Counting cards

Card counting gives blackjack players an undeniable advantage. This mathematical fact has been proven by numerous scholars, particularly in the United States and Italy. A deck rich in high cards benefits the player for several reasons: it increases the dealer's chance of busting, enhances the profitability of doubling down, splitting, and surrendering, and increases the likelihood of blackjack, which pays out at 3:2. Unlike the dealer, who must follow strict rules, a player can adjust their strategy based on the count.


The aim of card counting is simple: to evaluate and quantify the advantage of high cards by assigning values to each card. This allows players to bet higher amounts when they have a mathematical advantage over the house and bet minimally or even stop playing when the deck is rich in low cards, indicating a disadvantage. There are many different counting systems, developed by experts, that assign various values to the cards.

To analyze the various blackjack counting systems rationally, it's essential to consider several factors:


True and Running Counts - The running count is a simple algebraic sum of values assigned to seen cards. The true count adjusts for the number of decks remaining, providing a more accurate measure of the deck's composition and its favorability towards the player.


Balanced and Unbalanced - Balanced counts, like the Hi-Lo system, end with a sum of zero after all cards are counted. Unbalanced counts, such as the Red Seven or systems by Arnold Snyder, result in a non-zero sum.


Level - This refers to the range of values assigned to cards. For instance, the Hi-Lo system, which uses only +1 and -1, is considered a first-level system.


Role of the Ace - Some systems treat the Ace as a neutral (zero value) card, known as Ace-neutral counts. Others consider the Ace as a negative number, known as Ace-reckoned.


Presence of Side Counts - Some strategies include a secondary count for specific cards, typically the Ace, which is then compared to the base count.


At this point, the natural question arises: "Which card counting system is best for blackjack?" There is no single answer. The most effective system conceivable could only be implemented by a computer, as simplicity often comes at the cost of effectiveness. The key is to find a balance tailored to one's unique abilities (memory, division skills, remaining card evaluation, alertness, multitasking capabilities, goals, etc.).


Effectiveness of a count is assessed through three factors:


1. Playing Efficiency (PE). Measures how closely a count's play decisions (hit, split, double down, etc.) match the optimal game strategy based on knowing the exact remaining cards.


2. Betting Correlation (BC). Assesses how closely a count's betting decisions (how much to bet based on advantage/disadvantage) align with the optimal strategy based on the exact remaining cards.


3. Insurance Correlation (IC). Evaluates how closely a count's insurance decisions align with the optimal strategy based on the exact remaining cards.


No counting system is optimal for all three metrics simultaneously. A system optimal for BC might not be for IC or PE and vice versa. It's also noted that while perfect counts exist for IC and BC, this is not the case for PE. To improve PE to about 0.95, side counts, especially of cards 7, 8, and 9, would be necessary, a task suited for computers or the extremely gifted.


The table below outlines the perfect blackjack counts:

I tre valori "non pesano tutti allo stesso modo". 

Per quanto riguarda un gioco a 6 mazzi, la BC è il valore più importante.

Uno dei più semplici metodi di conta è la strategia detta HILO, (HIght and LOw). Tale tecnica fu introdotta nel 1963 da Dubner.

A ciascuna carta viene assegnato un valore, nel modo seguente:

2, 3, 4, 5, 6= +1

7, 8, 9 = 0

10, J, Q, K, A = -1

Ad ogni carta verrà aggiornata la conta.

Ad esempio, se sortisce 2 noi memorizzeremo +1.

Se sortisce 5, andremo ad aggiungere un ulteriore + 1 al punteggio precedente, onde ottenere +2.

Se sortisce 4 andremo ad aggiungere un ulteriore + 1 al punteggio precedente, onde ottenere +3.

Se sortisce 2 andremo ad aggiungere un ulteriore + 1 al punteggio precedente (+3), onde ottenere +4.

Se sortisce 10, aggiungeremo -1 (ovvero leveremo un unità) dal conteggio precedente onde ottenere +3.

E così via….

Chiaramente le carte neutre non faranno variare il conteggio.

Il valore della conta deve essere rapportato alle carte non ancora viste per ottenere la true count.