Sonny: Calculating TC to decimal points

[Francis Salmon]

> No, an average of the decimal numbers would
> not provide an accurate index.

And an average of truncated numbers would?May believe who wants!

The TC must
> be calculated in the exact manner as the
> player will calculate it.

What do you know about a player's method to calculate TC.If a TC correctly calculated should be 2.8, he will probably round it up to 3 and you consider this as 2.You're rewarding imprecision.
I told you right from the start that I calculated both TC and Index to the tenth and this has to be more precise. It's a mathematical law.

(This is at the
> heart of simulation.) Billions of plays are
> simulated at all relevant penetrations and
> the results tracked. A weighted average is
> calculated. But, and this is important, the
> truncation/flooring/rounding must occur on
> each play before the weighted average is
> calculated. Therefore, there is no
> "point" calculated. No
> "point" exists.

And what is that weighed average? Isn't that a point? Ok, you truncate it again, so you lose even the benefit of that weighing!

This would be the
> end of index determination if TC advantages
> were linear. But, they aren't.

Not linear?Are you kidding. When I run my CA-program with a loop over all TCs from -10 to +10 with steps of 0.1, I can see with my own eyes that the results are very close to linear to say the least. Every child knows that 1 TC corresponds to a shift in advantage of roughly 0.5%.It's the basis of card counting.

Francis Salmon

[Norm Wattenberger]

> No, an average of the decimal numbers would
> not provide an accurate index.

And an average of truncated numbers would?May believe who wants!

More accurate yes. If that's the way the player counts. And ALL players trucate, round or floor including you. One decimal is no more magical than zero.

> The TC must
> be calculated in the exact manner as the
> player will calculate it.

What do you know about a player's method to calculate TC. If a TC correctly calculated should be 2.8, he will probably round it up to 3 and you consider this as 2.You're rewarding imprecision.

I know because he tells me through the numerous options. And, no I am not rewarding imprecision. I am realistically simming human capability.

I told you right from the start that I calculated both TC and Index to the tenth and this has to be more precise. It's a mathematical law.

Realism is more accurate. Precision is not the be all and end all.

(This is at the
> heart of simulation.) Billions of plays are
> simulated at all relevant penetrations and
> the results tracked. A weighted average is
> calculated. But, and this is important, the
> truncation/flooring/rounding must occur on
> each play before the weighted average is
> calculated. Therefore, there is no
> "point" calculated. No
> "point" exists.

And what is that weighed average? Isn't that a point? Ok, you truncate it again, so you lose even the benefit of that weighing!

No, it is not at all a point. And no, you do not lose that benefit at all.

This would be the
> end of index determination if TC advantages
> were linear. But, they aren't.

Not linear?Are you kidding. When I run my CA-program with a loop over all TCs from -10 to +10 with steps of 0.1, I can see with my own eyes that the results are very close to linear to say the least. Every child knows that 1 TC corresponds to a shift in advantage of roughly 0.5%.It's the basis of card counting.

This is old thinking. You go through all this extra work for extra 'precision' and then throw it all away with a statement that 1 TC is worth .5%. Nonsense. Advantage kicks in as indexes kick in. For example, there will always be a large jump when Insurance kicks in. And advantage for defensive plays meanders all over the TC curve. Forget you ever heard that and you will be much better off.

[Francis Salmon]

> You
> go through all this extra work for extra
> 'precision' and then throw it all away with
> a statement that 1 TC is worth .5%.
> Nonsense. Advantage kicks in as indexes kick
> in. For example, there will always be a
> large jump when Insurance kicks in. And
> advantage for defensive plays meanders all
> over the TC curve. Forget you ever heard
> that and you will be much better off.

1 TC = 0.5 is for me just a rule of thumb but it's still good enough for determining bet size. I'm perfectliy aware that there are differences according to rules and ranges and penetration (see my answer to your post on the main page).
Here I was simply responding to your somewhat exaggerated statement that there is no linearity at all. Your "discoveries" haven't put the rule of thumb out of effect and people can still safely use it for bet sizing.Always making optimal bets is anyway impossible in real life situations.

Francis Salmon

[MGP]

I don't know the answer to all the questions posted here but I'd like to point a couple of unsolicited things out.

> What do you know about a player's method to
> calculate TC. If a TC correctly calculated
> should be 2.8, he will probably round it up
> to 3 and you consider this as 2.You're
> rewarding imprecision.
> I told you right from the start that I
> calculated both TC and Index to the tenth
> and this has to be more precise. It's a
> mathematical law.

No one said it's not more precise. What they said is that the effect is negligible. I'm not sure if they're correct or not but the way I can think of testing this is simple. Simply generate indices with your count as integers. Figure out the advantage by simulating billions as always. Multiply your count by 10 and then do the same thing but using the same betting ramp at the corresponding points and then see what the advantage is.

> Not linear?Are you kidding. When I run my
> CA-program with a loop over all TCs from -10
> to +10 with steps of 0.1, I can see with my
> own eyes that the results are very close to
> linear to say the least.

I don't see why he'd be kidding. Even you admit it's not linear since "very close to linear" and "linear" are not the same thing.

I'm still working on my full CA to get exact values (and I mean exact given an assumption that deck comps probs are based solely on removals and not effected by playing strategies - so they should be closer than any sim), but my CA does do insurance calcs exactly in this manner.

Below are the exact values for insurance expectations for 2D based on the exact Hi-Lo TC's. I used 2 decks because there are fluctuations between positive and negative EV's as seen below. In 1 deck there are also up/down fluctuations but not between positive and negative. It's important to note for this discussion though that even within any given exact TC, there can be many subsets that are pooled and these subsets do not all have the same expectation. So even within a given exact TC results are not linear. Anyways - here are the values:

 

Count		EV		Prob		EV*Prob		Sum(EV*Pr) 

2		-0.008307116	0.002162763	-1.79663E-05	-1.79663E-05 

2.025974026	-0.009294555	0.00057123	-5.30933E-06	-2.32757E-05 

2.039215686	-0.008645806	0.000700784	-6.05884E-06	-2.93345E-05 

2.052631579	-0.003271964	0.0005512	-1.80351E-06	-3.1138E-05 

2.08		-0.006155593	0.00217214	-1.33708E-05	-4.45088E-05 

2.108108108	-0.005095736	0.00056175	-2.86253E-06	-4.73713E-05 

2.12244898	-0.01098195	0.00076957	-8.45138E-06	-5.58227E-05 

2.136986301	-0.006029999	0.000610501	-3.68132E-06	-5.9504E-05 

2.144329897	-0.010309278	0.00010723	-1.10547E-06	-6.06095E-05 

2.166666667	-0.006833983	0.002371784	-1.62087E-05	-7.68182E-05 

2.189473684	-0.00837717	0.000201088	-1.68454E-06	-7.85028E-05 

2.197183099	-0.000248163	0.000546889	-1.35717E-07	-7.86385E-05 

2.212765957	-0.005231034	0.000876093	-4.58287E-06	-8.32214E-05 

2.228571429	-0.00262123	0.000606111	-1.58876E-06	-8.48101E-05 

2.23655914	-0.008040041	0.00026114	-2.09957E-06	-8.69097E-05 

2.260869565	-0.002290383	0.00248055	-5.68141E-06	-9.25911E-05 

2.285714286	-0.004705672	0.000325025	-1.52946E-06	-9.41206E-05 

2.294117647	-0.002896043	0.000604702	-1.75124E-06	-9.58718E-05 

2.311111111	0.000508239	0.001015	5.15863E-07	-9.53559E-05 

2.328358209	0.001355228	0.000598426	8.11004E-07	-9.45449E-05 

2.337078652	-0.003807173	0.000359713	-1.36949E-06	-9.59144E-05 

2.363636364	0.002761779	0.002474197	6.83319E-06	-7.11149E-05 

2.390804598	0.001484744	0.000325971	4.83983E-07	-6.53216E-05 

2.4		0.00100324	0.000602508	6.0446E-07	-5.86583E-05 

2.418604651	0.000661438	0.00111267	7.35963E-07	-5.61188E-05 

2.4375		0.000387156	0.00054501	2.11004E-07	-4.2537E-05 

2.447058824	0.003715623	0.000386717	1.43689E-06	-3.82376E-05 

2.476190476	0.002616516	0.002709996	7.09075E-06	-2.26955E-05 

2.506024096	0.003274295	0.000412141	1.34947E-06	-1.76647E-05 

2.516129032	0.005470656	0.000597707	3.26985E-06	-1.32894E-05 

2.536585366	0.003442248	0.001107006	3.81059E-06	6.72995E-06 

2.557377049	0.006329472	0.000540509	3.42113E-06	1.18356E-05 

2.567901235	0.002619531	0.000423812	1.11019E-06	1.30815E-05 

2.6		0.00442608	0.002701857	1.19586E-05	2.9623E-05 

2.632911392	0.001543417	0.000422358	6.51874E-07	3.18637E-05 

2.644067797	0.010571792	0.00059039	6.24148E-06	4.02047E-05 

2.666666667	0.008050885	0.001092398	8.79477E-06	5.46809E-05 

2.680412371	-0.010309278	2.60629E-05	-2.6869E-07	5.59417E-05 

2.689655172	0.004505934	0.000596071	2.68586E-06	6.03788E-05 

2.701298701	0.013258835	0.000407963	5.40912E-06	6.5272E-05 

2.708333333	0		4.51399E-05	0		6.4461E-05 

2.736842105	0.011655827	0.002785261	3.24645E-05	9.8295E-05 

.

When the index is floored you get an index of 2. If you want the EV maximizing exact index you get 2.363636. If you take the weighted EV of all values from 2 up to but not including 2.363636 you get:

-9.59144E-05 or -0.01%,

or if you use 2.3 as the cutoff which would be the floored TC to 0.1 accuracy we get:

-9.58718E-05 or -0.01%

which represents the lost EV by flooring with a unit bet. So in the case of insurance at least with Hi-Lo in 2D, the potential EV lost is small by rounding.

It's not clear if the aggregate effect over the whole game may be bigger or smaller, but since insurance pays 2-1 which is greater than any other bet, it's probably safe to assume the effect is less for any given play. Since there are 550 different plays - if we assumed the effect was about the same for each play and that we could gain 0.01% on every play - there is a potential to gain of about 5%.

However, it's obvious that not every play has an index that appears during game play - if we assume only 22 plays actually matter - then we could potentially gain 0.2% if the bet were the same at each affected TC and more if you include the effects of the betting ramp. So it may be possible to get 0.3% when including the betting ramp.

It would be interesting to see the results of the index*10 experiment I suggested above.

Sincerely,
MGP

[Phinitum]

Good first choice, I believe that in choosing the insurance decision you gave the 'more precision' supporters the best case they can have. It is linear being based on just the probability of one card being a specific rank.

> Below are the exact values for insurance
> expectations for 2D based on the exact Hi-Lo
> TC's.

[MGP]

> Good first choice, I believe that in
> choosing the insurance decision you gave the
> 'more precision' supporters the best case
> they can have. It is linear being based on
> just the probability of one card being a
> specific rank.

Thanks, but I guess you missed my point. While it is probably the most linear play - it is still NOT linear. The two other advantages of this play are the high return (2:1) and the simplicity of the analysis.

[Norm Wattenberger]

[Francis Salmon]

Sorry I had overlooked your post,otherwise I would have answered earlier.
At least you admit, as opposed to Norm, that there is a gain for using decimals and you also admit that there is an approximate linearity.
Your argumentation wants to show that the gain is too little to be worth the effort but I don't ses where the additional effort lies.On the contrary, this saved me a lot of time because I didn't have to do your extensive simulations and at the table I don't even have to floor or to truncate( I never know which is the one you recommand).
So these little gains are absolutely for free!

Francis Salmon

[pm]

Don mentioned early on that he, Norm, Cacarulo, and Karel Janacek were all in agreement that flooring is the best method to use, and that using decimal places doesn't result in a significant gain in ev.

Obviously you're a proponent of doing your own research and thinking outside of the box and whatnot in order to come up with the best possible solution to a problem. But these four gentlemen are researchers as well; surely you can't believe that all of them missed a concept that is very obvious to you. I mean, look at Karel Janacek alone. The man's got a diploma in math and probability theory, an MBA in finance, and an MSc. and Ph.D. in Mathematical Finance from Carnegie Mellon. You can't seriously believe that a man that's that educated and intelligent, and who has done so much research in the field of blackjack, is dense and unable to understand that decimal points are better than flooring. If this guy doesn't know what he's talking about, then who in the world would? And what about Cac? Don said he probably knows more about index generation than anybody anywhere. Surely you couldn't believe that Cacarulo is actually not very bright and is missing concepts that are obvious to you. And Norm? I may not know much, but I know enough to be able to see that Norm is extremely intelligent; he is always on point for very complicated topics, and like Sonny said, he always comes packing evidence. It couldn't be easy to dismiss what he's saying. Don't you think the case is that these four researchers have a full understanding of your argument and why it is flawed, and that you're not understanding what they're trying to say? Or do you think that they're not understanding what you're trying to say, and if they were able to, they would finally see that their work on this subject was erroneous?

[superdupont]

How something mathemathicaly exact, could not be more precise than simulation?

Index for 16 vs 10 is zero, but all serious player follow BS(except for "camouflage"), BS is the best way to play when RC is zero!

IT RC is+1 we all stay because of the decimals...
And we know that those decimals are money!

But I am not an expert and I shall work on both views because it is very interresting to see intelligent people to not reach agreement on this kind of questions.

FS is not only one of the best european player, but he is also a famous chessmaster, may be because he has a special way of thinking, that I(we) don't have(unfortunetely!).

Anyway, I am waiting for arguments.

Thanks to all contributors and please continue the ddiscussion as you are able to do as gentelmann..........

Superdupont

"Salmon" a fish swimming against the riverstream to reach his goal. On his own way, he can observe most of the other fishes swimming in the other direction.....

It is true?

Soory for my very imperfect english language.

[Norm Wattenberger]

How something mathemathicaly exact, could not be more precise than simulation?

First, no one argues that higher levels of accuracy theoretically improves EV. Only that it is essentially worthless, even assuming that it is error free. Secondly, Salmon's calculations are less accurate then simulation because he uses an invalid method. Simulation can certainly create indexes with one decimal accuracy. CA cannot take into account the cut card effect. And his method isn't even accurate combinatorial analysis as he uses a short-cut based on an invalid assumption.

[Francis Salmon]

Thanks for the support! Are you a chessplayer? Can you give me a subtle hint who you are?
Just curious.

Francis Salmon

[Francis Salmon]