"Hit on the Left" method for using indices.

Posted by Richard Reid on Saturday, 16 May 1998, at 11:33 a.m.

Greetings:

MathProf correctly indicated below that there is no clear convention regarding the use of indices. The following is a modified version of a BJ21 Green Chip post outlining my method of using indices in addition to providing some reasoning for doing things this way. But, as MathProf mentions, please note that this is not the only method of using indices and others such as MathProf and Don Schlesinger use a different method which works well for them.

Sincerely:
Richard Reid

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(NOTE: The HOTL method is for use with Hard Hit/Stand and Hard Doubling index numbers. There are many exceptions if attempted for Splitting, Soft Doubling and Surrender.)

Hit on the left method

The method I outline below eliminates the delay and potential confusion or frustration that may result when first learning how to use index numbers. If one's index numbers are set up so that one can use my method, then a single rule covers how to use virtually all the Hard Hit/Stand and Hard Doubling index numbers (with only one exception, 17 vs A). If the index numbers are not set up so that one can use my method, then after reading further, one may wish to "change" them. I'll talk about when and how to do this further down the post.

Of course no practical method eliminates error totally, but this method minimizes the worst case error that results from the inherent rounding which occurs when generating integer indices.

If the index numbers are set up according to plan, then the only rule one needs to remember is: RULE: HIT on the left.

That's it. Just remember the rule "Hit on the left."

How to use the "Hit on the left" method

To explain this rule, let's take a look at the following number line.

{ . . ., -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, . . . }

When making a playing decision, simply visualize a separation in the number line immediately to the left of the index number. It doesn't matter if the index number is positive or negative, the same rule applies. For example, if the index number for the play is -3, then separate the number line between -3 and -4 because -4 is immediately to the left of the index number on the number line.

One might visualize a barrier or fence between the two numbers as illustated below.

                     BARRIER

                     BARRIER

{ . . ., -6, -5, -4, BARRIER, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, . . . } 

                     BARRIER

                     BARRIER  

To show what I mean by hit to the left, the picture can be expanded to something like the following:

                                 BARRIER

                                 BARRIER

{ -4, . . ., -3.00002, -3.00001, BARRIER, -3, . . ., -2, -1, 0, +1, . . . } 

                                 BARRIER

                                 BARRIER  

The barrier can be moved even closer to -3 if needed. I am basically saying to hit on any number less than the index number.

Compare the true count to the index number and simply apply the one rule. Hit on the left. This means you hit if the true count is on the left of the barrier. So, for example, if the true count is -6, you hit of course. If the true count is -3.000000000001, then one would still hit.

What should one do if the true count is on the right? In other words, what does one do, for example, if the true count is -2?

Well this depends on the type of index number being used. For Hit/Stand index numbers one will stand. For Hard Doubling index numbers, one will Double.

So, for the most part, if one knows the type of index number being used then one simply needs to remember "Hit on the left" and virtually everything else falls into place. As I mentioned before, the sole exception is 17 vs an Ace.

(REMINDER: This method is geneerally for use with Hard Hit/Stand and Hard Doubling index numbers as there are many more exceptions when Splitting, Soft Doubling and Surrender.)

Analysis of published indices (illustrating when to rewrite the indices)

Of course, this assumes that the index numbers have been set up to allow a person to use this method. No problem. Just make sure that the index numbers are changed (rewrite them if necessary) such that the barrier is set so that one must always "Hit on the left." Let's look at the literature and see what to do.

On p254 in "The World's Greatest Blackjack Book," the remarks to the table indicate to "STAND if True Count >= table number. HIT if true count < table number." Hmmm. This explanation looks an awful lot like our rule "Hit on the left." It should be clear that we can use these index numbers with no adjustment.

On p253 in the 1994 edition of "Professional Blackjack" Stanford writes: "If your count per deck is lower than the number in the table, then hit . . ." This explanation also looks an awful lot like our rule. Again, it seems clear that we can use these index numbers with no adjustment.

Let's look at another example. In the earlier 1981 edition of "Professional Blackjack" on p158, Stanford writes "A number from a table means stand, double down, split or surrender if your count per deck is higher than a number in the table. If your count per deck is lower than a number in the table, then hit . . . If your count per deck is equal to a number in the table, take your pick."

Looks like we can still use the rule as is. Of course, if we increase each of the negative index numbers by one, then the index numbers will be the same as in the new version. So you ask, "What would happen if we just left the index numbers the same and applied the rule as is?" The answer is, "Not much will be different." In negative counts we are betting the minimum or have Wonged out and at the index number, the expected value is close, so there will not be much difference. With the exception of a few reversed index numbers, one can still apply the rule. To be slightly more accurate, add 1 to the negative index numbers and then apply the rule.

How about the index number in "Million Dollar Blackjack"? The explanation on p112 is as follows: "Deviate from basic strategy if the half deck true count equals or exceeds the numbers in the matrix."

Let's say we have a 13 vs a dealer's 3. The index number is -3. The basic strategy play is to Stand. Now the explanation in "Million Dollar Blackjack" says to deviate from basic when the half deck true count equals or exceeds the matrix number. This means at -3 or -4 or -5 or -6, etc. we should hit. To apply our rule, we need to change (rewrite) the matrix number to -2. In fact, if we add 1 to all the negative matrix numbers, we can then dispose of any confusion and simply apply our one rule: Hit on the left (with the exception of two reversal index numbers on p113).

Read the author's explanation of how to use the index numbers and if necessary, adjust the documented numbers. Future authors may wish to make things easier for their readers. Using the "correct" index numbers will allow one to follow the one rule:

Hit on the left.

Enjoy!

Sincerely,
Richard Reid