Zenfighter: TOB, my 2004 working agenda.

[Zenfighter]

References

1) TOB (4th Edition) Chapter 3. How much can be gained by Perfect Play? (page28).
2) EoR?s table, Vegas rules, page 44, Chapter 4.
3) SD with a max. cut at the 61.54% (20 cards remaining)
4) Hi-lo count.




Amount gained by betting one extra unit when the deck is favorable for BS

 

 

   Unseen cards	                      Total Gain (%)	      Hi-lo Gain (%) 

 

	20				1.66785			1.61416 

	21				1.60124			1.54967 

	22				1.53821			1.48865 

	23				1.47835			1.43069 

	24				1.4213			1.37545 

	25				1.36674			1.32263 

        26				1.3144			1.27195 

        27				1.26403			1.22319 

	28				1.21543			1.17613 

	29				1.16839			1.13059 

	30				1.12274			1.08639 

	31				1.07832			1.04339 

	32				1.03498			1.00143 

	33				0.992578		0.960373 

	34				0.95098			0.920099 

	35				0.910056		0.880477 

	36				0.869679		0.841385 

	37				0.829721		0.802698 

	38				0.790049		0.764289 

        39				0.750526		0.726024 

	40				0.711003		0.687758 

	41				0.671314		0.649332 

	42				0.631269		0.610563 

	43				0.590647		0.571234 

	44				0.549173		0.53108 

	45				0.506499		0.489765		 

	46				0.462158		0.446836 

 

Unimportant facts

a) The decimals.
b) The slightly discrepancies with Griffin?s figures.

Important facts

a) Amount gained = f {depth of the deck} in agreement with the Fundamental Theorem of BJ.

b) The betting efficiency of any given point count, increases with the actual depth of the deck.

We can see easily, that with a 1/4 dealt out:

HL effic. = .726024/.750526 = .967354

While at the ? level:

HL effic. = 1.27195/1.3144 = .967704

Admittedly, nothing to fear or worry about it, this meagre loss of efficiency of our point count at the early stages of the pack.

Chin up. The point count works! (?system?, according to SW).

Enjoy!

Sincerely

Z

[Don Schlesinger]

As always, some very interesting work.

Thanks for the contribution.

Don

[Cacarulo]

[John Lewis]

"Amount gained by betting one extra unit when the deck is favorable for BS"

Pardon me if this is a naive question.

What is meant by "when the deck is favorable for BS"?

[Don Schlesinger]

> Pardon me if this is a naive question.

> What is meant by "when the deck is
> favorable for BS"?
Zenfighter's native tongue is not English. What it means is that you bet one extra unit when the deck is favorable and that you employ BS for the play of the hand.

Don

[John Lewis]

Please excuse me for asking so many questions about this. Zen's study seems to be an important one, and I'd like to fully understand it.

Does Total Gain minus Hi-lo gain equal the small gain innate in increased penetration?

Does the Hi-lo gain equal the gain obtained by knowing the count is favorable and betting an additional unit?

This study examines only a one unit betting strategy gain vs. penetration, correct? It does not take into account playing strategy gains from Hi-lo, correct?

[Zenfighter]

A few clarifications may help you

Total gain: a linear estimate of the player gain given a perfect knowledge of the remaining cards, and betting one extra unit.

Hi-lo gain: a linear estimate of how much you can win by a perfect application of the Hi-lo index, used to determine and advantage and betting one extra unit. You will play your hand with BS.

Hi-lo efficiency: the ratio of Hl gain/Total gain.

This study examine only a one unit betting strategy gain vs. penetration, correct? It does not take into account playing strategy gains from Hi-lo, correct?

Yes.

Thanks for your interest in the article.

Sincerely

Z

[John Lewis]

[Zenfighter]

This amazing and humorous math professor called P. Griffin, deserves a special recognition on this page; I hope that our Host will agree on this. Within my limitations, I?ll try along this year, to stimulate the love for his priceless work.

And only here, at DD!

Sincerely

Z

[John Lewis]

"This amazing and humorous math professor called P. Griffin, deserves a special recognition on this page; I hope that our Host will agree on this. Within my limitations, I?ll try along this year, to stimulate the love for his priceless work."

Zen

Fantastic news. Your posts are always good, and often very significant. Your mathematical studies are the best new, original mathematical posts on blackjack sites at this time, in my (yes, humble) opinion. And the first post of your planned series was a very good one.

I'm sure many readers are looking forward to your subsequent posts in your Griffin series.

[Don Schlesinger]

> I'm sure many readers are looking forward to
> your subsequent posts in your Griffin
> series.
And, I believe we should be archiving the series, as well.

Don