difference in expectation between the best player and the worst player in this bonus feature was 7 percent.
Other companies have followed suit, with games such as IGT's Centipede and GTECH's Zuma offering skill-based bonus features.
More recently, in October 2014, the New Jersey Division of Gaming Enforcement that it was "currently authorized to approve" and "eager to receive" skill-based game submissions for review under its New Jersey First program.
New Jersey First was designed to encourage the development of casino games in New Jersey article source both the social and skill-based elements found in games like Candy Crush and Words with Friends by allowing games with such features to be fast-tracked to the casino floor within 14 days of approval, provided that the game is "submitted to New Jersey prior to or simultaneously with any other jurisdiction or testing lab.
Oddly, completely absent from the discussion about the demand for social and skill-based games is the area of the casino floor that historically has been both the most social and most demanding of skill.
That area is the blackjack count comparison games pit.
Let's start by first talking about the state of blackjack, the most popular casino skill game of them all.
The rise and slow death of blackjack Ever since Ed Thorp introduced the first card counting system in 1962 in his book Beat the Dealer, blackjack has led the way as the game of choice for intelligent gamblers in the table games pit.
For reference, in 1985, blackjack for 81% of table games units and over half of table games revenue in the state of Nevada.
Part of the reason for blackjack's popularity was the fact that some gamblers like to make decisions and have some level of control over the outcome.
But the chief reason for blackjack's exceptional popularity gmslots the idea that the game was beatable, and the idea that blackjack represented a fair game.
The fact is that most people who play blackjack don't even play perfect basic strategy; moreover, relatively few people know how to count cards, and even fewer among them can do it proficiently enough to beat the game.
But the idea that a gambler can walk into a casino and beat a game that's not intended to be beatable — and in a place in which the player is not supposed to win — is a romantic one, and has been strong enough to power the brand of blackjack for the past something blackjack lucky excellent decades.
And even setting card counting aside, blackjack count comparison has indeed represented the fairest gamble in the house, with house advantages under perfect basic strategy generally in the 0.
The result is that in the history of legalized and regulated gambling in the United States, blackjack has been the game that smart people play.
But all of that is changing.
Over the past decade, casinos have taken the most extreme steps to eliminate risk from card counters in particular, as there is no fundamental reason why the casino is obligated to offer a mathematically beatable game.
The first big trend was the increasingly widespread use of continuous shuffling machines CSMswhich continue reading up the game but also eliminates card counting.
Another more recent trend is that some casino operators have moved to make a more drastic step of paying 6:5 on blackjack not only on single-deck alternatives, but also on two-deck and multideck shoe games; paying 6:5 rather than 3:2 adds 1.
What's happened in the process is that the casinos are gradually and probably unintentionally eliminating any incentive to learn a complex basic strategy for a game that not only is no longer beatable, but in an increasing number of cases does not even offer a more favorable house advantage than can be found in games requiring no skill whatsoever.
By way of comparison, the Banker bet in baccarat offers a 1.
And for the most part, the modern gambler has begun to move on from blackjack.
At its peak in 2000, there were 3,682 blackjack units in the state of Nevada, representing 64.
Note that the decline as a percent of all table games revenue in the table below is largely a function of the spectacular rise in predominantly blackjack classic model 7 stakes baccarat blackjack count comparison on the Las Vegas Strip over this time period.
Nevada: Blackjack table count and revenue Year Units % of Units Revenue % of Revenue 1985 3,049 80.
These games are typically protected by patents and trademarks Pai Gow is a notable exception, though several modified variations of Pai Gow are patentedand are generally leased to casinos.
This is an area that has long been dominated by SHFL Entertainment now part of Scientific Games as a result of SHFL's merger with Bally Technologies in 2013, and Bally's subsequent acquisition by Scientific Games in 2014.
In 1985, non-traditional games represented 2.
Nevada: Non-traditional games Year Units % of Units Revenue % of Revenue 1985 85 2.
The next question is how well these new games satisfy the demand for skill games.
Let's establish two key baseline ideas: 1.
If blackjack count comparison game is going to require any skill whatsoever, the game should have a lower house advantage than that being offered by games with bets requiring zero skill.
The more skill a game requires, the lower the house advantage should be.
Requiring skill in a game is pointless if it means reducing the house advantage from 15% to 5%, as a gambler can always find better bets; rather, there must be an incentive for the player to acquire the skills to play a game the player knows is designed to beat him.
The best example of this is blackjack, a game which has incentivized gamblers to learn a relatively complex basic strategy by a historically being beatable and b by offering a lower achievable house advantage under basic strategy than other games like craps and baccarat.
The second point is a natural extension of the first.
The more decisions a player has to make, the more mistakes the player will make, and the less likely it is that the player will achieve the theoretically optimal house advantage.
This leads to player value risk, or the risk that the player is losing more money faster than he should be.
This needs to be compensated for with a lower theoretical house advantage.
In finance and investing, we have a theoretical risk-free rate of return, which serves as a benchmark against which all decisions are made.
In casino gambling, we have what I'll call the skill-free rate, which serves as a benchmark house advantage against which games requiring skill should be compared.
At a minimum, the adjusted house advantage better known as "element of risk," which I'll explain in a minute for a game requiring skill should be lower than the 1.
These are typically the lowest house advantages offered by the casino without requiring any decision-making or skill.
As the lowest number, the Banker bet in baccarat represents the skill-free rate.
Entry-level games such as Three Card Poker SHFLGalaxy Gaming's High Card Flush, and Crazy 4 Poker SHFL have optimal strategies that can be expressed in as little as one or two rules.
In Three Card Poker, the player starts with an initial ante wager and is dealt three cards; optimal strategy is to bet with Q-6-4 or better, which is all you need to know to get to the house advantage of 3.
In High Card Flush, the player antes and is dealt seven cards; according tothe correct strategy is to bet the maximum allowed when dealt four or more cards of the same suit, or a three-card flush of J-9-6 or higher 9-7-5 to J-9-5 are borderlinewhich will get close to the house advantage of 2.
In Crazy 4 Poker, the player starts with two initial wagers an Ante and equal Super Bonus wagerand is dealt five down cards; the perfectly optimal strategy is to bet the maximum 3x the Ante with a pair of aces or better, and bet the minimum 1x with K-Q-8-4-x or better the best four-card hand plays.
These games are strategically simple by design, and are intended to serve as lowest common denominators.
The advantage of these games is that virtually anybody can play these games perfectly or near-perfectly in the case of High Card Flusheven if very few people who play these games seem to actually know the strategies for them.
But at the same time, the limitation of these games is that they satisfy the demand for skill games only on the most cursory level.
But how well are players being incentivized to learn more complicated strategies?
The classic smash hit Caribbean Stud SHFL requires for effectively perfect play, to approximate the theoretical house advantage of 5.
Even adjusting for an average bet of 2.
This in large part explains why Caribbean Stud is in decline, particularly when compared to other new alternatives.
Bet Click Hand Units Four Card Poker SHFL has a theoretically optimal house advantage of 2.
At an average of 2.
Easily the two most advanced proprietary games with wide circulation at present are Mississippi Stud SHFL and Ultimate Texas Hold'em SHFL.
Mississippi Stud is a game that features a currently unique combination of scalable betting the player can bet 1x-3x https://chakefashion.com/blackjack/blackjack-pch.html ante on three successive betting rounds, for a total of up to 10 units wagered in a single hand and scalable payoffs all wagers pay according to a pay table, resulting in some potentially large payouts.
However, the game requires 23 strategy rules to be played optimally, which gets the player to a house advantage of 4.
Ultimate Texas Hold'em is by far the most attractive of these games, with a theoretical house advantage of 2.
This house advantage is not practically achievable — Stephen How of Discount Gambling presents with 23 categories of rules that get the player to 2.
Michael Shackleford aka the Wizard of Odds presents a with 13 rules six if you are an expert poker player and can count 33+, Ax, K2s+, K5o+, Q6s+, Q8o+, J8s+, JT as one ruleone of which is bet the river with "less than 21 dealer outs beat you"; that strategy gets to 2.
On a per unit basis, this puts Ultimate Texas Hold'em roughly in the same range as blackjack.
Proprietary games: Skill requirement and adj.
Bet Per Hand Adj.
That may be true, but it's also a copout.
The simple fact is that even as gamblers continue to get smarter and smarter, there are fewer and fewer games for intelligent gamblers to play.
Card counting in blackjack is being systematically eliminated.
This is completely understandable, in the context that there's no fundamental obligation for the casino to offer a mathematically beatable game.
But as noted earlier, with the increasing adoption of 6:5 blackjack with an additional 1.
And thusly, blackjack is dying a slow death.
Meanwhile, the new proprietary table games are not filling the void left by countable blackjack, and are not meeting the demand for skill games.
Many of the most popular games currently on the market such as Three Card Poker, High Card Flush, and Crazy 4 Poker are extremely simplistic by design.
And aside from perhaps Ultimate Texas Hold'em with an adj.
The point is, if casino operators are serious about marketing to a more sophisticated generation of gamblers — millennials — there's clearly room to offer games with both higher skill components and lower house advantages to compensate.
Jeff is also the best-selling author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced PLO series.
Jeff owns shares of MGM Resorts Click the following article />The Motley Fool has no position in any of the stocks mentioned.
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In this post I will give a foundation for evaluating and comparing the risks associated with card counting blackjack side bets. To accomplish this ...


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The K-O card counting strategy is also known as the Knockout card counting. how the system works can be found in the blackjack bookKnockout Blackjack. the house because of the number of high cards compared to low cards in the deck.


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Compare the top card counting systems to find out which is the right system for you to beat the casino! We've.


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The Death of Blackjack and What Games Are Replacing It | The Motley Fool
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Introduction Continuing fromrecall that card counting systems may be used in two different ways: to vary betting strategy, betting more or blackjack count comparison on each round based on an estimate of the current expected return; but possibly also to vary blackjack count comparison strategy, affecting decisions to stand, hit, etc.
My objective in this still-introductory post is to focus on the first of these two roles, describing how typical card counting systems work, and how they are used to estimate expected return.
The True Count Given a playing strategy which we are currently assuming is the fixed, total-dependent basic strategy from the last postwe can compute the exact expected return for a round played with that strategy, as a function of the shoe composition prior to the deal.
A shoe composition is specified by a vector s indicating the number of cards of each rank ace through ten.
For example, a full n-deck shoe is given bywhere The actual expected return is a complicated non-linear function of s.
A typical card counting system estimates this expected return using the true count TCa blackjack count comparison linear function that a player can compute in his head: basically, the true count is a weighted average of the probabilities of card ranks remaining in the shoe.
Different systems use different tags; for example, the very common Hi-Lo system, first described by 50 years ago, uses the tags Then the true count for a given shoe composition is defined to be where, if we temporarily define n s to be the blackjack count comparison number of cards remaining in the shoe, we see that the true count is just a sum of the card probabilities, weighted by — t.
We need to revise this definition slightly, though, to reflect how the true count is actually computed at the table.
First, the numerator in the formula is the running count RC ; the reader can verify that we can mentally maintain the running count throughout a shoe by adding the tag for each blackjack perfect of rank i that we see dealt, starting with an initial running count IRC of for a full n-deck shoe.
Note that blackjack count comparison IRC for the Hi-Lo system above is conveniently equal to zero for any number of decks; more on this later.
Whenever we need to compute the blackjack count comparison count, we simply divide the running count by n s.
The problem is that it is difficult to blackjack count comparison track of exactly how many cards remain in the shoe.
The solution in most card counting systems is to instead divide by the number of decks remaining i.
For example, if we estimate the number of decks by rounding to the nearest half-deck, then the true count divisor is I will use this definition of the true count divisor for the rest of this discussion.
At this point, I think it is important to note two effects of this change.
First, we have relaxed the amount of mental effort required, by approximating the number of cards remaining in the shoe.
But a second effect, perhaps more important but rarely made explicit, is that we have effectively introduced a scale factor, multiplying all of our previously computed true counts by 52.
This is also helpful for the human player, since the resulting true counts range over a wider interval and may be approximated by integers, instead of being confined to small fractional values typically in the interval -1, 1.
Accuracy of true count estimation of expected return So how well does this work?
The following figure shows the actual expected return— still using fixed total-dependent basic strategy— vs.
Here again, the color is an overlaid smoothed histogram to show the greater density of points near the origin.
Hi-Lo true count, using fixed total-dependent basic strategy.
Can we do better than this?
It turns out that click the following article can… but only if we relax some constraints on the counting systems we are allowed to use.
First, recall that the initial running count IRC for the Hi-Lo system is zero.
At any rate, if we expand our space of possible counting systems to include unbalanced counts, then the Knockout, orwhich counts sevens as +1, has a slightly higher correlation of 0.
The best overall Level 2 count is the blackjack count comparisonwith a correlation of 0.
Note that the optimality of these counting systems depends on the specific rule variations, penetration, and fixed playing strategy assumed so far.
But before diving deeper into betting efficiency, we are now in a position to address playing something probability of getting a 21 in blackjack have where these systems generally suffer.
For example, basic strategy is to always hit hard 16 against a dealer 10.
But we can improve performance by allowing playing strategy to vary based not only on the cards in the current hand, but also on the current true count.
Next time, I will describe how this is done, including new software for evaluating the https://chakefashion.com/blackjack/card-game-blackjack-pick-up-five.html improvement in expected return, compared with the best possible go here from perfect play.

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Provided here is a detailed analysis of the Mentor System for counting cards in blackjack. Learn how to use this system that was originally presented in Blackjack. of multiple card counting systems compared at Norm Wattenberger's QFIT site.


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A full account of how the system works can be found in the Knockout Blackjack by Olaf Vancura, PhD, and Ken Fuchs.
No Need to Convert to a True Count Various card counting strategies exist, but they all try to do the same thing.
They measure the visit web page that a player has over the house because of the number of high cards compared to low cards in the deck.
The K-O Card Counting strategy eliminates the need for a conversion to a true count.
The simple ace-five count I described in the last paragraph is a balanced system.
The unbalanced nature of the Knockout system eliminates the need for doing the division, because it compensates for the additional decks.
For example, in the Hi-Opt II counting strategy, 2s and 3s count as +1, but 4s and 5s count as +2.
That makes it easier to actually accomplish in a casino.
Lots of card counting systems have a single level, but many card counting systems try to be more accurate by including the additional levels.
No Side Counts Another way that some card counting systems try to improve their accuracy is by keeping a side count.
How to Count Cards with the Knockout Blackjack System All card counting systems keep track of the ratio of high cards to low cards by assigning a heuristic value to each card in the learn more here />In a single-level system, that value will blackjack count comparison be +1, 0, or -1.
In the KO system, all cards from 2 through 7 are worth +1.
All tens and aces are worth -1.
The blackjack count comparison with the KO system is that the running count does NOT start at 0.
The starting count is based on the number of blackjack count comparison that are being used—this is what eliminates the need to convert to a true count.
The starting number is calculated using the following formula 4 — 4 X the number of decks.
When the count becomes positive, you increase the size of your bet by that many units.
If you want to become truly proficient at it, you should read the book Knockout Blackjack.

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Donald "Don" Schlesinger is a gaming mathematician, author, lecturer, player, and member of the Blackjack Hall of Fame who specializes in the casino game of blackjack. His work in the field has spanned almost four decades. He is the author of the book Blackjack Attack - Playing the Pros' Way,. Creating the Illustrious 18, an abridged set of the most efficient card counting ...


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Therefore, when the higher-count method tells you that you have an advantage, it's more likely to be accurate. So, *when you place your big bets*, you're more likely to be placing them at a point when you have an advantage. In other words, big-bet losses are less likely with a higher count system.


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