KO vs balanced count
- Thread starter rams
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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.
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.
---
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.
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this is correct, but the way the math works over many many hands negates these disparities. With low counts less than 1/3 of the time early you will be overbetting (slightly), greater than 1/3 of the time you will right on the money, and less than 1/3 of the time you will be underbetting. Same goes at high counts. Net result, same as if you were doing true count calculations.
if you have really thought about how unbalanced counts work you can rapidly look at the discard rack and see if you are at roughly the right count for a certain bet. or if you have calculated depth dependent wong in and wong out points, then you can easily double or 1/2 your bet depending on where you are in the shoe, eeeking out a small net gain from your normal bet ramp.
e.g. using KO, IRC for 6D = -20, When RC = +4, TC = +4. When RC = -4 then TC = +1 (typically). Well the wong in point for KO if I recall (i calculated it awhile ago) is something like after one deck RC = -8 === TC = +1, so if the count rises 12 points in 1 deck, then you have a slight advantage, throw out an extra unit. your advantage from this won't be that great.
when the count is super high, with one deck to go, let's say RC = +10, then your edge is probably closer to TC = +5 or 6. If your max bets come out at RC=TC=+4 then you really can't "under bet" your advantage in a very late high count.....
if you have really thought about how unbalanced counts work you can rapidly look at the discard rack and see if you are at roughly the right count for a certain bet. or if you have calculated depth dependent wong in and wong out points, then you can easily double or 1/2 your bet depending on where you are in the shoe, eeeking out a small net gain from your normal bet ramp.
e.g. using KO, IRC for 6D = -20, When RC = +4, TC = +4. When RC = -4 then TC = +1 (typically). Well the wong in point for KO if I recall (i calculated it awhile ago) is something like after one deck RC = -8 === TC = +1, so if the count rises 12 points in 1 deck, then you have a slight advantage, throw out an extra unit. your advantage from this won't be that great.
when the count is super high, with one deck to go, let's say RC = +10, then your edge is probably closer to TC = +5 or 6. If your max bets come out at RC=TC=+4 then you really can't "under bet" your advantage in a very late high count.....
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