I see you and Arnold continue to post nonsense on this subject where I am not allowed to respond. I have been simming True Edge for seven years and have run thousands of such sims. Arnold has never run a TE sim, and I strongly doubt you have either. TE has a significant impact on Zen costing over 20% in many cases. As for the claim that I don�t understand math; then why did ETS give me an 800 on my math SATs? I suggest that you try to prove your case instead of making broad, childish insults and claiming that you are going to release software at some future date that is accurate. The software that you are releasing isn�t even capable of SCORE calculations and therefore cannot be used to accurately compare strategies. It merely squares DI. This is not the same. Also, your claim that my software was used to validate incorrect calculations in BJAP is a complete falsehood.
Now here is the scoop on TC calculation:
Level I systems should use TC divisors of full decks or greater. (Some people actually use two decks or even unusual numbers like 100 cards or tables with different divisors or multipliers. That is acceptable as long as they follow the basic full deck or greater rule.) Level II systems should use TC divisors of half-deck or more. Otherwise you suffer from True Count Compression. I have run literally thousands of sims on this question. Clearly fractional TC's can be used to overcome this problem. But that would be true whether you called the result True Count, True Edge or Glurg. True Edge is a shortcut to calculating advantage. But like most shortcuts, it adds inaccuracies. Not just from TC Compression; but also from the inaccurate assumption that edge is linear over counts.
Fortunately, we now have tools to calculate actual optimal bets instead of relying on shortcut estimates.
Here's an example of this very thing...
A few weeks back, a fairly new counter (I met him at work in a strange way, but we started comparing notes and he seems to know what he is doing) came by my office and asked "what do you think I am doing wrong... here is what happened to me in Biloxi this past week..."
"I went to Biloxi, and had a $1000 trip bankroll and was spreading $5-$40 in a DD game (yes we had compared notes previously, I'd showed him some CVCX data, etc, and he was using the spread I normally use on DD.) I bought in for $300 and started playing. After about 8 hours over 3 days, I had increased my bankroll to $2600 plus. Then over the next two hours of my last session, I ran it all the way down to $1400. What on earth did I do wrong?"
I pointed out that CVCX says the hourly win rate should be about $20 at 100 rounds per hour which is pretty fast for DD unless you get a heads-up game with a really good dealer. His "winnings" represented about 20 hours of play, but he had accomplished that in 10 hours. I then told him "you did nothing wrong. You are on the positive side of variance and did well.
He responded with "But I was up over $1600 at one point. And then I lost most of it." I tried to explain "You ended up with 2x the expected win. You had a good winning streak going. Then you got into a less significant losing streak. Anytime you end up to the "right" of the mean on the normal curve, you are doing just fine.
Before I finish, let me point out this guy has a degree in computer science, so he has a decent math background, and he has a basic understanding of statistics and probability since those are commonly used in CS. But understanding variance, and normal distributions, and sample sizes, and all that does not always transfer to a real-life blackjack understanding. I tried to explain that in BJ, you spend 99+% of your time below your "peak bankroll level". But over time, that "peak" should keep climbing. But that once you reach a peak, that is not suddenly some "floor" that you won't drop below any more. You'll drop below it _many_ times. I also told him that losing that much that fast shows reasonable play. Because he kept pushing the big bets when called for, even while losing. Takes intestinal fortitude to do that...
I started this thinking I would be invincible like Superman. Discovered that kryptonite is everywhere in a casino. :) Once I got past that, I've enjoyed the game, knowing that losing streaks will happen, but that there will be more winning streaks ahead...
that when you say "level 1 should use full decks" you mean that in my normal SD/DD games, that my 1/2 or 1/4 deck resolution is in terms of full decks (3/2 for 1/2 deck played in a DD game)??? (as opposed to being in terms of 1/2 decks where the RC would be divided by 3. rather than 3/2???
One note is that in reading BBiBJ, I got the idea that Arnold uses fractional results. Which means that in a 6D shoe with 4 decks left and a running count of 8, I would get a TC of 2 (8/4) where Arnold would get 1.0 (8/8). But further, in a DD game with 1.5 decks left and a RC of 1, I would get a TC of zero (1 divided by 3/2) where Arnold would get a true edge of .333. Which is 1/2 the value I would get were I dividing in decimals. And .333 is the approximate advantage in a TC of +.666 were I doing decimal math???
I'm not sure I follow why TE is worse assuming you can get used to doing that math in your head... If it were rounded to pure integers, I could see it failing, but in BBiBJ he specifically gives examples with fractional TE values if my memory is any good???
that when you say "level 1 should use full decks" you mean that in my normal SD/DD games, that my 1/2 or 1/4 deck resolution is in terms of full decks (3/2 for 1/2 deck played in a DD game)??? (as opposed to being in terms of 1/2 decks where the RC would be divided by 3. rather than 3/2???
Correct
One note is that in reading BBiBJ, I got the idea that Arnold uses fractional results. Which means that in a 6D shoe with 4 decks left and a running count of 8, I would get a TC of 2 (8/4) where Arnold would get 1.0 (8/8). But further, in a DD game with 1.5 decks left and a RC of 1, I would get a TC of zero (1 divided by 3/2) where Arnold would get a true edge of .333. Which is 1/2 the value I would get were I dividing in decimals. And .333 is the approximate advantage in a TC of +.666 were I doing decimal math???
Yes but.
I'm not sure I follow why TE is worse assuming you can get used to doing that math in your head... If it were rounded to pure integers, I could see it failing, but in BBiBJ he specifically gives examples with fractional TE values if my memory is any good???
I came to the conclusion long ago that sims are useless if they don't sim in the manner actually played. People aren't computers. You can use fractional TCs or fractional TEs, or round, truncate or floor either one. But to compare fractional TEs with truncated TCs makes no sense. Particularly since TE is actually more difficult if done correctly. (That is memorizing different edge's per count for every different set of rules and penetration as well as different house edges.) If he wants to claim it is much easier to use then TC; then he can't use sims that include fractional TEs.
Further to this, people simply do not use fractional TEs. In the 12 years that I have been providing BJ software, zero people have asked for fractional TEs. And my users are not shy. I have been asked for numerous other methods of TC calculation. So many that CVData/CVCX now has a customized method on top of the normal parameters.
Without fractional TEs, TE performs very poorly. Arnold/Radar have not been able to come up with a single sim that shows otherwise. Only comments that current software is all wrong, nobody but they understand card counting, they are the only counters in the world, and a promise that some software will later prove their point. Only the promised software they are talking about cannot calculate SCORE accurately. It only calculates DI squared. SCORE is far more complex to calculate.
I stand by my sims.
However, there are people that apparently do decimal math in their head quite readily. Francis Salmon if you remember his fractional TC discussion. The first counter I knew in 1966 used .xxx EoR numbers for his counting system...
For me, I really don't even do a TC conversion. I play enough using CVBJ and at casinos that the RC and decks remaining are all I need. For example RC=3 decks left=1.5 gives me a TC of 2. But I don't think about the 2, I just habitually know the correct bet and index play without doing the fractional math. At least for SD/DD which is about all I play, I apparently have turned this into a two-dimensional table look-up of some sort that is instinctive...
Also, it would seem that if the TC is done in decimal numbers, that it and the TE numbers would be _identical_ in terms of accuracy, since with decimal numbers, the size of the denomimator has no influence on accuracy...
I don't use TE since I learned the TC method, and I learned to ramp my bet based on the TC, not the true advantage, although it would seem the two are identical if the factor of 2 is taken into account.
Also, it would seem that if the TC is done in decimal numbers, that it and the TE numbers would be _identical_ in terms of accuracy, since with decimal numbers, the size of the denomimator has no influence on accuracy...
Not really. TE and TC are used differently after the division. TE makes the assumption that edge is linear over counts. It isn't.
I was having trouble understanding why all the contentiousness over what appeared to be simply a matter of scaling, precision of calculations, comparing apples to apples, etc. But this point sheds a little different light on it.
So (please correct me if I'm wrong), you're saying that if someone uses TE the way Arnold seems to present it -- i.e. using that number as an estimate of your advantage to calculate a fractional-Kelly bet -- then that system will have a lower SCORE than a system that uses an optimal-bet calculator (whether it pegs to TC or TE), because 1/2 point TE is not always the same thing as 0.5% advantage, and in fact it doesn't really mean the same change in advantage as the count goes higher?
is two different methods of estimating the optimal bet. Each has its problems. One problem with TE is that there really isn't an accurate edge per count. But that is not the major problem. The major problem is that because of the True Count Compression problem described in my Obsolete Thinking post, TE requires fractional counts for acceptable accuracy. Only very few humans will bother with fractional counts. In particular, people looking for what is described as an easier method aren't going with decimal calculations.
TE cannot be advertised as both more accurate and simpler and you can't compare fractional TEs with integer TCs and call it a fair comparison.
... but suppose the sim that ET Fan is apparently going to produce puts the two methods on an equal footing with respect to "compression" by limiting TE betting to 1/2-point "buckets" and TC betting to integer buckets: will the TC-with-optimal-bet-calculator method still show a higher SCORE than the TE-with-fractional-Kelly method?
even if you use half-integer for TE and full-integer for TC, TC-with-optimal-bet-calculator method still show a higher SCORE than the TE-with-fractional-Kelly method. But not enormously higher.
A completely fair test would require numerous different sims with different penetrations and the exact methodologies used.
In Arnold's posting on blackjackforumonline.com, responding to your posting here, he seems to directly disagree:
I switched to using True Edge because it's slightly more accurage [sic] than a standard true count method (not less), and technically, the score with True Edge is higher than with true count methods if you make the adjustments as finely. [Bold emphasis in the original; blue text my emphasis]
I'm not going to keep playing this game where Arnold responds on a forum where I can't respond. But quickly, TE cannot possibly give a higher SCORE under the same conditions since it uses an artificially linearized addantage and no std. dev. while optimally generated betting ramps as defined by SCORE use accurate numbers. One is optimal and the other is an estimate.
Doesn't TC assume that the count is linear over advantage? For example, most use the advantage = house_edge + 2 * TC as a rough approximation...
I personally don't believe in linear behavior here either, as at extremely high counts, the advantage must start to fall, since if the deck has nothing but 10's left our advantage is back to zero.
Doesn't TC assume that the count is linear over advantage?
NO.
For example, most use the advantage = house_edge + 2 * TC as a rough approximation
That's closer to True Edge, not optimal betting by True Count. And that's one of the problems I'm talking about. These are rough estimates. Optimal bet calculators make exact calculations.
And I'm really getting tired of the absurd lies they are posting on BJFO. I haven't said one of the things they claim. These people cannot handle an honest debate but simply make up stuff and refuse to allow responses.
True Edge was not devised for optimal use in computer sims, or to make programmers happy. It was devised for the use of actual players in real life play in real casinos. A link to Arnold's explanation of the problems with Norm Wattenberger's thinking on compression and the rest of this is included below.
Arnold has indeed run sims on True Edge and optimal betting, including the betting methods you advocate. That is why he recommends True Edge, as he explains in the post the link will carry you to. Norm's software is misleading about the results players will have in the real world.
I object to your characterization that the Blackjack Forum web site makes fun of card counters. I don't remember anyone ever making fun of a card counter or card counting. 90% of our library is about card counting. Many of our moderators are not hole carders or shuffle trackers, but are in fact primarily professional card counters.
My problem with your approach to card counting is that I view it as a cookie cutter approach that emphasizes going after very small improvements in edge with unrealistic means. The fact is, there are much simpler and more realistic ways to go after significantly bigger edges with card counting.
I want different free software on the Blackjack Forum site because I am never able to simulate with your software what I feel a player actually needs to do to in real world casinos to beat games with a high edge over the long term with card counting. We do not discuss these techniques on the public board, because casino people have access to those boards and that would destroy the techniques we are using. But we are impatiently awaiting the arrival of the software so that we can start going over these techniques in a meaningful way on our Players Only board.
I know that bj21ers tend to love your software. IMHO, that is because they have not had access in a very long time to a meaningful alternative.
I note you provide no argument whatsoever against a single one of my points here. Only on a forum where I am barred from responding.
Arnold is upset because independent sims show that True Edge does not perform as well as he claims. I am barred from responding. You post a link on bj21. I respond. Arnold posts again on his site, and you and the other people at your site claim that I said things I never said and that my sims make assumptions they do not make. You again post to bj21 a link to Arnold�s response. This is comical. Can�t he stand up for himself? Can�t he discuss this directly where the actual words I used are visible instead of absurd, made up words falsely attributed?
Look, I have been simming True Edge for seven years. If Arnold has a problem let him post where I am allowed to respond or call me � he has my number.
Meanwhile, you have your clique working overtime. One of your group tried to get my announcement of CVCX Online busted. Having failed, he posted a slur on my sex life (thank you post-busters for removing it.) And your clan has posted comments that I don�t understand math, don�t understand counting, no one but you understands pro play, I am Whatascammer, I am Whataliar, I have a persecution complex, my software is full of bugs, My software was used to create false numbers in BJAP (an absolute lie,) no one should buy my software because you are going to produce free �professional� software (that even your own programmer admits can�t sim any of this or much of anything else) and on and on and on. Just in the last couple of days despite the fact I haven�t posted a word there! Just the way you have handled disagreements with so many, many other people.
These forums can be extremely useful. I was a bit worried when Stanford started this site because of the anonymity of posters. That is one of the reasons I use my true name. You proved my point when you posted as �Blackjack Historian� claiming Don stole the Illustrious 18 from your Arnold or your other aliases claiming Don�s articles in BJF were filled with errors. Incredible. You continue to prove my point with your other aliases (fake_handle, george_crumb, and on and on and on) claiming all manner of nonexistent crimes by everyone you dislike.
Look, we are supposed to be working against the casinos not each other. You and I have met a couple of times. I�ve known Arnold for over a decade. If there is a disagreement let us discuss it. One handle per person on a site that doesn�t bar all competing thought and doesn�t stoop to appointing a moderator that publishes photo�s of other forum managers. I have simmed orders of magnitude more BJ hands than anyone else alive. I give away more functionality in my demos and on my sites than any software you have any chance of creating. That does not mean that I am not willing to listen to suggestions. Just ask my users. But I will not compare raisons with oak trees. Comparisons only make sense between realistic scenarios.
And don�t say I�m impolite. I didn�t give away who you are or why you are making these posts.
I personally don't believe in linear behavior here either, as at extremely high counts, the advantage must start to fall, since if the deck has nothing but 10's left our advantage is back to zero.
First, for anything but deeply-dealt SD, this would occur so rarely that it would have no practical impact on edge. Second, most people (99%+ probably) use ace-reckoned systems. Advantage just gets bigger and better with each TC. A deck full of aces and tens actually has a much higher edge than would be implied by the TC point *.5 methodology most use, even with refinements to allow for insurance and the like.
that nothing but 10's and A's is good for us.
My point was that clearly, at some point up the TC ramp somewhere, advantage stops increasing and starts to go back down. In SD games I have generally side-counted aces anyway, since it is not much extra work, and I have played with this in DD games, to improve insurance accuracy. So it's possible to know there are no aces.
My only lack of information is _where_ this inflection point occurs in the advantage vs TC plot. I've seen some ridiculous TC values a few times, and noticed a matching ridiculous number of pushes, although I don't know for certain whether my advantage had slipped or this was just variance (I've seen ridiculously high TCs and gotten completely smashed also, but again that doesn't mean my advantage has slipped any...)
This might be a programming project for me a little later on, to randomly "stack the deck" at TCs from 0 to 52 and see what happens to the number of hands won/lost/pushed.
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