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Does advantage always increase with the count?

Posted By: Norm Wattenberger
Date: Thursday, 4 January 2007, at 2:48 p.m.

For some time I’ve been saying that advantage does not increase linearly with the True Count. But, does advantage at least increase with each count? By a strange coincidence, two CVCX users e-mailed the exact same interesting anomaly. Using Advanced Omega II at single deck with reasonably deep penetration, the advantage at TC +3 is lower than the advantage at TC +2. Is this possible? Yes, it turns out. For example, AOII, single deck, H17, nDAS, 62% penetration, two players, remaining cards estimated to quarter-decks; the advantages by TC are:

+1 0.35%
+2 1.11%
+3 0.85%
+4 1.42%
+5 1.50%
+6 2.30%

There is a dip in the advantage at TC +3. Why does this occur? First it should be understood that it does not occur if you divide the Running Count by the exact number of remaining cards. But, most people at single deck divide by quarter decks remaining. Clearly this introduces some error in the True Count calculation. In single deck this also introduces some interesting effects. For example, using HiLo at single deck with quarter-deck estimation and Flooring; you will not see a True Count of +3 or +7. You can see this in the Blackjack Attack tables. In a level 2 count you will see all the True Counts; but some occur only in certain circumstances. For example, a TC of +3 will only occur in this particular game in the second or third round of play. This means that the TC at +3 will be skewed when estimating by quarter decks. It also turns out that to obtain a TC of +3 that early in the deck, an unusual deck composition is likely to exist. A 37% higher than normal number of Aces will have been dealt. With AOII, Aces do not affect the TC – but the dealt Aces decrease EV.

There is also another minor effect. As penetration increases; the advantages at each TC increases. But not the advantage at a TC of +3 because there are no instances of a TC of +3 at deeper penetrations. So while the other TCs see an increasing advantage with increasing penetration – TC +3 remains frozen at the lower level.

So, it is possible that a higher TC does not mean a higher advantage in narrow circumstances.

Serious Blackjack Software

Messages In This Thread

• Does advantage always increase with the count? (views: 690)
  Norm Wattenberger -- Thursday, 4 January 2007, at 2:48 p.m.
  • Re: Does advantage always increase with the count? (views: 422)
    Brick -- Thursday, 4 January 2007, at 6:51 p.m.
    • Re: Does advantage always increase with the count? (views: 374)
      Norm Wattenberger -- Thursday, 4 January 2007, at 7:03 p.m.
  • Re: Does advantage always increase with the count? (views: 390)
    OldCootFromVA -- Friday, 5 January 2007, at 10:09 a.m.
    • Re: Does advantage always increase with the count? (views: 332)
      Magician -- Saturday, 6 January 2007, at 5:51 a.m.
      • Re: Does advantage always increase with the count? (views: 356)
        wantabe -- Saturday, 6 January 2007, at 10:54 p.m.
        • I used +6 *NM* (views: 291)
          Norm Wattenberger -- Sunday, 7 January 2007, at 8:45 a.m.
        • Re: Does advantage always increase with the count? (views: 350)
          Magician -- Sunday, 7 January 2007, at 11:51 a.m.
          • Interesting (views: 365)
            Norm Wattenberger -- Sunday, 7 January 2007, at 12:39 p.m.
      • Re: Does advantage always increase with the count? (views: 339)
        OldCootFromVA -- Monday, 8 January 2007, at 9:23 a.m.