rams said:
Does anyone know the logic or mathmatics behind this?
At a certain count, mathematically the RC equals the TC.
Let's say you have a n deck shoe. Over time, 4*n extra low cards come out. Assume that x decks remain (that is, n-x decks have been played). Based on probability, you would expect 4*(n-x) extra low cards to come out - 4 per deck times the number of decks played. As such, your true count is actually [4*n - 4*(n-x)]/x = [4*n - 4*n + 4*x]/x = +4.
Note that this ONLY works at ONE specific running count - when 4*n extra low cards come out. This is known as the pivot - a RC of (IRC + 4*n) is mathematically equal to a TC of +4.
This can actually be generalized for any imbalance - for Red 7, the imbalance is 2, so at a RC of (IRC + 2*n), you have a TC of +2. In general, call the imbalance I (K-O: I = 4, Red 7: I = 2) and you can replace any of the 4's in the first few paragraphs with I. You can create a system with a 3-card imbalance (I = 3). You can create unbalanced systems with more high cards than low cards (I < 0) if you want, but you probably don't want to, as discussed below.
The drawback to K-O (and other unbalanced systems) is that the further the RC moves from the pivot, the less accurate the correlation between RC and TC is. Going back to K-O, if instead of 4*n extra low cards coming out you have 3*n extra low cards coming out, then your true count is [3*n - 4*(n-x)]/x = -n/x + 4. If you have 2*n extra low cards coming out, then your true count is -2*n/x + 4. The further your RC is from the pivot, the more uncertain you will be about the TC (unless you can accurately estimate the number of decks (x), but the whole point of unbalanced systems is that you don't have to estimate the number of decks).
K-O and Red 7 minimize this disadvantage by putting the pivot where precise TC's are worth the most. From a TC of +2 to +4 is where most card counters make their decisions, so having a system with a TC +8 pivot isn't going to be very useful unless you're ramping from 1 to 100 units at TC +8. Likewise, a pivot at a negative TC is useless because you don't really care whether the TC is -1 or -1.5 or -2. A TC of +2 is about where people first get their advantage, and a TC of +4 is about where people max out their bets. So depending where your betting ramp jumps the most, you should pick a system with a pivot close to that point.
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Since this is a FAQ, note that the IRC doesn't matter at all in unbalanced counts. You can choose it to be whatever you want.
- One way is to choose your IRC to be -I*n+I (-20 for 6-deck K-O). This makes your RC at the pivot (IRC + I*n) to be +I (+4 for 6-deck K-O), which is what the pivot is as a true count.
- Another way is to choose your IRC to be -I*n (-24 for 6-deck K-O). Your RC at the pivot is now 0.
- Another way is to choose your IRC to be 0. Now your RC at the pivot is +I*n (+24 for 6-deck K-O).
- Another way (if you don't like negative numbers) is to choose your IRC to be 100. Now you'll probably never have to go negative, but your RC at the pivot is 100+I*n (124 for 6-deck K-O).
Choose the one that is easiest for you.