I started this thread because it seems pretty much nobody understands the limitations of reducing everything to a number on a number-line versus taking the deck populations that populate the TC bin associated with that number and dividing that into related deck composition subsets.
First the traditional method:
You will find these two links very useful for visualizing what traditional counting can do. The first one looks at Hilo and gives a glimpse of how the range and frequency of deck compositions in a TC bin fall around the average.
https://www.blackjacktheforum.com/s...e-per-True-Count-using-Combinatorial-Analysis
If you look at the distribution of advantage around each true count average (Look at the second graph. The one in blue with the red dot to indicate the TC bin average for the conditions being investigated using a Combinatorial Analysis), you see the average is about one third of the way from the low advantage edge of the range. That tells you that you are looking at a right skewed graph. That is most of the deck compositions in this graph fall somewhat below the average and rarer deck compositions range much further above the average. This usually pulls the average or mean away from the median and mode for the graph. This is for a simple balanced ace reckoned level one count, Hilo.
The other interesting link compares the best traditional count for computer play against Hilo. It is useful for looking at the difference in distributions for the range of traditional ways of using information. Basically you are moving deck compositions from one TC bin to another TC bin based on the 2, 3, 6 and 7 being counted as half the T in a balanced count and side counting aces to increase the strength of playing decisions. The posts to compare are #17 for Hilo and #30 for the equivalent Hiopt2/ASC TC:
https://www.blackjacktheforum.com/showthread.php?16620-Advantage-at-tc-1/page2
What you are looking at is the change in the width of the advantage bell curve when tagging the 2,3, 6 and 7 as half the other counted cards for an ace neutral level 2 count. Notice that both bell curves are right skewed but the range of advantage is very different. Including the tails Hilo ranges from a -2% advantage t a 3%+ (5%+ range) advantage around the 0.36% average for the conditions being looked, while Hiopt2/ASC -1% to 2% (3% range) around the average of .43%. If you look at the range between the vertical climb areas were the meat of the bell curve is Hilo ranges from -0.5% to 1.25% (a 1.75% range) around the .36% average. Hiopt2/ASC ranges from 0% to 0.9% (a 0.9% range) around the 0.43% average. So arrange deck compositions into more appropriate bins using traditional counting techniques, level2 and ace neutral, narrows the distribution of the advantage bell curve for the deck compositions that populate each TC bin considerably. But you still have the same right skewed shape. Most of the time you are over betting the deck composition by a little and under betting by a lot more rarely.
This is the issue you face when you rearrange everything into very large bins. The results may be more a lot more accurate but bins are still populated by very different deck compositions. If you could find a way to divide things into smaller bins that aren't populated by a random cross-section of unrelated deck compositions you have the chance that the sorting will become something more useful than moving them to another bin that has a large range of unrelated deck compositions. That is what happens when you reduce everything to one dimension, or as I like to call it a number on a number line.
If you figure out how to divide the TC bin of a very accurate (small range of advantage distribution around the TC average like the Hiopt2/ASC distribution rather than the Hilo distribution) betting count indicated by the narrow range of distribution of the TC bell curve around the TC average without adding them to another bin as is cone with a linear system, details about the related deck compositions appear that are washed away if you add them to other unrelated deck compositions. This may open doors for use of that very specific information that the linear approach to using data would never even see. What I have found the most interesting about various types of deck composition distinctions across various games is the ability to shape the short term which makes you look either more threatening or hardly a threat at all and can keep you sane when you go to extreme swings to mild swings in the short term.
In another thread I tried to explain some things but every expert didn't understand what can happen when you group highly related deck compositions together in smaller bins rather than just move the deck compositions to other really large bins where the added insight is diluted away by far more frequent and totally unrelated deck compositions or end up with smaller bins that are just random unrelated deck compositions from the parent population if the TC bin. The added ability to shape results by how related deck compositions behave similarly is lost with either of the latter. So to get the benefit you must figure out ways to group subsets of TC bins into groups of highly related deck compositions. There are a lot of ways to do this but I will leave it at that. I gave one example in the other thread. It is a weaker example but does work well at smoothing the ride in BJ when used properly.
My caution is this type of grouping into related deck compositions can smooth the ride or make it more volatile or have no effect on it. I have found it most useful to simply worry about taming crazy swings rather than SCORE or EV. To tame the ride you will always be giving up a little EV and SCORE. Like I said you can use this technique to increase SCORE and EV but that can cause the ride to the long run to get a lot crazier. Increased buy-ins and wide ranging results on the way to practically the same long run can flag you as a threat. I think the biggest benefit of doing this is lowering buy-in requirements to play through opportunities and smoothing results to being much less extreme in the short run with little change in EV. If getting to pretty much the same long run EV involves much fewer large wins or losses with smaller buy-in requirements you are often not even noticed. Suits worry that you will ruin their day, week, or month. If they know you aren't likely to do that from looking at your history they are much more comfortable letting you play.
So the point is to gather information on specific related deck compositions and figure out how to use that without increasing swings or diluting those specific deck compositions by adding them to a bin filled with much more frequent unrelated deck compositions. By reducing bets for over bet deck compositions that also far comparatively poorly on the doubles and splits it makes does wonders for muting swings, especially downswings. It isn't about maximizing EV. It is about generating EV in a more efficient way. I like doing that by giving up the EV that causes too much volatility from both over betting the actual deck composition and poor performance when you put more money on the table during the round. Often this is exactly why the deck compositions populate the low end for advantage of the TC bin.
I know this is probably more work researching and learning to be a more skilled counter than most want to do. But some either like doing research or are have more counting skills that are going to waste by not being used to their full efficiency. If you are described by both of these characteristics then you might consider learning a much more effective way to gather and use information. You will find all the rules taught by the traditional way of doing things don't necessarily apply in more than one dimension. Many are the exact opposite of what multi-dimension reality is. Where that is the case you can both increase performance and look like a total idiot.
First the traditional method:
You will find these two links very useful for visualizing what traditional counting can do. The first one looks at Hilo and gives a glimpse of how the range and frequency of deck compositions in a TC bin fall around the average.
https://www.blackjacktheforum.com/s...e-per-True-Count-using-Combinatorial-Analysis
If you look at the distribution of advantage around each true count average (Look at the second graph. The one in blue with the red dot to indicate the TC bin average for the conditions being investigated using a Combinatorial Analysis), you see the average is about one third of the way from the low advantage edge of the range. That tells you that you are looking at a right skewed graph. That is most of the deck compositions in this graph fall somewhat below the average and rarer deck compositions range much further above the average. This usually pulls the average or mean away from the median and mode for the graph. This is for a simple balanced ace reckoned level one count, Hilo.
The other interesting link compares the best traditional count for computer play against Hilo. It is useful for looking at the difference in distributions for the range of traditional ways of using information. Basically you are moving deck compositions from one TC bin to another TC bin based on the 2, 3, 6 and 7 being counted as half the T in a balanced count and side counting aces to increase the strength of playing decisions. The posts to compare are #17 for Hilo and #30 for the equivalent Hiopt2/ASC TC:
https://www.blackjacktheforum.com/showthread.php?16620-Advantage-at-tc-1/page2
What you are looking at is the change in the width of the advantage bell curve when tagging the 2,3, 6 and 7 as half the other counted cards for an ace neutral level 2 count. Notice that both bell curves are right skewed but the range of advantage is very different. Including the tails Hilo ranges from a -2% advantage t a 3%+ (5%+ range) advantage around the 0.36% average for the conditions being looked, while Hiopt2/ASC -1% to 2% (3% range) around the average of .43%. If you look at the range between the vertical climb areas were the meat of the bell curve is Hilo ranges from -0.5% to 1.25% (a 1.75% range) around the .36% average. Hiopt2/ASC ranges from 0% to 0.9% (a 0.9% range) around the 0.43% average. So arrange deck compositions into more appropriate bins using traditional counting techniques, level2 and ace neutral, narrows the distribution of the advantage bell curve for the deck compositions that populate each TC bin considerably. But you still have the same right skewed shape. Most of the time you are over betting the deck composition by a little and under betting by a lot more rarely.
This is the issue you face when you rearrange everything into very large bins. The results may be more a lot more accurate but bins are still populated by very different deck compositions. If you could find a way to divide things into smaller bins that aren't populated by a random cross-section of unrelated deck compositions you have the chance that the sorting will become something more useful than moving them to another bin that has a large range of unrelated deck compositions. That is what happens when you reduce everything to one dimension, or as I like to call it a number on a number line.
If you figure out how to divide the TC bin of a very accurate (small range of advantage distribution around the TC average like the Hiopt2/ASC distribution rather than the Hilo distribution) betting count indicated by the narrow range of distribution of the TC bell curve around the TC average without adding them to another bin as is cone with a linear system, details about the related deck compositions appear that are washed away if you add them to other unrelated deck compositions. This may open doors for use of that very specific information that the linear approach to using data would never even see. What I have found the most interesting about various types of deck composition distinctions across various games is the ability to shape the short term which makes you look either more threatening or hardly a threat at all and can keep you sane when you go to extreme swings to mild swings in the short term.
In another thread I tried to explain some things but every expert didn't understand what can happen when you group highly related deck compositions together in smaller bins rather than just move the deck compositions to other really large bins where the added insight is diluted away by far more frequent and totally unrelated deck compositions or end up with smaller bins that are just random unrelated deck compositions from the parent population if the TC bin. The added ability to shape results by how related deck compositions behave similarly is lost with either of the latter. So to get the benefit you must figure out ways to group subsets of TC bins into groups of highly related deck compositions. There are a lot of ways to do this but I will leave it at that. I gave one example in the other thread. It is a weaker example but does work well at smoothing the ride in BJ when used properly.
My caution is this type of grouping into related deck compositions can smooth the ride or make it more volatile or have no effect on it. I have found it most useful to simply worry about taming crazy swings rather than SCORE or EV. To tame the ride you will always be giving up a little EV and SCORE. Like I said you can use this technique to increase SCORE and EV but that can cause the ride to the long run to get a lot crazier. Increased buy-ins and wide ranging results on the way to practically the same long run can flag you as a threat. I think the biggest benefit of doing this is lowering buy-in requirements to play through opportunities and smoothing results to being much less extreme in the short run with little change in EV. If getting to pretty much the same long run EV involves much fewer large wins or losses with smaller buy-in requirements you are often not even noticed. Suits worry that you will ruin their day, week, or month. If they know you aren't likely to do that from looking at your history they are much more comfortable letting you play.
So the point is to gather information on specific related deck compositions and figure out how to use that without increasing swings or diluting those specific deck compositions by adding them to a bin filled with much more frequent unrelated deck compositions. By reducing bets for over bet deck compositions that also far comparatively poorly on the doubles and splits it makes does wonders for muting swings, especially downswings. It isn't about maximizing EV. It is about generating EV in a more efficient way. I like doing that by giving up the EV that causes too much volatility from both over betting the actual deck composition and poor performance when you put more money on the table during the round. Often this is exactly why the deck compositions populate the low end for advantage of the TC bin.
I know this is probably more work researching and learning to be a more skilled counter than most want to do. But some either like doing research or are have more counting skills that are going to waste by not being used to their full efficiency. If you are described by both of these characteristics then you might consider learning a much more effective way to gather and use information. You will find all the rules taught by the traditional way of doing things don't necessarily apply in more than one dimension. Many are the exact opposite of what multi-dimension reality is. Where that is the case you can both increase performance and look like a total idiot.
