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

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

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.

Now we need to determine the frequencies of these hands, and for that we go to Wong's PBJ pages 296-7, Tables D3 & D4. This is where it gets *a little* complicated. You see, we can't deduce an _exact_ frequency of stiffs v. 7-T because we won't be landing quite as many stiffs, due to the fact that we won't be hitting stiffs into stiffs(ie. chance of hitting 12 to make 16). In this, I must confess, I took a shortcut (sorry)...I took the mean of the frequency of initial hands and the frequency of decisions, using a 3:1 ratio, weighting the decision figure more heavily because I believe the aforementioned effects to be fairly minimal. This methodology gives us a frequency of hands we are willing to bust of:

[(.31154 * 3) + .1962] / 4 = .282705

So 28.27% of the time we will be faced with the option of hit/stand on a stiff hand of 12-16 versus our selected dealer upcards (all except A when we have 2,3,4). But of this 28% we will only vary from BS on plays with a minimum wager out. To determine frequency of minimum bet we need a TC frequency figures for the game in question (anybody?). The only relevent double deck data that I have is for around 70% pen, and it shows a TC of >= +1 over 31% of the time. So for our deeper dealt game, I will assume a frequency of TC >= +1 occurs approximately 35% of the time. Therefore if betting up at a TC of +1, we will be playing 65% of hands with a minimum wager in the circle. So our adjusted frequency becomes:

.282705 * .65 = .18375825

So 18.38% of the time we will be deviating from basic strategy in order to facilitate recognition of the hole card. To convert this figure into number of rounds, which we need to calculate expected loss, simply take the product of (n) cards in play and penetration percentage, and divide this by 5.4.

(104 * .85) / 5.4 = 16.3703703703

So we will be playing, on average, 16.37 rounds per pack in this double deck game with 85% penetration. Subsequently, we will be placing an average of 16.37 wagers, and will make a minimum of 16.37 strategy decisions.

Now to determine the frequency, in wagers (rounds), all we must do is multiply this number by our adjusted frequency of 18.38%:

16.3703703703 * .18375825 = 3.00819061109

Here it tells us that we will deviate from basic strategy on 3 hands per pack, effectively replacing the "stolen" 3% penetration, improving expectation on that note, though obviously detracting from expectation due to misplay.

Now glancing back at our "Loss from standing over drawing" chart, we again see that the mean (average) loss we can expect to see, on average, is -.1199 for each hand we misplay. So assuming $5 minimum bets:

-.1199090909 * 5 = -.5995454545

Here we see that the expected loss on our minimum wager for deviating from BS is less than 60 cents. We now simply multiply this by its frequency of occurance in the pack, 3 times:

-.5995454545 * 3 = -1.7986363635

So the total expected loss on the pack for our deviations in play made to facilitate recognition of the hole card is less than $1.80. Now we compare this to our prior stated increase in expectation, to determine if I'm totally nuts or not;-).

Remember earlier in the post we saw gains of 10.4% to 15.7% in shoes. As I stated I believe this effect will be more substantial in our double deck game, but favoring being conservative, we will use the mean of these figures as our expected increase:

(15.7% + 13.6% + 10.4%) / 3 = 13.23_%

So now it's time to make our final, and deciding comparo (for varying win rates, all figures assume $5 minimum bet, heads-up):

___WR_____gain_____loss_____net$_____net%____

__$15____$1.98____$1.80____$0.18_____1.20%___

__$20____$2.65____$1.80____$0.85_____4.25%___

__$25____$3.31____$1.80____$1.51_____6.04%___

__$30____$3.97____$1.80____$2.17_____7.23%___

__$35____$4.63____$1.80____$2.83_____8.09%___

__$40____$5.29____$1.80____$3.49_____8.73%___

__$45____$5.95____$1.80____$4.15_____9.2_%___

__$50____$6.62____$1.80____$4.82_____9.64%___

__$55____$7.28____$1.80____$5.48_____9.96%___

__$60____$7.94____$1.80____$6.14____10.23%___

Well, are we convinced yet??? The figures are here...in black and white...4%-10% increases.

Take note that variance would increase ever so slightly due to the reduction in hitting frequency, as we will tend to push less because of standing on stiffs (impossible too push w/ <17) more often than usual. This effect will be minimal, but existant. Despite this, I believe SCORE would show even more dramatic improvements than our expectation, because of the key role penetration plays in risk.

Ouchez, I commend you for your improvisation concerning this matter, sometimes you have to improvise and adapt to overcome.

Adam "outside the box" Subtractum