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Why learn a balanced system??

Posted by Brh on 19 February 2000, at 4:32 a.m., in response to Unbalanced Systems , posted by Foreigner on 19 February 2000, at 3:06 a.m.

Foreigner,

You appear to be under the misconception that you need to learn a balanced count in order to do a true count conversion. Since you already know how to count K-O, which is the best level-1 ace-reckoned count, stick with it, it would be a backward step to learn Hi-Lo for instance.

What you can do is to calculate the true count for K-O. In order to do this, your IRC must be set to a specific value, which is different to the recommended value in the book.


IRC = -4 * (Total Decks in Shoe) = - pivot

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That means that for six decks, your IRC must be -24, and for 5 decks it must be -20.

Then by definition, when the running count reaches the pivot, you will have a running count of zero. This is important, because for any balanced count, when the RC is zero, the TC is also zero, this is taken for granted, and corresponds to a neutral deck. But the same principle applies for the Unbalanced True Count (UTC), when the RC is zero, so is the UTC. But since we have started our IRC at -pivot, we know that an RC of zero corresponds to the pivot, and hence the UTC is also zero. If you have ever wondered why the pivot is always accurate in terms of advantage, this is the answer.

You calculate the UTC in exactly the same way as for a regular balanced TC:


UTC = RC / (decks remaining)

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and when the RC=0 (pivot) the UTC=0. But we also know that at the K-O pivot, we are very close to a Hi-LO TC of +4. But this is no coincidence, since +4 is the net unbalance per deck of K-O.

Take a different example, right at the start of the shoe. Since we have defined our IRC to be -4*(total decks), and the UTC is equal to the RC/(decks remaining), then it is obvious that the UTC at the start of the shoe is equal to -4, which again is no coincidence.

So to summarize, using IRC=-4*(total decks), the UTC can be defined in the same way as the TC for a balanced count. But there is one crucial difference, the UTC is shifted backwards by U, where U is the net unbalance per deck of the system, compared to what is called the 'Equivalent Balanced Count'. The EBC is calculated by simply subtracting U/52 from each tag value, so that the count is 're-balanced'. For K-O this means subtracting 1/13 from each tag.

Usually the EBC is not a usable count, since it contains non-integral values, but there may be other known balanced counts which are close enough to the EBC, to allow the indices to be used if the player does not have the facility to generate their own.

The closest known balanced count to the K-O EBC is naturally enough Hi-Lo. This is why a UTC of zero from K-O corresponds to TC=+4 for Hi-Lo. Similarly at the start of the shoe, Hi-LO has TC=0, whereas the K-O UTC=-4. So all you have to do is get hold of Hi-Lo indices, copy the indices into another table, subtracting 4 from each value as you go. Then you memorise the UTC indices for true K-O. So for example, the Hi-Lo index for insurance in six decks is TC=+3, so the TKO index is -1. For the 16-T index is TC=0 in Hi-LO, in TKO it is UTC=-4.

Since these are true count values, they are almost insensitive to the numbers of decks in play, apart from the well known reduction in the insurance index in Hi-Lo, the fewer decks are used. This contrasts with running count indices, which are extremely dependent on the number of decks used, and is why Fuchs and Vancura had to shift the IRC's around to create a running count system which minimises the differences in plays as you go from six to eight deck games for example.

In EVERY mathematical sense, the UTC is just as accurate as the TC for a balanced count. It is a linear predictor of advantage, and in the case of true-K-O, like Hi-Lo, advantage increases by approximately 0.5% per increase of one true count unit.

To read about how the UTC works, and why it behaves mathematically just like a TC for a balanced system, go to Richard Reid's excellent page below. Click on Table of Contents in the left frame, then look under the 'Counting Strategies' heading, and click on the article entitled Unbalanced True Count Proof. This was my original post on the subject from back in 1996, when I discovered how to true count an unbalanced system, based on my dissatisfaction with running count Red-7. This then quickly led me to develop the Ubalo count for Over/Under-13, the first commercial system to use the UTC.
Even now, the only commercially sold UTC systems for regular BJ are Brh-0, Brh-I and Brh-II in my Brh Systems Book. You may notice the discussion on this page between T-Hopper and Ken Fuchs regarding T-Hopper's plans to sell true count K-O.

Cheers,
Brett.

The Mathematics of Blackjack


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