Blackjack counting methodology dictates making betting and play decisions by calculating true count and and comparing TC to the appropriate index. There is another way to perform this comparison that has some advantages.
From algebra we know that the expression
if true count >= index
which is the same as
if (running count divided by number of decks remaining) >= index
is equivalent to (by multiplying both sides of the expression by number of decks remaining)
if running count >= (index multiplied by number of decks remaining)
Let’s define running index (or RI) as index multiplied by the number of decks remaining. Comparing RC to RI will always give the same result as comparing TC to the index.
Here are some of the advantages of RI over TC:
1. Multiplication is much quicker and less error prone than division, especially when the number of decks is not an integer. Moreover, the difference is more pronounced when the number of decks is expressed in smaller units such as quarter decks. Speed is of the essence, not only to conserve mental energy but to enable smooth play without giving a tell (to borrow a poker term) by taking time to calculate TC.
Try doing the math for a case where the running count is 11, the index is 3, and there are 3.5 decks remaining. Using TC you divide 3.5 into 11, getting a true count of 3.14 (or approximated as 3+) which is greater than the index. Using RI, you muliply 3 x 3.5 getting 10.5, and running count is greater than the running index giving the same decision result. Try simple and more complicated cases and I believe you will find the RI is never slower than TC.
2. If you are playing at a table where there are multiple players and are not playing first base, RI has an advantage over TC in that you can calculate the RI as soon as you identify the relevant index for your first decision. Unless the players drawing cards ahead of you take enough cards to change the number of decks or fraction thereof, the RI remains constant as players take cards, while the running count may change. You have already done the math to calculate RI, so when it is your turn all you have to do is the comparison of the current RC to RI.
True count may have an advantage over running index when you have to make multiple decisions in the same hand and the running count doesn’t change enough to have to recalculate TC, but these situations are relatively rare.
The RI can help to quantify situations that experienced players know instinctively whether to calculate accurately or to approximate, such as whether to insure. If you have an 8 deck shoe with a 2 deck cut, the running index for insuring (assuming the index is 3) varies linearly from 24 at the start of the shoe to 6 at the end of the shoe, and is easily recalculated as the shoe progresses.