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This article discusses the costs of error in true count conversion for unbalanced blackjack card counting systems.
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Six Deck Unbalanced Red 7 Running Count Conversion to Equivalent Hi-Lo Balanced True Count

 
unbalanced card counting system versus Hi-Lo and errors in true count conversion
 
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Six Deck Unbalanced Red 7 Running Count Conversion to Equivalent Hi-Lo Balanced True Count and Sensitivity of True Count to Errors in Estimating Decks Remaining

By Conrad Membrino
(From Blackjack Forum Vol. XVII #4, Winter 1997)
© Blackjack Forum 1997

rc.u = 23456p + (7p/2) - TAp

Red-7 is almost equivalent to hi-lo count + counting all the sevens as (1/2) each.
rc.u = unbalanced running count = 23456+ (7p/2) - TAp
tc.b = balanced true count
n = number of decks
dp = decks played
dr = decks remaining
rc.u(tc.b) = unbalanced running count corresponding to a balance true count of tc.b
rc.hl = hi=lo running count = 23456p - TAp
rc.u = hi-lo + (7p)/2
if hi-lo has a true count of "t" then rc.hl = t*dr and

rc.u = rc.hl + ExpVal(7p)/2 = t*dr + 2*dp = (t+2-2)*dr + 2*dp = (t-2)*dr + 2*n

rc.u = 2*n + (tc.b - 2) * dr

Number of Decks = 6

Red-7 Running Counts Corresponding to Various True Counts for a Six Deck Game

Six Deck Game rc.unbal
rc.unbal = 23456 + (7p/2) - TAp decks played
tc.bal rc.unbal 1 2 3 4 5
0 12 - 2*dr 2 4 6 8 10
1 12 - dr 7 8 9 10 11
2 12 12 12 12 12

12

3 12 + dr 17 16 15 14 13
4 12 + 2*dr 22 20 18 16 14

 

 

Sensitivity of True Count to Errors in Estimating Decks Remaining

 

Estimation of True Count Using the Red 7:

rc.r7 = red 7 running count n = number of decks
tc = true count dr = decks remaining

rc.r7 = 2*n + (tc - 2) * dr

 

Number of Decks = 8

Red-7 Running Counts Corresponding to Various
True Counts for an Eight Deck Game

Eight Deck Game rc.r7
rc.r7 = 23456 + (7p/2) - TAp decks played
tc rc.r7 3 4 5 6 7
2 16 16 16 16 16 16
3 16 + dr 21 20 19 18 17
4 16 + 2*dr 26 24 22 20 18

 

Estimation of true count with the Red 7
in an Eight Deck Game:

  1. Estimate decks remaining
  2. Compare Red 7 running count with 16, 16 + dr, or 16 + 2*dr for true counts of 2, 3, or 4
  3. Use calculated true count with High-Low strategy indices.*

(*Ed. Note: Membrino is suggesting here that you may use this true count method not only to estimate your advantage, but also to alter your strategy with all Hi-Lo strategy indices. This is not the way I have developed the Red 7 in the new Blackbelt, but if you used a Starting Count of 0, then you could use this true count methology with any standard set of Hi-Lo count-per-deck indices. --Arnold Snyder)

 

Sensitivity of True Count to Errors
in Estimating Decks Remaining:

  1. The closer to the pivot point, the less sensitive the true count is to errors in estimating the decks remaining.
  2. At the pivot point, the true count is independent of the decks remaining
  3. Pivot Point of the Red 7: True Count = 2
  4. Pivot Point of Hi-Lo: True Count = 0
  5. At True Counts ≥ 2:
    (a) Red 7 is closer to its pivot point (tc=2) than the Hi-Lo is to its pivot point (tc=0)
    (b) Red 7 is less sensitive to errors in estimating decks remaining when calculating true count.
    (c) Red 7 gives more accurate true counts than Hi-Lo.

Example:

A = Actual E = Estimated
dr:a = actual dr dr:e = estimated dr
tc:a = actual tc tc:e = estimated tc

Eight Decks

r7 = red 7 hl = hi-lo
tc.r7 = 2 + (rc.r7 - 16)/dr tc.hl = rc.hl/dr

Eight Decks
dr:a = 4 and tc:a = 3

    Red 7     Hi-Lo  
    estimated error   estimated error
dr:e rc.r7

tc:e

(tc:e - tc:a) rc.hl tc:e (tc:e - tc:a)
6 20 2.7 -0.3 12 2.0 -1.0
5   2.8 -0.2   2.4 -0.6
4   3.0 0.0   3.0 0.0
3   3.3 0.3   4.0 1.0
2   4.0 1.0   6.0 3.0



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  Converting a Running Count from an Unbalanced Blackjack Card Counting System to the Equivalent of a True Count
Converting a running count from an unbalanced blackjack card counting system to the equivalent of a balanced card counting system's true count can improve your bet sizing. But in this Blackjack Forum article, Conrad Membrino shows it may not improve the betting accuracy from your card counting very much. Membrino shows the huge effect of inaccuracy in deck estimation in blackjack card counting, and advocates using the simplest unbalanced blackjack card counting systems as is for improved accuracy.