does this category = your edge at each true count? Why does it say for Hi-lo i have a .48 win/loss? Does cvcx NOT factor in the house edge? Isn't hi lo .56 per true count - house edge i should have somewhere around the neighborhood of .10 to .20 at +1, why does it say .48 advantage at +1?
No, HiLo is not .56 per TC. That is a rough rule of thumb. TC EV is non-linear and dependent on many variables. CVCX gives the correct edges -- not rough rules of thumb. See http://blackjackincolor.com/truecount2.htm.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Also extreme counts in a pitch game will have TC calculations for partial decks more often. If you are flooring the TC buckets or bins look like this:
3/4 deck left to be played:
TC 0: RC 0,
TC +1: RC +1
TC +2: RC +2
TC +3: can't happen with whole number count tags
TC +4: RC +3
1/2 decks left to be played:
TC 0: RC 0
TC +1 can't happen
TC +2: RC +1
TC +3 can't happen
TC +4: RC +2
TC +5 can't happen
TC +6: RC +3
When the graphs get wavy it is often the sample size but when it zig zags you are most likely seeing the affect of very deep pen (less than 1 deck) along with the rarity of extreme counts being much more represented at the extreme pen situations when certain counts are impossible than the pen that has it as a possibility.
A few things to keep in mind:
1. As the count gets higher, the percentage of hands at that count decreases, substantially. We don’t see TCs of 13 and 14 often. So, a simulation is less accurate at those counts. However, this was a 10 billion round sim – so it should still be accurate enough at those counts.
2. Extreme counts often occur only with unusual remaining card combinations.
3. Extreme counts normally occur later in the shoe. How we estimate the remaining decks can result in jumps in the data like this. This sim estimated by half-decks. So, one card difference in depth can cause the TC to change substantially, even though there may be only a small advantage change, causing such aberrations.
4. At different counts, different indices come into play. Advantage jumps around as these indices become useful.
In summary, blackjack isn’t linear.
[EDIT: Boy, you have to answer quickly around here.]
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Norm that is so trueOriginally Posted by Norm
A few things to keep in mind:
1. As the count gets higher, the percentage of hands at that count decreases, substantially. We don’t see TCs of 13 and 14 often. So, a simulation is less accurate at those counts. However, this was a 10 billion round sim – so it should still be accurate enough at those counts.
2. Extreme counts often occur only with unusual remaining card combinations.
3. Extreme counts normally occur later in the shoe. How we estimate the remaining decks can result in jumps in the data like this. This sim estimated by half-decks. So, one card difference in depth can cause the TC to change substantially, even though there may be only a small advantage change, causing such aberrations.
4. At different counts, different indices come into play. Advantage jumps around as these indices become useful.
In summary, blackjack isn’t linear.
[EDIT: Boy, you have to answer quickly around here.
I gueis you were referring to the second graph, the bar graph, not the line graph. Sorry my bad. The deepest the pen for this graph is 1.19 decks remaining and he used truncation instead of flooring with half deck estimates. The frequency TC frequency differences due to bin sizes have little to no affect here. At the most extreme 1.5 decks estimated as remaining the bins are not equal but the amount of times it happens is small. Of course extreme counts are most likely at extreme penetration but the most extreme 1.5 pen estimate doesn't happen for much of the shoe. When it does those extreme bins are:
1.5 decks remaining:
TC 10: RC +15 to +16
TC +11: RC +17
TC +12: RC +18 to +19
TC +13: RC +20
TC +14: RC +21 to +22
The odd bins are half the size of the even bins.
At 2 decks estimated left to play the bins are equal sized but with 2.5 left we see this affect again to a lesser degree:
2.5 decks left:
TC +10: RC +25 to +27
TC +11: RC +28 to +29
TC +12: RC +30 to +32
TC +13: RC +33 to +34
TC +14: RC +35 to +37
The odd bins are 2/3rds of the size of the even bins.
This TC frequency affect continues at 3.5 and 4.5 decks left but the odds of such a high TC after so few decks are played is small and the amount the bins sizes are different decreases as more decks remain to be played.
This doesn't affect the advantage at each TC but it does affect the sample size at each TC. The extreme TCs will have a small sample size and the odd TC's at that extreme will have a smaller sample size than one might expect. Of course the small sample size simply adds to the error for the advantage estimate from the sim. That could be in either direction. It is interesting that the smaller samplings of TC +9, +11 and +13 all have a decrease in the increase of advantage for the 1 TC increment from their even TC neighbors. As Norm stated BJ is not linear but I think this points to the affect of index plays that kick in at TC +10, +12 and +14.
Here is a curious chart that may shed light on the subject:
http://www.blackjackincolor.com/truecount3.htm
Full indices have the largest advantage at most of the extreme TC's. Look at the advantage increase estimates for the sim for various numbers of indices:
Full Indices, I18 & Fab4, no indices @ extreme TC's:
TC +8: 0.78%, 0.64%, 0.43%
TC +9: 0.65%, 0.57%, 0.37%
TC +10: 0.83%, 0.66%, 0.34%
TC +11: 0.57%, 0.44%, 0.23%
TC +12: 0.82%, 0.57%, 0.28%
TC +13: 0.23%, 0.20%, 0.30%
TC +14: 0.80%, 0.66%, 0%
TC +15: 0.17%, 0.31%, 0.39%
TC +16: 0.8%, 0.62%, 0.20%
It seems for whatever reason the advantage increase to using full indices is lower on the odd TC's. The really weird thing is at TC +13, of the three choices for number of indices, full indices is the worst, I18 and Fab4 is second worst and no indices is by far the best for advantage increase over their TC +12. This gets weirder when you look and see that the affect of full indices are highest at the even extreme TC's but gets muted at odd extreme TC's +9 or higher. At TC +13 and +15 the gain from full indices is 1/4 that of the even extreme counts.
Anyone care to try to explain this? Norm?
Last edited by Three; 09-06-2014 at 12:31 PM.
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