Sonny: Calculating TC to decimal points

[Sonny]

I?m so intrigued by this concept that I wanted to start a new thread about it.

> An extra 0.6 means an extra advantage of 0.3%.

Sounds good. Recognizing a greater advantage means that I can push out a bit more money and get more action per hour. Have you been able to simulate using this method? I would be interested to hear how much this method can add to a player?s win rate. Wouldn?t it be similar to just adjusting your TC by half-decks (or, in this case, tenths of a deck) instead of full decks? You would just double all of your indices instead of adding decimal places.

> In other words,I don't correlate my bets
> strictly with TC, I correlate them with the
> actual advantage.

That?s an interesting concept. So you have memorized the fact that a 2% edge occurs at, say, 3.3 and calculated your bet spread that way?

> My CA-program was designed with the infinite
> deck approach.They work extremely well with
> multiple decks but their might be some slight
> distortions for DD because of the increased
> influence of the initial hand.

What about the argument that, because of rounding and whatnot, indices are not terribly accurate in the first place? If the numbers are not completely accurate at the whole number value, why bother with the fractional part?

-Sonny-

[Don Schlesinger]

There's virtually no advantage at all to calculating TCs to a decimal point. You can't claculate the edge of a TC a tenth at a time.

When we say that your edge at TC = 3 is, say, 1.0% or 1.5%, that value is an average edge over the entire interval. It isn't the edge at exactly 3. Therefore, it isn't true that, at 3.6, you have six-tenths more edge than a person would think, using just whole numbers, because the edge that he tells himself that he has at +3 is really the precise edge of about 3.4 or so (the edge isn't leinear, because the frequency of the TC decreases as one goes from left to right within the interval.

You need to trust me on this: What you or Francis would be trying to accomplish is a monumental waste of time.

Don

[Francis Salmon]

> You need to trust me on this: What you or
> Francis would be trying to accomplish is a
> monumental waste of time.

Trying to accomplish? I have put this into practice several years ago and it was anything else than a waste of time.
My concept is different from yours. For me an index (or a TC) is a fixed value, in other words a point on the number scale and as we have learnt from the old Greeks, a point has no dimension.
This point reflects a certain card distribution which in turn determines the advantage and the playing strategy in a given situation. Common sense says:The more precisely we calculate the point, the more accurately we can deal with the situation.

Francis Salmon

[Don Schlesinger]

> Trying to accomplish? I have put this into
> practice several years ago and it was
> anything else than a waste of time.

Francis, you know better than to think that you can quote personal results to support a mathematical concept. Read Norm below. I'm not going to debate this with you, and you are entitled to your opinion. This doesn't work the way you think it does, and the extra edge that you are quoting is surely nonexistent.

Don

[Francis Salmon]

I didn't except you to debate. I'm used to your backing out as soon as it gets tricky.
Anyway,you have a wedding speech to prepare:-).
So, have a nice day!

Francis Salmon

[Francis Salmon]

> Sounds good. Recognizing a greater advantage
> means that I can push out a bit more money
> and get more action per hour. Have you been
> able to simulate using this method? I would
> be interested to hear how much this method
> can add to a player?s win rate.

Sure I have simulated my system and the results were very encouraging and that's why I'm using it professionally now.As to the gain in win rate, I have no means of comparison but you can easily get an idea: If you can put out $100 more because of the additional 0.3%, this single situation added exactly 30 cts to your win rate. Assuming we get about 20 such situations an hour,your hourly win rate has risen by $6.

Wouldn?t it
> be similar to just adjusting your TC by
> half-decks (or, in this case, tenths of a
> deck) instead of full decks? You would just
> double all of your indices instead of adding
> decimal places.

I don't quite see your point here but let me say that I don't see decimals as a nuisance. May be the indexes are a bit more difficult to memorize but once you use them regularly you won't forget them again.

> That?s an interesting concept. So you have
> memorized the fact that a 2% edge occurs at,
> say, 3.3 and calculated your bet spread that
> way?

TC+3.3 is certainly less than 2% edge but you got the idea.
Actually I have bet schemes ready for various rule sets and during play I don't even have to bother about TC. I know the bet size depending on the RC and the level of penetration.TC is just for index plays.

> What about the argument that, because of
> rounding and whatnot, indices are not
> terribly accurate in the first place? If the
> numbers are not completely accurate at the
> whole number value, why bother with the
> fractional part?

I don't understand. The fact that indices are not accurate enough as whole numbers is the reason why we want fractions.

Francis Salmon

[Titan5]

How do people find an integer index number for certain play in the first place? Isn't it true that they have to first get a decimal number or a group of numbers averaged to a decimal number? The integer index number then can be obtained from using rounding, truncating or flooring the decimal number(s). If this is the case the data may have been available somewhere.
One suggestion. The infinite deck approach for one or two decks is inherently less accurate. Then the resulting decimal index numbers are useless. Only if you use 6 or 8 decks you can get relatively reliable numbers.

[Norm Wattenberger]

> How do people find an integer index number
> for certain play in the first place? Isn't
> it true that they have to first get a
> decimal number or a group of numbers
> averaged to a decimal number? The integer
> index number then can be obtained from using
> rounding, truncating or flooring the decimal
> number(s). If this is the case the data may
> have been available somewhere.

No, an average of the decimal numbers would not provide an accurate index. The TC must be calculated in the exact manner as the player will calculate it. (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. This would be the end of index determination if TC advantages were linear. But, they aren't. Therefore additional analysis must take place in the case that there exists more than one index to determine the best.

[Titan5]

Is simulation the only way to find out index numbers? Never say Never, Always or the Only way. I do agree there are situations the index numbers are of little use. Maybe there exists more than one index number for certain plays. Case in point, for 7,7 vs dealer 8 I remember reading your post a while back showing the relative flat curve for different TCs. That means the index number cannot provide useful information for us to act on. TC=0, TC=2 or TC=3; all have significant percentage of play deviation from the perfect play if one uses the index number to make play determination. (Perfect play - the one using remaining deck card composition.)

[Norm Wattenberger]

I don't think that there is a perfect method of creating indexes in a reasonable period of time. There are many methods. Normal simulation where you just play the game normally and record results as the game is played does not provide accurate indexes and is particularly bad at Splits. This is what index generators do in cheap software. I've tried several methods over the years and settled on a simulation method that includes some elements of combinatorial analysis. But it isn't perfect. If I had to guess, I would say Cacarulo knows more about index generation than anyone else at this point in time.

[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