Modern Blackjack nth Edition

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.