Value of penetration

[21frogman]

Hi, I need a reference on the theory/math of the increased value of deeper penetration when counting. Thanks

[iCountNTrack]

Hi, I need a reference on the theory/math of the increased value of deeper penetration when counting. Thanks

Not much math involved, you can look at the increased profatibility of deeper penetration from two different angles:

1) Deeper penetration, you will see high true counts more frequently.
2) Deeper penetration gives you more information about the remaining composition of the shoe.

See theory of blackjack for more detailed info

[Norm]

Plenty of discussion, software and charts are available. And as iCount says, Theory of Blackjack talks about the theory. But, mathematically, it's an intractable problem outside of simulation.

[21frogman]

Thanks iCountNTrack. I understand intuitively what is involved. I just haven't been able to find data showing how this very important determinant of advantage has been examined.
I looked in Theory of Blackjack as you suggested. If the answer is there, I can't find it.

[21frogman]

Thanks to you, too, Norm.
I have the answer in practical terms in SCORE, but I was hoping for a thought process.

[hitthat16]

Think about it this way:

Which is more meaningful, five extra high cards mixed into three decks, or five extra high cards mixed into half of one deck? At deeper penetration levels, those high cards you know are in there are more likely to actually come out.

[21frogman]

I guess I was looking for math that showed why a TC of 3 at 70% pen is apparently more advantageous than a TC of 3 at 50% pen

[iCountNTrack]

I guess I was looking for math that showed why a TC of 3 at 70% pen is apparently more advantageous than a TC of 3 at 50% pen

What you are talking about is called the floating advantage. Check Blackjack Attack.

[21frogman]

You're right. That's what I was looking for. Disappointing though, "the 'floating advantage' is of more theoretical than practical import." (BJA p. 79). So penetration isn't all it's cracked up to be. I thought that the accepted teaching is that adequate penetration is very important in counting.

[Three]

I thought that the accepted teaching is that adequate penetration is very important in counting.

It is. It doesn't have to do with floating advantage.

Several posts already have tried to make it click for you. If the TC is +9 with 5 decks left what are the chances the next 10 cards will be low cards? What about if there is one deck left with the same TC? How good does that make you feel about your chances when doubling an 11 in each case? What is the affect on the TC of each of those cards as they are dealt in each situation? That first low card doesn't change the TC with 5 decks left or to be exact it changes it by 0.2 but with 1 deck left i changes it by 1.0. So if you double your 11v5 with 5 decks left heads up and draw a stiff the dealer chances of having a T under and hitting a T hasn't changed much as the TC is +9.2 but at 1 deck left the TC just went up by 1 to +10.

If you are playing with others between you and the dealer with 5 decks left the count won't change much after your decision until the dealer acts but with 1 deck left the count may change considerably. It all averages out for the large changes in the long run as the TC theorem states it will tend to remain the same.

I hope the differences at different levels of pen and why pen is so important are starting to become apparent.

1) Deeper penetration, you will see high true counts more frequently.
2) Deeper penetration gives you more information about the remaining composition of the shoe.

ICount summed it up short and sweet here.

[Bodarc]

I ran a small simulation of only 10,000,000 hands using a 50/50 cut on hi-lo with S17 DAS and another one using same parameters but with cut 5.5 decks out of 6.

at 50/50 cut the count of +3 was hit 217,870 times +6 count was hit 8,297 times
at 5.5/6 cut the count of +3 was hit 662,794 times +6 count was hit 114,203 times

I don't know anything about a formula for it, but the above should give you the answer you are looking for.

PS If anyone wants to check that I'm in the ballpark, feel free because this is the first sim I ran with this program.

[Bodarc]

http://qfit.com/book/ModernBlackjackPage101.htm

[DSchles]

You're confusing two very different issues. Penetration certainly IS all that it's cracked up to be. Penetration is more important than rules, by a wide margin. The deeper you deal, the more you win. Period. The deeper you deal, the more frequently you encounter the better counts.

Floating advantage says something altogether different. It affirms that, the SAME true count, once you achieve it, is worth more, the deeper it occurs in the pack. This is NOT intuitive and was not widely understood until John Gwynn and I did our ground-breaking research. And, the quote that you mention explains that, unfortunately, the FA does not really surface until rather late in the shoe game, at levels of penetration that, more often than not, are not offered nowadays.

Do you understand the difference?

Don