Blackjack Card Counting Systems: Reversed Counts, Total Count, ABC Best System

I. Marketing Stunt by Casinos: Blackjack Card Counting
II. Not Even the Best Possible Counting System Can Win at Blackjack
III. Total Count: Counting Every Blackjack Card in the Deck

• ABC: The Best Blackjack Card Counting System by Ion Saliu

IV. Combinatorial Mathematics of Reversed Card Counting Blackjack System

• The Best Blackjack Strategy: Shoe-Start System

V. Science and Law in Gambling Matters

• First captured by the WayBack Machine (web.archive.org) on September 1, 2015.

1. Marketing Stunt by Casinos: Blackjack Card Counting

It is noticeable that businesses and economic entities want the world to know that the economy is improving. That's the first tool employed in marketing. Then, the tool of advertising is put to work.

The casinos, as business entities, do the same thing. They let the world know that the economy is getting better and better. Then they advertise by all means available. I know because they opened table games in the newly opened casinos in Pennsylvania. Since table games are a novelty in Pennsylvania, the business in booming. Everybody around here complains loudly that they can't find enough people to hire, especially as dealers at table games! Unemployment is still very high in the U.S. — but they can't find enough people to employ in the casino regions of Pennsylvania! Go figure!

To make things even more dramatic, there are already stories of cheating at blackjack. The card-counters are characters of exciting stories again! Translation: Blackjack is a highly winnable game, people! Come down and play — and leave the casino a rich person!

There is a personal side to this. I get more clearly the impression that some want to involve me again. More messages attack my new mathematics of blackjack odds, probability and house edge. There are more and more public opinions attacking my theory of blackjack gambling streaks (the only theory founded on undeniable mathematics).

They attack my gambling theory by contrasting it with the same fanatic religion of counting cards at blackjack. There are even new counting systems devised! I am informed about such systems most likely by the authors themselves. Possibly, their cronies also bring the BJ counting systems to my attention… you know, trying to make me change my mind! I don't change opinions regardless of what others' opinions are — no matter how loudly they are expressed. Only verification, especially mathematical, matters — that's how I found, and sometimes change, my opinions.

I didn't dismiss the new counting system beforehand. I checked it out in the name of research. I even watched a YouTube video. It was pathetic — it resembled somehow a self-therapy session in a mental institution. The new “blackjack counting system” mixed the 8 and 9 (high cards) with the 2 and 3 cards in the group of small cards. How “small” is a 9-value card compared to a 2? The video showed a blackjack shoe with insanely high positive counts. The three players at the table won very frequently, while the dealer busted way too frequently.

I hit the “author” of the counting system with my remarks in Bishop Snyder blackjack forum. I bluntly opinionated that the “developer”cooked the books in his video. He replied in a manner characteristic to fanatics. He affirmed that, actually, his system had lost in the three sessions previous to the final version of his video! Such a winning system! Lose three consecutive sessions — then fabricate a fourth winning session! The strongest indication of cooking the books: The dealer busted far more often than any of the players! The “blackjack” players rarely busted in the YouTube video. The blackjack dealer busting more than the players combined never happens in a real casino — ever!

• Preaches Bishop Arnold Snyder:
  • "When I self-published my first book, 'The Blackjack Formula' in 1980, and advertised it in 'Gambling Times Magazine' with the catchy, upbeat slogan: 'Card Counters Beware' … stating in the ad that most of the blackjack games available in the casinos of the world were unbeatable with any card counting system … It is easier to make a living writing about this game than it is playing it. I have tried both, and I much prefer the keyboard to the cold green felt."

2. Not Even the Best Possible Counting System Can Win at Blackjack

The counting system I referred to in that forum was not touted as mine. As a "rule" in the twenty-first century gambling world, Ion Saliu is taboo. You might read virulent attacks directed at a gambling author... with no name! They are "frightened" of using the Ion Saliu (or Parpaluck) name — because the mentioning would send new visitors to my website.

So, I said the new card counting blackjack system was the discovery of Mnionin Vintejay, formerly a mathematics professor and currently a Buddhist monk. He spent time in totalitarian jails. Mnionin Vintejay got into trouble because of his computer programming abilities. His software helped him discover that there are no God(s) or entities to blindly believe in. Mnionin Vintejay is monkish only for the purpose of meditation.

This blackjack super card-counting system divides the values into three groups: A, B, C. The first group, A, consists of the low cards: from 2 to 6 — a total of 5 x 4 = 20 cards in a 52-card deck. The second group, B, consists of the pretty-high cards: 7, 8, 9 — a total of 3 x 4 = 12 cards in a 52-card deck. The third group, C, consists of the high cards: Ten and Ace — a total of 5 x 4 = 20 cards in a 52-card deck. From the blackjack player's perspective: Ace (A) is very high card. The player doesn't shoot for an Ace to be counted as 1. We want the Ace to value 11 far more often than not; and thusly make a blackjack natural; or strike 21 when we double down on 10.

There is a total of 12 + 20 = 32 pretty-high and high cards, or 160% more than the amount of low cards. So, the count being so high, inherently leads to the conclusion that the blackjack shoe is favorable to the player to begin with! Well, then, why do we need card-counting systems?!

We start analyzing this counting system in the simplest form: One deck of 52-cards, 100% penetration (all cards are dealt… it must be 0% penetration!), one player against the dealer. I got a distribution of cards like this to begin with (starting with the player, the second card in the round goes to the dealer). 2, 10 | 4, 6 | 9, 4 | 10 – player busted! The new count is obtained via... deducting. 4 low cards came out; one pretty-high card; 2 high cards. We say mentally the new count in this manner: A16, B11, C18. After a while we don't need to specify A B C as we go from low to pretty-high to high. We only say mentally 16 11 18.

Traditionally, they say the new count is high, something like +2. “Raise your bet,” they scream in their videos or CD blackjack software! How about those 11 cards in the middle? It is a pretty good amount of them remaining in the deck. Truth is, the possibilities are countless (permutations or factorial of N can reach numbers of 20+ digits in length). But the real painful truth for the card-counting afflicts is this. The counter who raises his or her bet encounters too many losses compared to the wins. Therefore, the counter loses way too many times big bets compared to the winning big bets. Because of such mathematical reality (named combinatorics or combinatorial mathematics of permutations and arrangements), the BJ card-counter can lose the entire bankroll far more quickly than a non-counter. Honest analysts of the theory of blackjack will stress that painful reality.

Of course, I didn't memorize this counting system! It offers, however, far more information than all other blackjack card-counting systems. I applied the system in the privacy of my home, at my leisure. I wrote down everything on paper, hand by hand. I accurately recorded the counts for each group. I coined also a new parameter: group deterioration. The parameter was derived by comparing the new group count to the initial values of 20, 12, 20. If group A deteriorated at a higher rate compared to the initial value of 20, the remaining deck was considered to be clearly high. If, in addition to deteriorated A, there was deterioration in group B, that constituted the best-case scenario. An increase in betting was mandatory.

But there is the rub. I was unable to find anything consistent in order to win… consistently. I still lost my bankroll more often than not. And that even if such situations would win more hands than the dealer. Problem was the balance between the winning and the losing situations when my bet was bigger. The blackjack card-counting system cannot afford too many misses — the winning cases may not recuperate the increased losses — more often than not.

Those cards in the middle (the pretty-high group) play a very important role. What I noticed, however, is the effect of accented deterioration in groups A and C, but not in group B. It creates more hands to double down. You and the blackjack dealer get equal opportunities regarding such hands. The advantage is the dealer may not double down, while the player is allowed to — and him player wins about 60% of the double downs!

I tell the truth, I don't make a concession next. There are cases when groups A and B are greatly deteriorated compared to group C. Seasoned blackjack players know what that means. There is a much higher probability for blackjack naturals (A + Ten-value). Both the blackjack player and the dealer get equal opportunities regarding such hands. Once again, the advantage goes to the player: He or she is paid 150% (3 to 2, usually; many casinos, however, collapsed to the bad habit of paying the natural 6 to 5). The dealer still gets the same 100% payout (1 to 1) for a natural blackjack. One strong reason to never take insurance on your blackjack natural!

The analysis got much more complicated by enabling two blackjack players. It was a lot more inconsistent on how to increase the bet when group C was less deteriorated than groups A and B. The high cards get distributed among all the participants at the table more often than not. That's one more factor of increasingly fast losses for the counter. You, the card counter, might expect that you'll be the beneficiary of all those high cards! NOT! Too many times, there is an equitable distribution of the cards, including that nemesis of ours, the dealer!

I never analyzed for more than two blackjack players. The inconsistency is insurmountable. Forget about more than one deck of cards! The inconsistency makes the blackjack analysis mission impossible.

I used inconsistency several times throughout. There is consistency, however. In a majority of cases, blackjack card-counting leads to higher losses in shorter sessions. The card counter does need a really substantial bankroll. The bankroll size is of the essence. The counter must withstand all those misses when the bet was raised significantly. And thus the counter must wait (or, should I say, pray) for those extremely rare situations when the count is extremely rich in Tens and Aces. The winning situations create a 50% profit compared to the losing situations (when only the dealer gets the blackjack naturally). And here is another rub. The counter might not get to play those profitable situations. The pit boss already smelled blood. The counter lost serious money. It's time to throw him counter out, before reaching those streaks with lopsided deterioration in groups A, B!

• Would you believe it! The delusionals (card-counting afflicts) already adopted this very system of mine! They call it different names — the handles of posters in various blackjack forums. They even fight over "ownership" (i.e. copyrights) of the best possible card counting system!
• The proponents also blame other counters for not using this system of mine. Apparently, my "counting" system is the only one that wins over blackjack. Counters lose because they don't apply this very counting system. Alas! I stressed again and again that I could not find any formula to guarantee consistent winning with this blackjack system — in the cult-following manner. Because –
• The count per se cannot be a bet-determining factor. However, the count can be applied to alter the decisions (i.e. basic strategy BS) during the current round. There are special circumstances that warrant such deviations from BS (don't ever confuse for standard deviation σ).
• To that end, I improved this system similarly to taking insurance as I presented on the page dedicated to blackjack insurance. Thus, I disregard the Ace and divide the cards in 3 groups of equal sizes –
  • A = the low group: cards 2, 3, 4, 5 (delta = 3 between the lowest and the highest card in the group)
  • B = the middle group: cards 6, 7, 8, 9 (delta = 3 between the lowest and the highest rank in the group)
  • C = the high group: 10-valued cards (10, J, Q, K)

  • The norm (theoretical appearance) is the same for each group. You calculate it by dividing 12 by 3 groups: 4 cards per 12 total cards. It is very close to a quarter of a virtual deck (13). The Ace doesn't alter the norm significantly. Ace simply equals 1 in cases of cutthroat hit/stand situation.
  • It is more accurate, however, indeed it can be easier, if we multiply the number of cards on the table by 0.3 (4/13). In this case, we count the Ace in our calculations.

  • The quarter of a deck (13) is strongly correlated to the FFG deviation as calculated by the Fundamental Formula of Gambling (degree of certainty DC = 25%).
  • I always adjust the norm to the number of players at the table. For example, 7 players plus dealer generate 2*8=16-1 (we don't know what's in the hole) cards on the table (current round and before I make a playing decision, if necessary). In this example, the norm is 5 for each group.
  • If you sit at the first base, the current count is determined by the first two cards of all players. Still, the best place is at the third base, where you can count more cards, thusly increasing the system efficiency. If 7 players, you add to the 16 sub-total as per above. The 6 players before you might add around 4-5 cards; new total: 20; new norm: 6.

  • I can see easily on the table (this round, or previous round plus current round) how each group fares (under or over the norm). The norm for Ace is 7.7%; 1 in 13, of course. No Ace on the table: the chance is higher to get one next.
  • Now, I can make better decisions in cutthroat situations, especially when I have to hit or stand, double-down or hit, split or hit; or stand.
  • In the example with 7 players and my sitting at the third base, if I see 7 or more cards from group A, I stay in the infamous case of 16 versus dealer's 7/8/9/10/A. The bust chance increased dangerously while the chance of improving my hand diminished badly. I do the reverse (i.e. draw) if I counted 5 or fewer cards from group A on the table.

  • If this particular count equals the norm (6), I go with the basic strategy. Keep in mind, the blackjack basic strategy (BBS) was tooled based on norms. It was calculated for the beginning of the deck, considering one player versus the dealer. The beginning of the deck (the shoe start) is composed according to the norms — for each card, for each card-group. Only 3 cards affect the deck composition: the dealer's up-card and the first two cards of the player.

• Worth mentioning again: I never correlate my bet size to the count. A so-called favorable count does not always lead to a winning situation for me. In fact, the winning situations occur less than 50% of the time for me.
• There are other players at the table. It takes a larger number of “favorable situations” to line up… in my favor!
• If the count is rich in Tens and Aces, maybe another neighbor at the table will get the natural 21; perhaps the dealer, instead of me.
• Counter or not, the winning situations hit randomly. I am a lesser beneficiary with an increased number of players at my table.
• No doubt, the best situation for a “favorable count” to come to fruition (especially natural 21) is the heads-up play. The situation deals with fewer cards to be distributed, therefore the favorable line-up has a higher probability. But it is far from implying that every “favorable count” will lead to a winning situation for him Player (the overly confident C(o)unter!) Not to mention how hard it is nowadays to find heads-up play tables in any casino (talking about 99% of all blackjack players).
  • Obviously, the famous High-Low (a.k.a. HiLo or hi-lo) card-counting system can be easily derived from the comprehensive ABC counting system. We simply deduct C from A; the Ace is kind of side-counted. If group A (lows) has 5 cards and group C (highs) has 7 cards, the count is A – C = 5 – 7 = –2. If group A (lows) has 8 cards and group C (highs) has 5 cards, the count is A – C = 8 – 5 = +3. We might as well call such figures true true-count (TTC).
  • We build a much better system, as we do the calculations in the most precise manner by applying the norms. The result is HiLo on steroids. Just a few case-scenarios –
    • A – C = 5 – 7 = –2 TTC (and below — e.g. –3, –4): we play aggressively by hitting any 12, including against dealer's 4, 5 or 6.
    • A – C = 7 – 5 = +2 TTC (and above — e.g. +3, +4): we play aggressively by doubling down even large bets; double down all 10/11-hands versus dealer's Ace; the dealer can't have a Ten in the hole, while the player has a good chance at 20 or 21.
    • We also have a grip on the so-called neutral cards (7, 8, 9). The simple (or simplistic?) hilo counting system has no clue about those cards, as important as they might be.
    • Interesting situation, unique to yours truly —
      B – C = –2 TTC (and below — e.g. –3, –4); I play very aggressively by doubling down 12 versus dealer's 4/5/6. Beware! The dealer will immediately shout to the pit boss: "Double down on 12!"

  • The "traditional" counting systems ignore the number of players at the same table. Say, the "true count" is +2: You double your bet. It doesn't matter... from heads-up to 7 players at the table! That's really bad, as the more players, the worse is diminished the effect of the count.
  • Still, I caution again. Do not increase your bet every time the hilo count is positive! Not even if TTC is positive! The more players at your blackjack table, the more you're going to lose... unless you are the dealer!
  • Also importantly: Disparaging the "negative count" misses out on double-down opportunities, the most favorable situations for the blackjack player. The Ten-valued cards are the only ones that do not contribute to double-down hands. Still, I do not imply that every "negative/low" count leads to hands favorable to doubling down!
  • Comparatively, the natural 21 probability is about 5%; the probability for a legitimate doubling down hand is 8%. Read the in-depth analysis later in this eBook. The chapter "Combinatorial Mathematics of Reversed Card Counting Blackjack Strategy, Systems" deals with blackjack hands that can be legitimately doubled down.
  • Just remember how many double down hands you won... alas! at the minimum bet... because the count was "negative"!
  • If you really think you can't live without counting cards, this very ABC system is the only way to go — period.

Meanwhile, playing my blackjack strategy based on winning - losing streaks does have a solid mathematical foundation. You know that a gambling session consists of wins and losses. The wins and the losses come in streaks of different lengths. The number of streaks of various lengths can be calculated by mathematical formulas. It is undeniable mathematics that a majority of streaks come in shorter lengths (e.g. L, or LL, or WW, or WW, etc.)

The theory of streaks does have virulent opponents. Some vociferously hate my theory. A clear majority of them haters represent the core of gambling authors, developer, vendors, system distributors… and the like. The group also includes casino agents who are paid to attack me. When the attacks in public places don't succeed, the haters can't take it anymore! They attack me directly, in my forums, or in email messages. To the attacks I say: Resquiant in pace, zombies!

3. Total Count: Counting Every Blackjack Card in the Deck

Only computers can count 100% accurately every card. It is fairly easy to write special blackjack software. Even a spreadsheet can be set up to record every card dealt and deduct 1 from total of that particular value. Problem is, nobody is allowed with a computer inside the casino. Yours truly did write such software way back when his compilers were 16-bit. But the program was not meant for use in brick-and-mortar casinos. The software was meant for online play only.

There was an initial time when gamblers believed that the Internet gambling was legitimate and honest. NOT! Most gamblers learned quickly that the online casinos were grossly fraudulent. You played for fun (without real money) — you won huge amounts of "money". When you played for real money — the online bandits took the shirt off your back! It happened to me and to many other online gamblers. I wrote several articles on my website about fraudulent online gambling and Internet casinos.

Nonetheless I have played with several blackjack software applications created by non-casino companies. I found such applications to be honest, as the programs don't care who wins and who loses. I played also manually, by dealing cards from one deck.

I ran the third-party blackjack software on my main computer (desktop). I ran my special card-counting software on my secondary computer (laptop). Every card dealt in the blackjack game on the desktop was entered in my app running on the laptop. At the end of the round, my specialized program calculated 100% accurately and quickly every imaginable chance for the next round. For example — blackjacks: 60 in 1081 or 5.6%; double-down hands: 108 in 1081 or 9.7%; current losing streak (Ls); current winning streak (Ws). Furthermore, the player can see how many cards remain in the deck for each and every point value. Say, 4 Sevens left or 7.7% (the norm); or 2 Aces left or 6.3% (depleted, in this case); etc.

I was able (in the 2000s) to play heads-up; every shuffle was announced and lasted a few seconds; my specialized software refreshes data for a new shoe.

The count per se is not a guarantee of big wins. I won big, however, thanks to tracking the streaks: W for win, L for loss. See the reference below for the specialized Web page I published in the year of grace 2004. Indeed, the player can beat the online casino mercilessly. Without a doubt, every player can bankrupt any online casino as if it were one of Donald Trump's casinos!

Of course, every online gambling operator is aware of such grand-scale risks. Yet, the Internet casinos still operate big-time. I revealed the reason a few paragraphs before: The online casinos cheat big-big-time! Their cheat is also the last word. The casinos guarantee themselves hefty wins, regardless how the gamblers play, or what tricks the players invisibly employ.

Again, even this complete, total card-count cannot beat the game of blackjack automatically. It certainly helps to know the amount of each and every point-value card remaining in the deck (shoe). The biggest obstacle remaining is the sequence of the cards: No count can figure out the card sequences. The difficulty is further increased by the penetration and multiple decks. Not to mention multiple players. The degree of difficulty increased drastically when simulated multiple players at the same blackjack table. Most of “us” lost in a majority of rounds. It happens very rare to see all players win in the same round.

• Axiomatic ones, one incredible situation occurred to me. I call it the pefect card counting case-scenario. Conditions: One deck, no penetration, heads-up play.
• There are 6 cards left in the deck: 2 Aces and 4 Tens. I did a combinatorial analysis and that would be a deadly situation for casinos. They would go bankrupt, therefore they would be forced to discontinue the game of blackjack.
• Simply by enforcing the penetration, the casinos avoided such a devastating situation. The casinos also added more decks of cards, therefore hugely increasing the number of possible card sequences (permutations).
• You can freely download the analysis. The text file contains all 720 permutations of the 6 cards and the results for every case: PermBJ-AATTTT.txt.
• Player splits A + A; Dealer is not allowed to split.
• No insurance was considered, the devastation would be even greater and more outrageous. The player would be thrown out with a vengeance!

  Marks

• D = Dealer win (always 1-to-1).
• P1 = Player win 1-to-1
• *PJ = Player win 1.5-to-1 (blackjack natural)
• **P = Player win 2-to-1 (by splitting and getting 2 hands of 21 against Dealer 20).
• No marks = pushes (ties).

• D = 199 situations of 720; 27.7%
• P1 = 50 situations of 720; 6.9%
• *PJ = 192 situations of 720; 26.7%
• **P = 50 situations of 720; 6.9%
• Pushes = 229 situations of 720; 31.8%

• Player wins adjusted by payouts
• P1 = 50 * 1 = 50
• *PJ = 192 * 1.5 = 288
• **P = 50 * 2 = 100
• Total Player's wins: 438 or 60.8%
• Player's advantage compared to losses (Dealer's wins): 438 / 199 = 220%. WOW!

  This is a very rare occurrence in blackjack, even IF the penetration was 100% (all cards dealt). That's why card counting was devastating for the casinos when they offered single-deck games with no penetration.

  Of course, a TOTAL COUNT was considered in this combinatorial analysis of blackjack. That is, Player counts absolutely all cards dealt. Who can do that in the head?!

  Problem with card counting, including this of the most perfect situations, is the occurrence of favorable situations. They are NOT in the majority, but under 50% of the time. The card counter, however, always increases the bet in positive-count situations. So, he loses more often than not. Overall, the bankroll is lost before finding greatly favorable situations, like the one analyzed here.

  Generating software: PermuteCombine, function P = Permutations, option 3 = Words, Sequentially (lexicographic order)

• Combinatorial Mathematics: Exponents, Permutations, Arrangements, Combinations.

  Penetration adds trillions of permutations to the table, as it were. Even 75% penetration (the best from Player's perspective) takes at least 14 cards out of play. Adding the 6 AATTTT paradise cards: Permutations of 20 is over 2 billion billion. Dividing our best case-scenario of 720 to 2 billion billion possible permutations results in a figure very, very close to zero. Granted, not all those billions of possibilities translate to losses for Player. Player will lose, however, according to the house edge — which I calculated for the first time to be 7.5% (one deck of cards; higher in multiple decks).

4. Combinatorial Mathematics of Reversed Card Counting Blackjack Strategy, Systems

I discovered one paradox regarding counting cards. I ran my special software that calculates the blackjack odds precisely mathematically. Clearly, Player would have an advantage in negative-count situations! There is a high percentage of double down sequences: 4+6, 5+5, 5+6, even 3+6, 4+5. All these situations, however, are squandered because they must occur in a low count (negative). Of course, the dealer and the player have an equal chance to get the double-down hands. You know the difference: the blackjack dealer may not double down.

We simply count the Ten-valued cards as 1, 2, 3... as they are dealt. We don't have to remember the previous rounds. We don't even count the Aces, as they become also 1-values (serving the purpose of doubling down). Of course, we, as the traditionalists, don't bother to count the neutral cards (7, 8, 9). The neutral cards are worthless in the traditional plus-count blackjack systems. In this reversed card counting strategy, however, the neutrals serve well the purpose of doubling down because of cases such as 9+2, 8+2/3, 7+2/3/4/A. We know that the neutrals can't hurt our mission. The 10-valued card is the only one that cannot appear in a 2-card-double-down configuration.

If our simple count tells that more than one third of the cards dealt in the previous round were Tens (10 or J, Q, K), the count is negative. That is, the next round is favorable to double down hands. Two cards in a double down configuration also increase the chance for a Ten-value card to land across our D-down hand!

Mathematics does back up this type of card-counting strategy. We can calculate with acceptable accuracy the probabilities, odds of hands leading to double down situations.

• We work with a single deck. At the beginning of the deck (shoe): Total combinations of 52 cards taken 2 at a time is C(52, 2) = 1326 hands. Possible 2-card combinations that can be double-down hands:
  • 9-value cards AND 2-value cards: 4 9s * 4 2s = 16 two-card possibilities
  • 8-value cards AND 2-value cards: 4 8s * 4 2s = 16 two-card configurations
  • 8-value cards AND 3-value cards: 4 8s * 4 3s = 16 two-card possibilities
  • 7-value cards AND 2-value cards: 4 7s * 4 2s = 16 two-card configurations
  • 7-value cards AND 3-value cards: 4 7s * 4 3s = 16 two-card possibilities
  • 7-value cards AND 4-value cards: 4 7s * 4 4s = 16 two-card configurations

  • 6-value cards AND 3-value cards: 4 6s * 4 3s = 16 two-card configurations
  • 6-value cards AND 4-value cards: 4 6s * 4 4s = 16 two-card combinations
  • 6-value cards AND 5-value cards: 4 6s * 4 5s = 16 two-card possibilities
  • 5-value cards AND 4-value cards: 4 5s * 4 4s = 16 two-card combinations
  • 5-value cards AND 5-value cards: C(4, 2) = 6 two-card hands (5 + 5 can appear 6 ways).

  • Ace AND 2-value cards: 4 As * 4 2s = 16 two-card combinations
  • Ace AND 3-value cards: 4 As * 4 3s = 16 two-card possibilities
  • Ace AND 4-value cards: 4 As * 4 4s = 16 two-card hands
  • Ace AND 5-value cards: 4 As * 4 5s = 16 two-card possibilities
  • Ace AND 6-value cards: 4 As * 4 6s = 16 two-card hands
  • Ace AND 7-value cards: 4 As * 4 7s = 16 two-card combinations.

  • Total possible 2-card hands in doubling down configuration: 262. Not every configuration can be doubled down (e.g. 4+5 against Dealer's 9 or A+2 against 7).
  • We look at a blackjack basic strategy chart for double down. Some 42% of the hands ought to be doubled-down (strongly recommended): 262 * 0.42 = 110. That figure represents 8% of total possible 2-hand combinations (1362), or once in 12 hands.
  • Total natural-21 hands at the beginning of the 52-card shoe: 64 (4.8%). There are 110 / 64 = 172%; there are 72% more double-down hands than natural 21 hands. That's the only reason why the beginning of the card deck is slightly more favorable to the player. But read on!

  • Let's analyze what happens if the card burned at the beginning of the shoe is a Tenner. C(51, 2) = 1275. The amount of other cards is unchanged. The proportion of double down hands is now 8.6%. The blackjack natural percentage decreased to (4 As * 15 10s) / 1275 = 60 / 1275 = 4.7% (slightly down from 4.8%). Evidently, just one 10 less favors the player by improving the double-down chances. Let's not forget that double downs pay 2 to 1, while the natural pays 1.5 to 1 (at best).
  • If 2 extra Tens are out comparatively to the rest of the cards, the scenario improves as far as doubling down is concerned. C(50, 2) = 1225. The amount of other cards is unchanged. The proportion of double down hands is now 9%. The blackjack natural percentage decreased to (4 As * 14 10s) / 1225 = 56 / 1225 = 4.6% (slightly down from 4.7% or 4.8%).
  • Let's consider now the full blackjack table: 7 players plus the dealer. The average blackjack hand consists of 3 cards (per playing agent) for all intents and purposes. Total cards dealt = 8 * 3 = 24. One third of Tens is equivalent to 8. (It is easy to see that one third is equal to the number of playing agents.) The cutoff value for favorable amount of Tens out is 4 over the one third; i.e. 12 Tens out. That makes 24 – 12 = 12 non-Tens out. The 2-card combination total is now C(28, 2) = 378. Total double down cases becomes 54, with a 54/378 proportion of 14% — a significant increase from 8% at the shoe start. The BJ natural chances drop to something like 12/378 = 3.2%. But, again, there is a 75% increase in doubling down possibilities.

  • The chance for double-down situations increases with an increase in tens out over the one third cutoff count. The probability for a natural blackjack decreases also — one reason the traditional plus-count systems anathema the "negative" counts. But what's lost in naturals is gained in double downs — and then some.
  • It becomes a fact now that mathematics favors the negative counts as far as the blackjack player is concerned. The double down cases are the most favorable situations for the blackjack player and they outnumber the natural 21s. The natural is the only mathematical factor that creates an advantage in plus count situations. The natural 21 percentage is significantly lower, however, compared to the double down amount of 2-card hands.
  • But, then again, the unfavorable sequences are prevalent. Therefore the application of the gambling system for streaks betting, Martingale progressions is a must. Read also: Blackjack Reversed Card Counting System.

  Shoe-Start Blackjack System

• It is a mathematical fact that the beginning of a shoe favors the player. There is a 4.8% chance for a blackjack and an 8% probability for a double down hand — 1 in 8 occurrence. That's so because the player is paid 1.5 times or 2 times the initial bet, while the dealer is always paid 1 to 1. Also importantly, the player will not bust in those two case scenarios, while the dealer can bust.
• Even the traditional card counters should be happy about this. I consider 9-value a strong card in the same category as 10 and 11 (Ace). There are traditionalists who include 9 in the high-cards. Some counting systems also count 10 and Ace together as they indicate chances for blackjack natural. The beginning of the shoe offers a +4 true count in my book — take it to the bank.
• I devised my sui generis blackjack system applicable to the beginning of the shoe only. Actually, I applied it only to my very first hand in a session. I always tried to start playing a session immediately after a shuffle. I recorded the results as W (win) or L (loss); I disregarded the pushes. I had a streak of 5 consecutive first-hand losses, while my longest winning streak was 2. You might say it was not a favorable string for my system. I martingaled after 3 consecutive losses; I also martingaled after 3 consecutive single W streaks; that way, I wiped out the losses and made a small profit.
• This blackjack system of mine should be applied to all after-shuffle situations (new shoes). That is, keep a record on the same piece of paper that shows the blackjack basic strategy tables. It is allowed at the blackjack table while you play. Just mark Win/Loss (e.g. LLWLWLWW…) on the back side — and apply the above gambling systems for streaks betting, Martingale progressions.
• This is the most efficient blackjack system of all time. It has the most solid mathematical foundation — the streaks are based on undeniable formulas. The player's losing streaks are the shortest as far as the shoe-starts are concerned.
• Caveat: CSM (Continuous Shuffling Machines) do not have a... beginning of the shoe! The CSMs should be avoided at all costs. The Continuous Shuffling Machines provide the most crooked form of blackjack. The ASM (Automatic Shuffling Machines) are somehow acceptable. The ASMs are simply more tiresome from the blackjack players' standpoint.

• The Best Blackjack Strategy, System Tested with the Best Blackjack Software.
• Test Ion Saliu's Mental Blackjack System to validate gambling streaks strategies with high roller blackjack software; the shoe-start is mainly covered.

5. Science and Law in Gambling Matters

The reverse comes to life when my theory of streaks is debated. All of a sudden, every opponent becomes a mathematics professor! They shout that the streaks can't be analyzed mathematically. And they make that overused irrational “argument”: The player can have a losing streak equal to infinity (sic!) But never the casino (the house, or Player's opponent), mind you! As "Wizard" Lizard of Odds put it: "Heads will come out 200 times in a row". I asked him to prove to me with real data in our lifetime. He reversed himself and replied with another email: "Okay, OK! How about 20 times in a row?" But what's the difference between 200 and 20 when you try to make a point like Wizard's?! "If 20 is equal to 1, then 200 must be equal to 1 as well..."

You know, he was wrong to reverse himself. He was closer to the truth and honesty the first time around. Yes, mathematically it is possible to get 200 Heads in a row in an incomprehensibly large number of trials. The probability to get Heads is always the same: p = 1 in 2. But none of them self-proclaimed experts comprehend that random events consist of two more fundamental elements: degree of certainty DC and number of trials N. Possibly, yes: Get 200 consecutive losses (or Heads, or Tails) in a very large number of trials with an extremely low degree of certainty.

As absurd as it might sound, the blackjack card counters are treated by the casinos in a criminal modality. Even more absurd, the courts of laws in the most law-worship-oriented nation rules in favor of the casinos (reminiscent of the Mafia era). But that's only a casino marketing stunt! Read more:

• Assaults on Mathematics of Gambling and Lottery
• Beware of the Myth and Deception of Counting Cards in Blackjack ~
  It only works for the system vendors; all authors, “gurus”, “bishops” of blackjack card-counting abandoned their “trade” (if they ever did practice it!) — some of them “notorious” started working for the casinos…
• The Best Blackjack Basic Strategy: Free Cards, Charts.
  All three color-coded charts in one file (the free, fast, accurate method), in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.

• Reality Blackjack: Real, Fake Odds, House Advantage, Edge.
  • Gambling related:
  • Doug Grant, Inc. v. Greate Bay Casino Corp: the Decision of the Federal Court of Appeals.
  • The easiest and most straight-forward free roulette system based on wheel bias.

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