Chart for penetration edge

[chessplayer]

Hi,

I have read very extensively on the web, including wizards of odds website and Arnold's(The expert on penetration). However I cannot find any chart which lists the advantage or edge you get per amount of penetration..

Say, whether 20% penetration with a TC of +2 is better, or 50% penetration with a TC of +1. Which of these is better I do not know.

 

[QFIT]

Do you mean like this: Modern Blackjack page 426?

 

[chessplayer]

Precisely! wow,that must have been a hard find.

 

[Deathclutch]

I bet he had a hunch it was there

 

[assume_R]

I bet he had a hunch it was there

:laugh:

 

[QFIT]

I bet he had a hunch it was there

Don't bet too much. I'm getting old.

 

[jack.jackson]

Hi,

I have read very extensively on the web, including wizards of odds website and Arnold's(The expert on penetration). However I cannot find any chart which lists the advantage or edge you get per amount of penetration..

Say, whether 20% penetration with a TC of +2 is better, or 50% penetration with a TC of +1. Which of these is better I do not know.

It sounds like, your asking two questions. Are you asking about the effects of pen, or the floating advantage?

Heres the article on Arnolds site about floating advantage, not the overall effects of pen. However it does show you your edge, per TC.

http://blackjackforumonline.com/content/howtrueisyourtruecount.html

4 decks

Zen Count Advantage (in %)          50%     62.5%	 75%	87.5%
-2	                            -.78	-.77	-.75	-.72
-1	                            -.79	-.77	-.75	-.70
0	                            -.38	-.36	-.35	-.32
+1	                            -.05	-.10	-.13	-.10
+2	                              .20	.18	.12	.16
+3	                              .35	.44	.49	.50
+4	                              .57	.62	.69	.76
+5	                              .79	.68	.76	.81
+6	                            1.26	1.28	1.32	1.33
+7	                            1.50	1.61	1.58	1.45
+8	                            1.70	1.82	1.72	1.84
+9	                            2.26	2.16	2.28	2.47

 

[Finn Dog]

Precisely! wow,that must have been a hard find.

I imagine writing it was harder! :grin:

FD

 

[Automatic Monkey]

Do you mean like this: Modern Blackjack page 426?

I'm not sure if this is the best verbiage on the page: "But it turns out that the advantage of a true count increases as we travel more deeply into the shoe."

Whoa, maybe not! What if the count is -4 ? As a corollary of the True Count Theorem, if a good count is better deep in the shoe a bad count should be worse, no?

 

[jack.jackson]

I'm not sure if this is the best verbiage on the page: "But it turns out that the advantage of a true count increases as we travel more deeply into the shoe."

Whoa, maybe not! What if the count is -4 ? As a corollary of the True Count Theorem, if a good count is better deep in the shoe a bad count should be worse, no?

No, it gets better as well. See my link above.

 

[QFIT]

It sounds like, your asking two questions. Are you asking about the effects of pen, or the floating advantage?

Heres the article on Arnolds site about floating advantage, not the overall effects of pen. However it does show you your edge, per TC.

http://blackjackforumonline.com/content/howtrueisyourtruecount.html

4 decks

Zen Count Advantage (in %)          50%     62.5%     75%    87.5%
-2                                -.78    -.77    -.75    -.72
-1                                -.79    -.77    -.75    -.70
0                                -.38    -.36    -.35    -.32
+1                                -.05    -.10    -.13    -.10
+2                                  .20    .18    .12    .16
+3                                  .35    .44    .49    .50
+4                                  .57    .62    .69    .76
+5                                  .79    .68    .76    .81
+6                                1.26    1.28    1.32    1.33
+7                                1.50    1.61    1.58    1.45
+8                                1.70    1.82    1.72    1.84
+9                                2.26    2.16    2.28    2.47

Those numbers don't look right. Possibly not enough rounds.

 

[QFIT]

I'm not sure if this is the best verbiage on the page: "But it turns out that the advantage of a true count increases as we travel more deeply into the shoe."

Whoa, maybe not! What if the count is -4 ? As a corollary of the True Count Theorem, if a good count is better deep in the shoe a bad count should be worse, no?

Sounds that way, but not true. Actually, I think there is a very slight miss-wording in the TC Theorem. This is covered in the next three pages of the book. See Modern Blackjack pages 427-429.

 

[London Colin]

I'm not sure if this is the best verbiage on the page: "But it turns out that the advantage of a true count increases as we travel more deeply into the shoe."

Whoa, maybe not! What if the count is -4 ? As a corollary of the True Count Theorem, if a good count is better deep in the shoe a bad count should be worse, no?

As I understand it, the essence of the floating advantage is this:

• Excessively large true counts (both positive and negative) are worse for the player than linear approximation would lead you to expect.
• The deeper you go, the more scope for seeing such counts there is.
• Since at any depth, the overall average advantage has to be the same as off the top, there must therefore be a corresponding increase in player advantage (or reduction in disadvantage) for the less extreme counts which we encounter most of the time.

(I could be wrong, though.)

 

[iCountNTrack]

As I understand it, the essence of the floating advantage is this:

• Excessively large true counts (both positive and negative) are worse for the player than linear approximation would lead you to expect.
• The deeper you go, the more scope for seeing such counts there is.
• Since at any depth, the overall average advantage has to be the same as off the top, there must therefore be a corresponding increase in player advantage (or reduction in disadvantage) for the less extreme counts which we encounter most of the time.

(I could be wrong, though.)

It all depends on your playing strategy . The following graphs show the different evs for all the possible compositions at 3 different penetrations for a 1D game (S17) using perfect play composition dependent combinatorial analysis. I however use Running counts instead of True Counts. The graphs on the left hand side show the range of evs for a given RC, while the ones on the right show the sum of weighted EVs (p_i*ev_i).
It can be seen clearly that irrespective of the magnitude or sign of the running count, on average we are moving to a positive regime, where at 10 cards remaining in the deck we will be virtually playing with an advantage at all times.

 

[London Colin]

It all depends on your playing strategy .

I was assuming unmodified Basic Strategy, which is what the floating advanatge relates to, as I understand it. But there is the implict assumption, I suppose, that this sets a baseline onto which you can add further gains from counting.

The following graphs show the different evs for all the possible compositions at 3 different penetrations for a 1D game (S17) using perfect play composition dependent combinatorial analysis. I however use Running counts instead of True Counts. The graphs on the left hand side show the range of evs for a given RC, while the ones on the right show the sum of weighted EVs (p_i*ev_i).
It can be seen clearly that irrespective of the magnitude or sign of the running count, on average we are moving to a positive regime, where at 10 cards remaining in the deck we will be virtually playing with an advantage at all times.

Very interesting. Thanks for posting those. How long does it take to produce them? All possible combinations sounds like a lot of computation!

 

[iCountNTrack]

I was assuming unmodified Basic Strategy, which is what the floating advanatge relates to, as I understand it. But there is the implict assumption, I suppose, that this sets a baseline onto which you can add further gains from counting.

Flaoting advantage is the worth of a given TC at different shoe depths.

Very interesting. Thanks for posting those. How long does it take to produce them? All possible combinations sounds like a lot of computation!

Each penetration takes on average one day, luckily i have 5 computers

 

[London Colin]

Flaoting advantage is the worth of a given TC at different shoe depths.

Yes, but isn't the surprising phenomenon, the thing which caused all the controversy, the fact that this worth changes for the Basic Strategist?

So I suppose the question is this -

If you subtract out the Basic Strategy gains associated with a given depth at a particular TC, are there further gains associated with strategy variation at that depth, compared to the same stategy variation at different depths.

Presumably you are saying that there are? But is that only true for perfect play? If employing indexes, rather than perfect play, is there a similar effect? Thinking about it, I suppose there must be, at least to some extent.

Each penetration takes on average one day, luckily i have 5 computers

:grin:

 

[Automatic Monkey]

No, it gets better as well. See my link above.

If all counts got better deep in the shoe, we could get an advantage by only playing at the end of the shoe without counting. We know that can't happen.

 

[London Colin]

If all counts got better deep in the shoe, we could get an advantage by only playing at the end of the shoe without counting. We know that can't happen.

All counts don't. Counts in the neighbourhood of zero do, both positive and negative. You still have to know the count to get any advantage.

 

[Automatic Monkey]

Sounds that way, but not true. Actually, I think there is a very slight miss-wording in the TC Theorem. This is covered in the next three pages of the book. See Modern Blackjack pages 427-429.

Ah OK, so you're saying the floating advantage is actually related to the cut card effect? Interesting. Makes sense, being that at any given low count you are still more likely to get a natural towards the end of the shoe than at the beginning.

We still need to reconcile this with the fact that you can grab a deck of cards at random from anywhere in a 8D shoe and the advantage is the same as for an 8D game, not a 1D game.