#### Relative difficulty of card counting strategies

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, 04-25-2012 at 05:44 AM (18529 Views)
I thought that I’d take a harder look a Blackjack card counting strategy difficulty. The point at which our minds are busiest with counting is just after the dealer has dealt the initial cards, or during the dealing of each player’s second card. At this point, we are counting pairs of cards. We know that many pairs of cards cancel each other, leaving a zero count for the pair, and that this greatly speeds counting as we can ignore that card pair. So, let us start by looking at the count of pairs of cards. The table below provides the percentage of card pairs that add to -6 through +6 for the more popular card counting strategies. For example, with Hi-Opt I, pairs of cards have a count of -2 10% of the time, -1 24% of the time, etc. Ignore the Difficulty column for now.

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 Difficulty HiOpt I 10 24 34 24 10 125 HiOpt I/ASC 10 24 34 24 10 165 Hi-Lo 15 18 35 18 15 130 K-O 15 12 38 14 21 99 K-O Full 15 12 38 14 21 109 REKO 15 12 38 14 21 79 Red Seven 15 16 36 17 16 120 Silver Fox 21 7 43 7 21 128 KISS 2 10 23 33 24 11 116 KISS 3 15 16 36 17 16 120 Hi-Opt II 10 14 19 15 14 17 10 2 217 Hi-Opt II/ASC 10 14 19 15 14 17 10 2 267 RPC 15 12 12 26 5 12 10 10 234 FELT 15 12 12 26 5 12 10 10 214 Omega II 10 5 10 17 20 11 12 11 5 232 Omega II/ASC 10 5 10 17 20 11 12 11 5 282 Zen 10 5 10 17 20 11 12 11 5 232 Mentor 10 10 7 12 24 12 7 10 10 242 UZBII 10 5 10 12 24 10 12 10 10 216 Halves 15 6 7 13 21 12 7 8 8 4 1 273 Uston APC 10 5 5 10 20 8 7 8 11 12 5 1 347 Uston APC/ASC 10 5 5 10 20 8 7 8 11 12 5 1 407 Uston SS 15 6 7 7 25 12 7 6 11 5 1 254

So, how do we come up with a difficulty number? First, let us assign penalties for non-zero count pairs. Obviously, it is easier to count up or down one than add or subtract 2, and easier to add or subtract 2 than 3, etc. I think it is also easier to count up or add than count down or subtract. Generally, even numbers are easier to deal with. Counting by twos is something the mind tends to develop at an early age. So, I came up with difficulty coefficients for each pair count as follows:

-6 8.0

-5 5.5

-4 4.0

-3 3.3

-2 1.7

-1 1.1

0 0.0

+1 1.0

+2 1.5

+3 2.8

+4 3.5

+5 4.8

+6 6.0

We can multiply the coefficient by the percentages in the table for a base difficulty level. The higher the number, the greater the difficulty. Now, let’s tweak this.

The number of columns with non-zero values is the number of different values that the counter must get used to adding or subtracting. Let’s add another penalty. Five times the number of non-zero columns.

Suit-aware strategies, like Red7, add a level of difficulty as this is another concept for the mind to deal with. Add a penalty of 10.

True counting is a clearly more difficult task. Add a penalty of 20.

Side counting is a very difficult additional task. Add a penalty of 40, 50 or 60 depending on the level of the strategy.

On the other hand, compromise indexes are a simplification. KO gets a bonus of 10, as it has three indexes, although some change according to number of decks. FELT gets a bonus of 20 with two indexes. REKO has only one index for any number of decks, which means it really has no indexes, but two basic strategies. Bonus is 30.

Now we have a formula for the difficulty column above.

Disclaimers:

- I assumed infinite decks so I didn’t have to deal with the different numbers for different numbers of decks.
- There are additional difficulty factors, and some of the factors have different effects depending on number of decks.
- Obviously, the difficulty coefficients used are solely my opinion. And, different people have different abilities. I am very interested in other opinions. And am certainly willing to recalculate this table in there is a consensus.