If Flooring the optimal method to get TC that generate the highest EV?

[San Jose Bella]

https://www.blackjackincolor.com/truecount4.htm
In this article, the graph shows a huge 0.25%(eyeballing the graph) difference in advantage between Floor and Round method. I've always using Floor method, but I wonder if the difference is that high?

https://www.qfit.com/CalculatingTrueCounts.htm
In this article, it says "Flooring and rounding are nearly equal in performance". I always thought rounding 1.6 to 2 is a mistake cause I should take deviation action when the TC is 2 or higher, 1.6 is lower than 2.

In Professional Blackjack by Stanford Wong, he suggests Truncating on page 37. Furthermore, on the deviation chart provided by Blackjack Apprenticeship, the deviation numbers are different than in Stanford Wong's book.
It's all the same Hi-lo counting system, why so many differences? I understand few different deviation numbers have little effect on performance, but the optimal choice has to be one. It boggles my mind for many years.

[San Jose Bella]

The first word in the title should be "Is" not "If". I can't edit the title, it was a typo.

[Dog Hand]

San Jose Bella,

For a TC of, say, -5, consider what range of fractional TC's (FTC's) this encompasses for each of the three calculation methods:

1. Flooring: -5 <= FTC < -4
2. Rounding: -5.5 < FTC <= -4.5
3. Truncation: -6 < FTC <= -5

Thus, the AVERAGE FTC is (roughly) -4.5, -5.0, and -5.5, respectively. Therefore, the edge at a TC of -5 is naturally highest for flooring and lowest for truncation, as shown in Norm's figure.

However, you are failing to account for an important missing variable: what is the FREQUENCY DISTRIBUTION of the TC's? The overall EV, or Initial Bet Advantage (IBA), for the player is found by summing (over all TC's) the product:

IBA = sum[(TC EV)*(TC Frequency)*(TC Wager)]

Thus, if the TC EV is higher for flooring than for the other methods, but its corresponding frequency is lower, you cannot know in advance which method will produce the highest IBA.

Hope this helps!

Dog Hand

[DSchles]

"Thus, if the TC EV is higher for flooring than for the other methods, but its corresponding frequency is lower [higher?], you cannot know in advance which method will produce the highest IBA."

This is true for positive counts only. For the negative counts in the example, we would replace your "lower" by "higher," no?

Don

[San Jose Bella]

San Jose Bella,

For a TC of, say, -5, consider what range of fractional TC's (FTC's) this encompasses for each of the three calculation methods:

1. Flooring: -5 <= FTC < -4
2. Rounding: -5.5 < FTC <= -4.5
3. Truncation: -6 < FTC <= -5

Thus, the AVERAGE FTC is (roughly) -4.5, -5.0, and -5.5, respectively. Therefore, the edge at a TC of -5 is naturally highest for flooring and lowest for truncation, as shown in Norm's figure.

However, you are failing to account for an important missing variable: what is the FREQUENCY DISTRIBUTION of the TC's? The overall EV, or Initial Bet Advantage (IBA), for the player is found by summing (over all TC's) the product:

IBA = sum[(TC EV)*(TC Frequency)*(TC Wager)]

Thus, if the TC EV is higher for flooring than for the other methods, but its corresponding frequency is lower, you cannot know in advance which method will produce the highest IBA.

Hope this helps!

Dog Hand

Thanks for the explanation, so flooring is the best way to go.
I assume all the different indexes from different sources are correct based on different method to get the true count. Professional Blackjack's indexes must be correct for truncating method, but not for flooring method, no? so what I need is the deviation numbers for flooring and flooring only, am I correct?


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[Dog Hand]

Don and SJB,

I think my point was poorly expressed. What I was trying to say with the IBA equation is that simply knowing that one TC calculation method produces a higher EV for a particular TC than does another method does NOT tell us which of those methods will produce the higher overall EV (or IBA): we also need to know the TC frequency distribution for each method.

We need simulation to obtain the frequency distribution.

Finally, SJB, the "best" (in the sense of most accurate) method to use is the method that was used to generate the index values for the system in question.

Dog Hand

[San Jose Bella]

Don and SJB,

I think my point was poorly expressed. What I was trying to say with the IBA equation is that simply knowing that one TC calculation method produces a higher EV for a particular TC than does another method does NOT tell us which of those methods will produce the higher overall EV (or IBA): we also need to know the TC frequency distribution for each method.

We need simulation to obtain the frequency distribution.

Finally, SJB, the "best" (in the sense of most accurate) method to use is the method that was used to generate the index values for the system in question.

Dog Hand

Thanks for the careful explanation, it's very helpful.
I think the hi-lo deviation number for different TC calculation methods are slightly different, but I'm not sure. Could you confirm that?

[DSchles]

Thanks for the careful explanation, it's very helpful.
I think the hi-lo deviation number for different TC calculation methods are slightly different, but I'm not sure. Could you confirm that?

They have to be different for the negative numbers, for truncating and for flooring.

Don

[San Jose Bella]

They have to be different for the negative numbers, for truncating and for flooring.

Don

then I assume the best approach is flooring method with flooring deviation numbers. Thanks

[Three]

Truncating has a TC 0 bin that is twice the range go all other bins. I don't see how this is beneficial. I don't like it. It cuts accuracy of TC 0 indices. It messes with symmetry. TC 0 is already your most common bin. The only important thing is to make sure you use the same method for generating a TC that the sim that generated your ramp and indices used.

[Three]

Truncating has TC 0 being the same as Flooring TC 0 and TC -1 combined. Then for truncating's negative TCs, they are the same as Floorings TC that is one increment more negative. If you look at your graph carefully you will see exactly that. Also you must use the same way of deck estimation as your sim did.

[davethebuilder]

In the past Blackjack players have been stuck with the flooring convention because that is how the older index generation programs worked, however it is not optimal. As the Hi Lo count moves away from neutral the frequency decreases dramatically so it's important to be as accurate as possible around the neutral count. If flooring is used then the average TC is around +0.5, not zero, so a players calculations and subsequent application of indices are inaccurate. If you have a choice then rounding will provide the most accurate method of determining true advantage and application of indices because the average TC is zero. The number of decks in play and the penetration also have an effect because the higher they are the greater the frequency of the higher and lower counts. In addition, rounding will provide a more accurate measure of true advantage towards the end of the shoe which is usually when larger bets are placed. A large simulation can be done to obtain the advantage at each true count and this shows that rounding provides a superior IBA to flooring or truncating.

[Freightman]

In the past Blackjack players have been stuck with the flooring convention because that is how the older index generation programs worked, however it is not optimal. As the Hi Lo count moves away from neutral the frequency decreases dramatically so it's important to be as accurate as possible around the neutral count. If flooring is used then the average TC is around +0.5, not zero, so a players calculations and subsequent application of indices are inaccurate. If you have a choice then rounding will provide the most accurate method of determining true advantage and application of indices because the average TC is zero. The number of decks in play and the penetration also have an effect because the higher they are the greater the frequency of the higher and lower counts. In addition, rounding will provide a more accurate measure of true advantage towards the end of the shoe which is usually when larger bets are placed. A large simulation can be done to obtain the advantage at each true count and this shows that rounding provides a superior IBA to flooring or truncating.

The same result, or close to same result can be achieved by flooring and interpolating.