Adam N. Subtractum
Well-Known Member
The following is a re-post of my response to a thread concerning the latest in casino "counter counter-measures" at AP.com, on the"Heartland 21" page. This counter-measure is dubbed "Blind Pitch", and invlolves the dealer not exposing his hole card when the player/s bust. This affects a deeply dealt double deck game to the tune of 3%, at first glance a minimal amount, but after seeing the effects of marginal increases/decreases in penetration presented in my post, I think you may change your thinking. Not to worry though, as I have conducted excruciating calculations that STRONGLY indicate that this effect can be neutralized to the point of near nill, and I present the methodology to apply theses figures to real-world play.
Enjoy,
ANS
*note that the menu on your left may need to be minimized in order for the tables presented to format properly.
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I've been viewing the threads here lately pertaining to the "Blind Pitch" game being used in some reservation joints. Intuitively I perceived a gain could be achieved if attacked in the appropriate manner, and I have calculated hard numbers I believe verify this notion.
I noted several misconceptions in the recent threads, most importantly the underestimation of the power of penetration. It seems we are constantly told about the upmost importance of penetration, yet there seems to be a notion going around that penetration increases in smaller increments (like the assumed 3%) won't have a substantial effect on Win Rate and DI...au contrair, in fact I intend to show the effect will be, dare I say, dramatic.
Another incorrect assumption I noticed was the Kid's figure on player bust frequency, this is actually around 19%. Once we get the details straightened out, I do believe it is indeed possible to sim this game, but it very well may require Norm's software to do so.
I'll start with the value of penetration rather than the cost of the mistakes, so the bored reader who wongs out of this post early
gets at least something good out of it.
Let us first and foremost determine the effective penetration of this game. Since we know our bust frequency is approximately 19%, and this game is getting 85+% penetration, we can calculate:
[(104 * .85) / 5.4] * .19 = 3.11037037035
Which is the number of times we will bust, through one pack, and subsequently the number of hole cards that will go unseen through one pack. Now our approximate loss in effective penetration is found to be:
3.11 / 104 = 2.99%
Since in the hypo we are receiving >85% pen, we can round up to %3 for accuracy, as well as simplicity. Now it has been expressed by some in prior related threads that this decrease is not of a notable amount, so let's take a good look at the effects of penetration.
Unfortunately, the only extensive data I have on effects of pen on WR, DI, etc., is for shoe games, but I believe this will only tend to UNDERestimate the effects on the double deck game in our hypo. You can see in this first link, to a chart by Norm Wattenberger and his Qfit software, the effects of penetration on an 8 deck game w/ KO, play-all and wonging:
http://bjmath.com/bin-cgi/bjmath.pl?read=3565 (Archive copy)
Now anylizing the data in the 84%-88% range reveals:
pen__84.5%_____87.5%____
WR___1.59______1.84_____
DI___4.27______4.80_____
You can clearly see here that the mere 3% increase in penetration increases Win Rate by 15.7%!!! and DI by 12.4%!!! And as I stated prior, I believe these effects will be even greater in the double deck case.
In that same post, you'll find the wonging case for the same conditions, which gives figures of:
pen__84.5%_____87.5%____
WR___1.03______1.17_____
DI___6.16______6.61_____
We see in this case Win Rate increases by 13.6%, and DI increases by 7.3%, again with a mere 3% increase in pen. Convinced yet? OK, I got another:
http://bjmath.com/bin-cgi/bjmath.pl?read=3544 (Archive copy)
Again, compliments of resident "Master" Norm W. and his masterpiece Qfit software, this is another wonging case, except with 6 decks and hi-lo.
pen__82.3%_____85.3%____
WR___2.50______2.76_____
DI___9.72_____10.55_____
Here we see gains of 10.4% and 8.5%, for Win rate and DI, respectively. If you get nothing else from this post at all, "get" the importance of small increases in penetration.
One more for the doubters, again courtesy of Norm W. Importance of pen is clearly seen here.
http://qfit.com/wrphh1.jpg
Now that we have determined that there is substantial ev to be gained (or should we say reclaimed, in this situation) by increasing penetration by three cards, so the next step is to determine the cost of the errors of our play strategy.
First let's look at some numbers derived from Thorp's BTD, page 191, Table 2a:
-Loss from standing over drawing-
d\p__12____13____14____15____16___
7___-209__-166__-114__-119__-110__
8___-189__-148__-145__-108__-102__
9___-141__-145__-103__-062__-055__
10__-156__-119__-075__-038__-029__
A___-----___-----___-----__-159__-146__
Perusal of the original table in BTD shows that it's more costly than its worth to stand with 2, 3, & 4 versus the dealer's Ace, but costs are not *too* detrimental in the presented cases. A quick calculation shows the mean (average) expected loss for standing on 12-16 v. 7-T to be -.119909090909.
continued...
Enjoy,
ANS
*note that the menu on your left may need to be minimized in order for the tables presented to format properly.
<><><><><><><><><><><><><><><><><><><><><><><><><>
I've been viewing the threads here lately pertaining to the "Blind Pitch" game being used in some reservation joints. Intuitively I perceived a gain could be achieved if attacked in the appropriate manner, and I have calculated hard numbers I believe verify this notion.
I noted several misconceptions in the recent threads, most importantly the underestimation of the power of penetration. It seems we are constantly told about the upmost importance of penetration, yet there seems to be a notion going around that penetration increases in smaller increments (like the assumed 3%) won't have a substantial effect on Win Rate and DI...au contrair, in fact I intend to show the effect will be, dare I say, dramatic.
Another incorrect assumption I noticed was the Kid's figure on player bust frequency, this is actually around 19%. Once we get the details straightened out, I do believe it is indeed possible to sim this game, but it very well may require Norm's software to do so.
I'll start with the value of penetration rather than the cost of the mistakes, so the bored reader who wongs out of this post early
gets at least something good out of it.
Let us first and foremost determine the effective penetration of this game. Since we know our bust frequency is approximately 19%, and this game is getting 85+% penetration, we can calculate:
[(104 * .85) / 5.4] * .19 = 3.11037037035
Which is the number of times we will bust, through one pack, and subsequently the number of hole cards that will go unseen through one pack. Now our approximate loss in effective penetration is found to be:
3.11 / 104 = 2.99%
Since in the hypo we are receiving >85% pen, we can round up to %3 for accuracy, as well as simplicity. Now it has been expressed by some in prior related threads that this decrease is not of a notable amount, so let's take a good look at the effects of penetration.
Unfortunately, the only extensive data I have on effects of pen on WR, DI, etc., is for shoe games, but I believe this will only tend to UNDERestimate the effects on the double deck game in our hypo. You can see in this first link, to a chart by Norm Wattenberger and his Qfit software, the effects of penetration on an 8 deck game w/ KO, play-all and wonging:
http://bjmath.com/bin-cgi/bjmath.pl?read=3565 (Archive copy)
Now anylizing the data in the 84%-88% range reveals:
pen__84.5%_____87.5%____
WR___1.59______1.84_____
DI___4.27______4.80_____
You can clearly see here that the mere 3% increase in penetration increases Win Rate by 15.7%!!! and DI by 12.4%!!! And as I stated prior, I believe these effects will be even greater in the double deck case.
In that same post, you'll find the wonging case for the same conditions, which gives figures of:
pen__84.5%_____87.5%____
WR___1.03______1.17_____
DI___6.16______6.61_____
We see in this case Win Rate increases by 13.6%, and DI increases by 7.3%, again with a mere 3% increase in pen. Convinced yet? OK, I got another:
http://bjmath.com/bin-cgi/bjmath.pl?read=3544 (Archive copy)
Again, compliments of resident "Master" Norm W. and his masterpiece Qfit software, this is another wonging case, except with 6 decks and hi-lo.
pen__82.3%_____85.3%____
WR___2.50______2.76_____
DI___9.72_____10.55_____
Here we see gains of 10.4% and 8.5%, for Win rate and DI, respectively. If you get nothing else from this post at all, "get" the importance of small increases in penetration.
One more for the doubters, again courtesy of Norm W. Importance of pen is clearly seen here.
http://qfit.com/wrphh1.jpg
Now that we have determined that there is substantial ev to be gained (or should we say reclaimed, in this situation) by increasing penetration by three cards, so the next step is to determine the cost of the errors of our play strategy.
First let's look at some numbers derived from Thorp's BTD, page 191, Table 2a:
-Loss from standing over drawing-
d\p__12____13____14____15____16___
7___-209__-166__-114__-119__-110__
8___-189__-148__-145__-108__-102__
9___-141__-145__-103__-062__-055__
10__-156__-119__-075__-038__-029__
A___-----___-----___-----__-159__-146__
Perusal of the original table in BTD shows that it's more costly than its worth to stand with 2, 3, & 4 versus the dealer's Ace, but costs are not *too* detrimental in the presented cases. A quick calculation shows the mean (average) expected loss for standing on 12-16 v. 7-T to be -.119909090909.
continued...