Brh Systems Synopsis and History…
by Dr. Brett Harris
The Brh Counting Systems arose out of my attempt to find an alternative system to Wong Halves, which has the same or better betting efficiency, combined with the ease of use and convenience of an unbalanced count. With my formulation of the Unbalanced True Count in mid 1996, there was no longer the constraint that a good true count system had to be balanced. This allowed the flexibility to find a better count while keeping the convenience of a pivot point. I preferred a count which had the equivalent net-unbalance per deck as Red-7, since I had used Red-7 in true count mode and found that a pivot set to approximate a Hi-Lo true count of +2, was very useful for backcounting, rather than the higher (TC=+4) pivot of K-O.
The obvious choice for an alternative Halves-type count was Uston SS, since it had precisely the net unbalance per deck that I desired. However, another choice was to simply set the ‘9’ to zero in Halves, this had the other advantage that the only negative tag value was -2 (assuming Halves doubled). Now I ran many simulations for six and eight deck shoes, for Halves, true count SS, and true count (what is now known as) Brh-I. To my surprise, Brh-I consistently outperformed the other two, despite the fact that both SS (99.4%) and Halves (99.3%) both had a much higher betting correlation than Brh-I (98.8%). Clearly something else was at work. Running simulations using Basic Strategy for playing, each system performed in the order expected. So it gradually became apparent that it was the omission of the ‘9’ in Brh-I which was making the difference. Counting the ‘9’ as a negative card has a detrimental effect on insurance and hard-12 decisions, while it improves the efficiency of hard 14, 15 and 16 decisions. After constructing a playing efficiency calculator along the lines described in Griffin, it was simple to see that while the net effect on the hard standing decisions was neutral, the gain in insurance by not counting the nine was substantial. This effect became even more pronounced when a non-flat betting spread is used.
So, Brh-I became my count for general play. Not only is it easier than Halves or SS, in true count mode it wins more. Independently John Auston arrived at the same count in the context of looking for a better running count system to UBZ11. He named this count AURC, but concluded (correctly) that this count in running count alone was no better than UBZ11, and so he saw little reason to pursue it. It is only in true count mode that its full power becomes apparent. However Brh-I is still a good running count system, and a player has the option to learn the system using the running count, and then upgrade to the full true count version later. The Brh Systems book has indices for running and true Brh-I for all decks and rule variations.
The logical next step was to examine the non-ace-reckoned counts, the most obvious example being Advanced Omega II. Since this system counts the ‘9’ as a negative card, I wondered what would happen if I dropped the ‘9’ from this system. Sure enough, the same results were obtained as in the Brh-I/Halves comparison, dropping the ‘9’ improved the system, and Brh-II was born. However, in this case, there already existed an alternative to AOII which did not count the ‘9’, namely HiOpt-II. At the time, HiOpt-II was a very expensive count to purchase, and while Brh-II was not quite as good as HiOpt-II, it was certainly going to be a lot cheaper to purchase. While this may no longer be the case, Brh-II still possesses the same ease of use as Brh-I in terms of having a Red-7 type unbalance. But Brh-II began to offer other possibilities. While the previous comparisons with AOII and HiOpt-II were true count, with ace-side count, it was also possible to add a 4-point secondary count to Brh-II to give Brh-I for betting. While this is clearly more difficult, in this mode it is more powerful than HiOpt-II, even if a corresponding 4-point secondary count is added to HiOpt-II to give RPC. Similarly the BrhII/BrhI secondary combination is also wins more than the analogous AOII/Halves combination, again because the latter counts do not count the ‘9’.
Now, Brh-II was always intended to be a true count system, since it was constructed to have a high PE. Using Brh-II in running count mode would seem to be inconsistent, since using the running count alone generally results in a very poor PE. But just to see what would happen, I tested it in running count alone, initially testing it using the secondary count to give running Brh-I for betting. To my surprise, this combination actually won more in shoe games than full true count Brh-I and was very close indeed to full true count AOII. I then tested it in single deck, using a simple ace subtraction instead of a traditional ace-side count. All I did was subtract 2 for each ace seen, to give a reverse-unbalanced running betting count. Normally a reverse unbalanced count (one with a negative pivot) is useless for betting, but combined with the positive unbalance of Brh-II and the low pivot in single deck, the procedure was sufficiently efficient to actually outperform true count AOII with full ace-side count. With some help from Karel Janecek who provided me with a modified SBA, I was able to test running Brh-II using a traditional ace-side count for betting. While this combination is not strictly a full running count system, since some deck estimation is required to perform the ace-side count, the ace-adjusted running count is still more than sufficient for betting, and again this combination outperforms full true count Brh-I and consequently Halves, Zen, RPC and other ace-reckoned count in both single deck and shoe games. The discovery of a pseudo-running count system with this sort of power, is I believe a significant breakthrough. The only downside is that different sets of indices must be learned for different numbers of decks, but if a player plays only single deck, or six deck for example, this is not a problem.
There had been opinions expressed that Brh-I was too difficult for many players to use, since it is technically a level-3 count. Since this whole process had arisen out of my investigation into a ‘Red-7’ type Halves count, the logical thing to do was provide a simpler count than Brh-I, but one that was similar enough to use the same indices and betting spreads. There was one such alternative, which was not Red-7, but which many people have confused with Red-7. That is a count which counts every seven, with half the weight of the other cards. This count has a 1% higher betting correlation than Red-7 itself, which only counts every other seven. I named this count Brh-0, and it in fact is to RPC, what Red-7 is to Hi-Lo. Brh-0 is a level-2 unbalanced count, but one which is sufficiently similar to Brh-I, that for all practical purposes, the same indices can be used in either running or true count mode. This way a player can learn all about the unbalanced true count, learn all the indices, but with a simpler count than Brh-I. Only once the player is comfortable with all these aspects, then they can attempt to upgrade the count to Brh-I. To make it even easier, Brh-0 can be modified to count every other seven, I call this Brh-0-lite, and in fact it is the same as Red-7, except the tags are doubled. However, what distinguishes Brh-0-lite from the published Red-7 count from Arnold Snyder, is that indices and betting spreads are provided for use as a true count, as well as a running count system.
While the above is a synopsis of the system content of the Brh Systems Book, the Book contains another major feature. It is be the first system book to provide a full range of Optimal Betting Spreads, using the new theory developed in 1997. I cannot take full credit for this theory, much of the work was also done by Winston Yamashita, ‘Grimy Fellow’, amongst others, in particular, Patrick Sileo independently arrived at similar conclusions a little earlier.
For a wide range of games, a range of Optimal Betting Spreads are provided for each system variant, both running or true count, and in the case of Brh-II for side count or secondary count. With the exception of single deck, there are spreads for different play styles, from play all to full backcounting, for single hands and for spreading to two hands in positive counts. In fact, the Optimal Spread Tables take up by far the largest fraction of the Book, with well over 500 different spread tables.
A 2 3 4 5 6 7 8 9 T Brh-0 -2 +2 +2 +2 +2 +2 +1 0 0 -2 Brh-I -2 +1 +2 +2 +3 +2 +1 0 0 -2 Brh-II 0 +1 +1 +2 +2 +2 +1 0 0 -2 Sec -2 0 +1 0 +1 0 0 0 0 0