Blackjack Rebel introduces the Table of Critical Running Counts (TCRC), a formula-based method for comparing the KO card-tracking system with the traditional High-Low counting model in six- and eight-deck sequencing scenarios.
Blackjack Rebel, an independent mathematics researcher, has published a new analysis proposing that the Knock-Out (KO) card-tracking system, when paired with a newly formalized Table of Critical Running Counts (TCRC), may offer measurable advantages in accuracy and simplicity over the widely used High-Low sequencing model when applied to six- and eight-deck multi-deck scenarios.
The analysis centers on the primary KO count and the TCRC. Unlike High-Low, a balanced statistical model, KO assigns a value of 1 to sevens, resulting in a structural imbalance of 4 per deck. According to the research, this design allows a running count to be compared directly against precomputed critical values rather than requiring repeated division to convert to a true count.
The critical running count is derived using the general formula crc(t) = 4 × n + (t − 4) × dr, where t is the desired true count, n is the original number of decks, and dr is the estimated number of decks remaining. For a six-deck scenario, the formula becomes crc(t) = 24 + (t − 4) × dr; for an eight-deck scenario, crc(t) = 32 + (t − 4) × dr.
The research identifies three principal advantages of the KO/TCRC approach: theoretical statistical power, improved estimation accuracy, and greater practical ease of use. KO is described as a theoretically powerful level-one sequencing model that provides more accurate estimates than High-Low at positive true counts of three or higher. Because KO’s pivot point occurs at a true count of four, errors in estimating the number of decks remaining have less impact at higher positive counts, allowing the remaining decks to be estimated to the nearest full deck.
Blackjack Rebel is an independent analyst and researcher specializing in probability theory and mathematical modeling related to multi-deck card games. He holds a bachelor’s degree in mathematics from the University of Connecticut and is an Associate of the Casualty Actuarial Society. His work combines formal mathematical analysis with practical, data-driven models developed for students of probability and quantitative game theory.
The KO/TCRC framework is also designed to reduce mental calculation during real-time application. Practitioners can memorize relevant TCRC values or apply the formula directly, rather than dividing the running count by the estimated decks remaining at every decision point. This is intended to make the method more practical in fast-paced, real-time environments where sustained accuracy is difficult to maintain. Most KO index values also align closely with High-Low index values, minimizing the amount of new material a practitioner must learn.
The TCRC analysis forms part of a broader series of publications by Blackjack Rebel examining advanced card-sequencing and probability models. The series progresses from High-Low-based strategies using side counts such as 7m9c, Am6c, and 57m9c, to KO-based approaches involving TCRC, 5m7c, 45m79c, AA89mTc, Am8c, and 7m9c. These works explore how supplementary counts can improve statistical accuracy, expected-value modeling, and decision-making without replacing an established primary counting framework.
The series also extends this mathematical research beyond standard multi-deck models to Spanish 21 variant structures. Related publications examine the High-Low model combined with a 5mAc supplementary count, and a subsequent 455m8AAc method intended to improve statistical efficiency. This progression illustrates how the research develops from foundational counting concepts into increasingly specialized models for different game structures.
Rather than treating KO as simply another sequencing model, the analysis examines how its structure, pivot point, supplementary counts, and critical running counts can simplify real-time decision-making while preserving the method’s underlying statistical principles.
The analysis applies specifically to six- and eight-deck scenarios, where deck estimation and true-count conversion are most demanding. For two-deck scenarios, the research recommends High-Low as the primary model, drawing a clear distinction based on the game’s structure.
More information about this research and the complete publication series is available at: www.blackjackrebel.com.
A preview of the TCRC analysis can be reviewed at: https://www.blackjackreview.com/wp/2025/09/14/ko-with-table-of-critical-running-counts-2/.
, a practical KO card-counting approach designed to improve accuracy and simplify decisions in six- and eight-deck blackjack games.){kind=link}