Hey guys!

(Sorry guys, I can’t make this post shorter )

I would like to improve the way I count down a deck of cards so as to make it more related to the game itself. I consistently count down a deck in about 23 seconds, but counting a full table, even without making playing decisions is MUCH more difficult to me. However, I really enjoy carrying a deck of cards with me to practice a bit at every little break during the day, so I would like to make these drills more profitable.

It seems that the consensus is that we should practice first by counting down cards one by one and then move to counting in pairs. There lie my problems:
1 – By counting in pairs, although I am using a level-1 system (REKO), I need to make a lot of +2 and -2 calculations. According to Page 259 of Modern Blackjack and to my own experience, this is much harder than to keep incrementing (or decrementing) by one;
2 – I keep looking for pairs that cancel each other out in full table drills, but I end up losing time by doing this and sometimes I even get lost, not knowing if I had already counted this or that card.

By paying attention to the way I actually count down a deck, I noticed that when two cards with the same non-zero tag come along, I sometimes hold the count until a card appears that would help canceling at least some of the previous cards. I decided that I could actually consider this in a slightly different technique to count the cards.

The way I am practicing now has the following advantages:
1 – I don’t make +2 or -2 calculations;
2 – I still profit for canceling pairs;
3 – It creates a framework for counting full tables in an orderly manner.

“Simply” stating, when I see a potential +2 or -2 pair, I count only the first card and wait (fractions of seconds) to see the next one; if it cancels out the previous uncounted card, I ignore the pair and go for the next card; if it is a zero-tag card, I count the previously uncounted card, ignore the zero-tag card and go for the next one; if it has the same tag value of the uncounted card, I simply count the uncounted card and wait for the next one.

Sorry if it’s confusing, I guess it is easier to show an example.

Using the same card sequence below, please note the way the different calculations are done (blank cells means we just ignore, we don’t count):

cards 2 9 5 4 T 5 T A T 3 8 6
1 by 1 +1 +1 +1 -1 +1 -1 -1 -1 +1 +1
by pairs +1 +2 -2 +1
my way +1 +1 -1 +1

The attached image shows 5000 possible realizations of the running count for each approach and the corresponding frequency distributions of the number we are adding or subtracting. (Note that the graphs don’t show zero counts, which are ignored, so the running counts are shorter than they should be.)

crazyCounting.jpg

Summarizing (year alright ):

- By counting one by one, we make an average of 44.2 actual calculations, because we only ignore around 15% of the cards, obviously (8 and 9 in REKO). So, 85% of the time we are making +1 or -1 calculations;
- By counting in pairs, we make an average of 16.5 calculations only, ignoring a total of 38% of the cards. However, we make around 35% of +2 or -2 calculations, which (for me) is VERY burdensome;
- By counting my way, we make just slightly more calculations than by counting in pairs - 18.2% - but we only make +1 or -1 calculations and more than 54% of the time we ignore the cards.

Any thoughts on this crazy analysis?

Thank you very much for reading it all (any survivor?).

Best of luck to you!