Card Domination Method:
Instead of explaining the method in abstract terms, I believe the ideas can be more easily grasped with the following two examples.
Example No. 1:
Let’s assume the following: You are playing in a four-deck game, the casino uses a single shuffle (remember the double shuffle is no good), the dealer deals out three and one-half decks and your count is -7. Now the dealer will place the – 7 half-deck on top of the discards split the discards into two deck stacks, and begin to shuffle.
Let’s further suppose that she shuffles in half-deck pieces; i.e., she takes half-deck increments off of each stack and intermingles them too build her newly shuffled stack. Now the -7 half-deck is located in the bottom one-deck interval of the newly shuffled stack. Hence, we now know where the bad cards are located.
When we are handed the four decks to cut, we place the cut card as near the top as possible so that as few cards as possible are sent to the bottom. Now, since we know that a half-deck with a -7 count is located at the bottom of shoe, we can start our count at +7 instead of at 0, and we can divide (for a true count) using three and one-half (decks) instead of four (decks). When the one-deck interval is reached, lower the count by 7 and increase the divisor by one-half (deck).
Now, suppose that instead of a -7 half deck, we have an undealt +7 half-deck. Since we are assuming a “balanced count,” this implies the other three and one-half decks total -7
7 – 7 =0
Which also implies that on average each half-deck contained in the three and one-half deck interval will have a count of -1
Hence, on average the bottom one-deck interval of the newly shuffled stack will have a count of +6.
-1 + 7 = 6