Floating Indexes

In Blackbelt in Blackjack Arnold Snyder relates that one reason why highly rounded indexes don't affect your results is that the actual index number moves around due to various factors, one of which is the current level of penetration.

I've been wondering if some unbalanced counts may unintentionaly be partly accounting for this in the apparent inaccuracy of their indexes early and late into a shoe, improving their results.

Has anbody investigated whether there is a consistent penetration effect on index numbers? Maybe there is a complication in there worth learning, something like "for a 6 deck shoe add/subtract from the index x * (number of decks played)."

I think the standard line of thought concerning "floating indexes" is that the potential gain from their use is offset by an increase in the likelihood of player mistakes and a loss of mental sharpness as a result of all the additional mathematical acrobatics needed to put them to use.

A rounded (or truncated, or floored) index tends to cover a heck of a lot of ground, anyway. If you have a TC of 2.6 at mid-shoe and a TC of 3.4 at 75% penetration, both TCs still round to 3. I suspect that most floating indexes wouldn't be expected to move through a range "wider" than "one" TC unless the number of cards remaining to be played gets incredibly small (which isn't likely to happen nowadays). So, you've already covered a majority of the entire "float" just by using a rounded index.

I'm not optimistic that combinatorial analysis has been done on most indexes through a wide range of penetrations because the number of possible compositional subsets gets enormous, which even today requires a lot of processor time to mush through. Someone may have used effects-of-removal algorithms to track an index through a range of penetrations and come up with good approximations, though.

In single deck, penetration dependent indices have some effect.
I played a lot of SD earlier and I developed a system based on
a modified R7 count with aces side counted.
In my set of indices I generated three numbers [A,B,C] for
the most important plays, corresponding to the 10,20 and 30 penetration levels, respectively.
For example in an R7A1 count system (ace counted as +1) my
SD insurance triplet index would look like [6,7,9].
These indices give an EV of 0.10% for insurance play in flat betting.
On the other hand, using an average index of +7 gives an EV of 0.093%
so there the gain is significant.
I noticed that for indices such as 12 vs 2,3,4,5 and
13 vs. 2,3,4 and 11vs.10, the indices will also vary significantly
with penetration. Usually, the more unbalanced a system is the greater
the variation with penetration will be.
My BJStrike simulator at http://www.dftsimulab.com/bjstrike/index.html
was originally designed for experimenting with
indices at various penetration levels as well as average indices.

/
Karl D.

Thanks for both the comments from both of you.

While I would consider learning a few penetration-based indexes for a balanced count, I agree with AZBL that retrieving those numbers could use up concentration that there would be better uses for. However, Snyder's rounding ends up uses indexes that are 'off' by as much as 2 from what a Wong HiLo counter has (divide by 2 then round to an even number), so there is the possibility for improvement if the reasons for that change not hurting results could be turned to our advantage. My hope was mostly that an unbalanced count could have a 'built-in' exploitation of a penetration effect on indexes. Another possibility is that somebody who exclusively back-counts would have a different average penetration level when they bet, and could have different indexes in a few cases.

My assumption would be that the further an index is from zero the greater the possible effect, and that an index at zero would not show any penetration effect. Of course the floating advantage improving expectation at a count of zero suggests I'm maybe wrong. With my assumption interesting indexes would be 15 v 10, 10 v 10, 10 v A, 16 v 9, 12 v 2. I ignore the 10 splits.

I realize that looking for increased advantage from playing efficiency is 'unfashionable', and probably for good reason. But, until you look you can't know whether there is an advantage to be gained that is worth the mindshare it will occupy.