Unbalanced are equivalent to balanced.
Hi People,
It's been a while, after I worked all this stuff out I went onto other things (quantum gravity anyone ;-).
Firstly let me clear up one thing:
There is NO difference between balanced and unbalanced counts !!!
That sounds weird, but its all about finding the best count with the best correlation to the game your are playing.
For shoe games, betting correlation is king, so we want a system with a high BC. But it is not everything, some playing decisions are important in shoes too.
The count with the highest BC (at the level I call 2.5) is USTON SS, followed by Wong Halves, followed by Brh-I.
A 2 3 4 5 6 7 8 9 T
-2 2 2 2 3 2 1 0 -1 -2 SS (unbal) 99.4%
-2 1 2 2 3 2 1 0 -1 -2 Halves (bal) 99.2%
-2 1 2 2 3 2 1 0 0 -2 Brh-I (unbal) 98.8%
These systems are all very similar and when I say balanced and unbalanced are equivalent, I mean that ALL of these counts can be used with a true count.
You just figure out the NET unbalance per deck (U=+4) for the systems above. Then you take the number of decks in use (eg 6 decks). If you multiply these together and take the negative you get the initial running count.
IRC = -U * (#decks) = -24
Notice at the beginning of the shoe, by definition, UTC = IRC / (#d) = -U.
So for the SS and Brh-I in six decks, the UTC = -4 at the beginning of the shoe. This corresponds to the count of 0 for a balanced count.
This is true for the entire game:
UTC = RC / (#decks remaining).
All indices are just shifted by the amount -U compared to the closest balanced count (Halves(x2) for Brh-I or SS).
Notice that balanced counts are a special case for which U=0.
So for Brh-I or SS, the IRC = -24 for six decks.
Also notice that when the RC=0, the UTC=0, this is the famous 'pivot' point for unbalanced running count systems. At this point, it does not matter how many cards are left, if the RC=0, the UTC=0 and we know for certain what the % advantage is. For these two counts it is the same as if the TC for Hi-Lo was +2, around +0.5% for typical shoe games. So even if you are bad with division, you always know that you are in the positive, whenever the RC>0, the UTC>0.
By defining an unbalanced true count this way, the same accuracy is achieved for unbalanced and balanced counts. This way, optimal bets may be better placed, and playing decisions are as accurate as any balanced count.
Now for a small plug - the playing decision which is most important is Insurance. Usually it kicks in at HiLo=+3. This corresponds to UTC=+2 for Brh-I and SS. But here's where a strange quirk kicks in. It took me a while to figure this one out, but if the 9 is counted as -1 instead of 0, it will screw up insurance decisions, because we are side-betting on the dealer having a BJ, and this depends on the density of Tens. This is enough to actually overcome the difference in BC between SS and Brh-I, and gives true counted Brh-I the edge over both SS and Wong Halves.
So its been a while - enjoy your lesson ;-)
Brett.