Am enjoying the new paperback BJA3 Effects of Removal charts. It's nice to have the multi-deck favorabilities included.
As I recall, TOB (3rd edition and beyond) includes a way to infer multi-deck favorabilities by providing a chart of infinite deck values and applying the method of interpolation of reciprocals.
I assume something similar can be used with the new BJA3 charts to infer the infinite deck values without losing too much?
> Am enjoying the new paperback BJA3 Effects
> of Removal charts. It's nice to have the
> multi-deck favorabilities included.
Glad you're enjoying.
> As I recall, TOB (3rd edition and beyond)
> includes a way to infer multi-deck
> favorabilities by providing a chart of
> infinite deck values and applying the method
> of interpolation of reciprocals.
Right.
> I assume something similar can be used with
> the new BJA3 charts to infer the infinite
> deck values without losing too much?
Just out of curiosity, why would you want such values? I've never been a fan of infinite-deck anything. Since the values correspond to no reality, why bother?
Don
> Glad you're enjoying.
> Right.
> Just out of curiosity, why would you want
> such values? I've never been a fan of
> infinite-deck anything. Since the values
> correspond to no reality, why bother?
> Don
Not a fan either, just someone who has created a few spreadsheets (to gain better understanding) where I have included EORs from TOB. A couple of examples.
One of them... A. Snyder's algebraic approximation method to construct decision indices. You might recall that his paper includes a table of indices for infinite deck Dubner Count values. This spreadsheet would get updated with the new values from your book. I believe that TOB (first edition) was used in Arnold's study, and the infinite deck favorabilities were not yet included.
Another, I made an assumption that in your Illustrious 18 example in BJA (15 vs 10) the numerator for z (3.48) was determined thru interpolation icw TOB (you mention that you used the 3rd edition) infinite deck favorabilities. Is that what you used? Or just coincidence?
Nothing more. Thanks.
> Not a fan either, just someone who has
> created a few spreadsheets (to gain better
> understanding) where I have included EORs
> from TOB. A couple of examples.
> One of them... A. Snyder's algebraic
> approximation method to construct decision
> indices. You might recall that his paper
> includes a table of indices for infinite
> deck Dubner Count values. This spreadsheet
> would get updated with the new values from
> your book. I believe that TOB (first
> edition) was used in Arnold's study, and the
> infinite deck favorabilities were not yet
> included.
Yes, correct. I would imagine you would see minute differences, but you may as well use the new, more accurate values.
> Another, I made an assumption that in your
> Illustrious 18 example in BJA (15 vs 10) the
> numerator for z (3.48) was determined thru
> interpolation icw TOB (you mention that you
> used the 3rd edition) infinite deck
> favorabilities. Is that what you used? Or
> just coincidence?
Must have. I can't remember offhand, but now that we have m2 and m6 in Appendix D, it will make life a lot easier if we care to do some similar calcualtions for, say, 2-deck or 6-deck games.
> Nothing more. Thanks.
Thank you!
Don
For years blackjack software do exist, that use the infinite deck algorithm. Essentially what we have here is an infinite supply of cards, so basically speaking sampling with replacement. It has been in vogue to calculate basic strategies for multi-deck, because according to those who advocate the employment of it, in multi-deck games the removal of any single card has a lesser effect on the total composition of the whole package. It?s not that this statement is complete wrong, but striving for the utmost possible accuracy, exact playing out of all valid card sequences (for player and dealer) has been used to generate the data, while using always a finite set of decks. As a result, the algebraic methods to extract possible indices, tend to work much better. No longer infinite-deck assumptions with our modern and fast computers. Something from the past, JMO.
Zenfighter
In the event the software would need them, just use Griffin?s formula (page 232) to extract them.
e.g. Dealer?s T (hitting vs. standing)
17 mi = -16.4737
16 mi = 0.0612
15 mi = 3.5969
14 mi = 7.1334
13 mi = 10.6686
12 mi = 14.2029
Sincerely
Zenfighter
> In the event the software would need them,
> just use Griffin?s formula (page 232) to
> extract them.
> e.g. Dealer?s T (hitting vs. standing)
>
> 17 mi = -16.4737
> 16 mi = 0.0612
> 15 mi = 3.5969
> 14 mi = 7.1334
> 13 mi = 10.6686
> 12 mi = 14.2029
>
> Sincerely
> Zenfighter
>
Thanks for taking the time to offer the example.
This would be my understanding as well.
I'm sure the following is rather moot...
Although there is negligible difference in using any of the mk values to substitute in Griffin's formula, it appears(?) that you chose m6 to determine your mi values. For example, for 12 vs ten, I get values for mi using each mk as follows:
Using m2, mi=14.2067
Using m6, mi=14.2029
Using m8, mi=14.2024
Griffin mi=14.21
Was there any reason in choosing your particular method that one should apply in determining the mi values?
Because Don's Illustrious 18 analysis is based on 4-deck rules, and missing m4 values in the new tables, would you suggest a different method yet (than using mi's)?
Thanks
Was there any reason in choosing your particular method that one should apply in determining the mi values?
No matter you?ll choose m8 or m6 to help your estimate of the mi values. The main problem you face here is that all the full-deck favorabilities are truncated to the fourth decimal. You will need here single precision figures to obtain accuracy at the 4th decimal place. See what I mean, here? You can?t trust all the decimals of mi.
Interpolating between one and six to infer the m4 value:
12 vs. T (hitting vs. standing)
m4 = (13.5765 + (3 * 14.0985))/4
m4 = 13.9680
While extracting the exact favorability yields:
m4 = 14.0470
That?s the main reason our tables have been designed to avoid any type of interpolation. You can?t avoid filtering some type of inaccuracies with these linear estimates.
Hope this will help, to try your best, anyway.
Zenfighter
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