The Pivot Point Revisited
 

We talked about the pivot point in Chapter 3, and briefly again in Chapter 6. Recall that when the running count is at the pivot point, we have good information regarding our actual expectation. Stated another way, unbalanced systems such as K-O are constructed so the pivot point coincides with a known player advantage. As such, it serves as a reliable reference to correlate our betting with our advantage.

Assume we're playing a 2-deck game, and that after one half of a deck (26 cards) is dealt out the running count is +4 (instead of the expected average value of-2; see figure 4, pg. 67). What would an equivalent true count be? Well, the excess count is +4 - (-2) = +6. That is, we are +6 above where we expect to be, on average.

The number of decks remaining is 1.5. Therefore, the true count is +6/1.5 = +4. So you see, at the pivot point of +4, the K-O running count is always exactly equal to a K-O true count of +4. This relationship holds true regardless of the number of decks in play or the number of cards already dealt out, so long as the Knock-Out IRC is calculated as prescribed.

What does this gain for us as practitioners of the K-O system? Well, it means that when we have a running count of +4, we have a very good idea of where we stand because we know, to a high degree of certainty, the expectation at a true count of +4. Remember that the true count is an accurate measure of the prevailing expectation. So when the K-O running count is at the pivot point of +4, we have good information about our expectation, regardless of how many cards remain to be played.

Then, based on a change in expectation of about +0.55% per unit of true count (roughly the High-Low equivalent), we find that whenever our Knock-Out RC is at the pivot point of +4, our expectation is approximately 4 x 0.55% = 2.2% above the starting basic strategy expectation. For a 6-deck game with standard rules, for example, our expectation at the pivot is nearly +1.8%, after accounting for the basic strategy expectation of about -0.4%

   
   
 
     
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