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Thread: Adam N. Subtractum: How to see "Blind Pitch"...EXPLOITED...(long)

  1. #1
    Adam N. Subtractum
    Guest

    Adam N. Subtractum: How to see "Blind Pitch"...EXPLOITED...(long)

    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


  2. #2
    Ouchez
    Guest

    Ouchez: I am humbled, join the Kid and I for steak, on me. *NM*


  3. #3
    Adam N. Subtractum
    Guest

    Adam N. Subtractum: "Blind Shoe"additional points, provisos & caveats

    Firstly,player's spread and/or bet size *may* need to be optimized to realize full potential of the penetration increase, though I'd deem it VERY unlikely, especially considering the data in Norm's sim printouts.

    Secondly, the approximations executed in my post will obviously cause an increased standard error to our outcomes, but looking over the data again the gain/loss is sure to be minimal, and will not substantially affect our overall outcomes.

    Allow me to briefly comment on a few provisos regarding the theory & methodology.

    -Calculations assuming heads-up play

    -Win Rate to min bet >3:1 ratio

    -Deviate from BS/Indice w/ MINIMUM bet

    One more point I should bring up is that Indices could be calculated/generated in order to minimize losses at extreme counts, further optimizing this technique.

    ANS

    ps: note that Norm's penetration figures, in the provided links, are in cards behind cut, whereas my figures are in percentage.

    pss: Your screen may need to be maximized in order to format tables properly.

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Hold the order! :-)

    Read the above (it may take me a few minutes to type it up). I'd withdraw the invitation if I were you. :-)

    Don

  5. #5
    Don Schlesinger
    Guest

    Don Schlesinger: No, sorry, not correct

    Although I do not read these pages, Parker asked me to take a look at what was going on here, because the logic seemed to fly in the face of good sense.

    There is a tragic flaw in your analysis, and, deviously, it doesn't come up till the very end, when things fall apart rather badly.

    I'll make a few comments along the way: If you really have good self-control, you won't "cut to the chase" immediately. :-)

    > 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.

    Reading BJA, pp. 126-128, might have saved you a ton of work, but no matter.

    > 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 [sic: au contraire], in fact I intend >to show the
    > effect will be, dare I say, dramatic.

    The effect of an extra three cards in DD can be quite decent. Of course, it depends on your spread, which I couldn't find anywhere in the posts. So, we can't tell how many extra dollars will be earned, which is all that really matters.

    > Another incorrect assumption I noticed was
    > the Kid's figure on player bust frequency,
    > this is actually around 19%.

    I'm not sure where you get that from. In BJA, p. 49, I found the figure to be roughly 16%. Here, if you purposely try to break less frequently, by not hitting certain hands, it will obviously be even less.

    > 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 read below where there would be difficulty. I'm not sure if the software you use allows for reversal indices (such as for splitting 8,8, v. 10), but, if so, why not just use a reversal index of zero for hit/stand decisions uniquely for 12-16 v. 7-ace? If the count is zero or above, we now hit, and if below zero, we stand. You could also introduce another higher index (two values) so that you could once again stand for plays such as 15 v. 10, etc.

    > 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%

    So far, so good.

    > 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.

    I wouldn't agree. It is notable. But, the mistakes are much more notable (he foreshadowed, ominously!).

    > 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 analyzing the data in the 84%-88% range
    > reveals:

    > pen__84.5%_____87.5%____

    > WR___1.59______1.84_____

    > DI___4.27______4.80_____

    Actually, none of the above really matters. What matters is the SCORE, or the DI squared.

    > 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.

    So, looking at the DI, the SCORE increases by 1.124^2 - 1 = roughly 26%. That is quite substantial. But, how many dollars per hour does it represent? Read on.

    > 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

    Same comments as above. No problems, ... yet.

    > 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.

    And, this is your undoing.

    > 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 it's worth to
    > stand with 2, 3, & 4 versus the dealer's
    > Ace,

    You meant to write, "to stand with 12, 13, & 14."

    > but costs are not *too* detrimental in
    > the presented cases.

    Yes they are!!!

    > A quick calculation
    > shows the mean (average) expected loss for
    > standing on 12-16 v. 7-T to be
    > -.119909090909.

    Did you include the above three hands, because I didn't see anyone suggest that they should be left out?

    > 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

    You might have saved yourself a lot of trouble if you had consulted pp. 126-128 of BJA. Everything you need: the frequencies of the holdings, the conditional penalties, and the absolute (weighted for frequency) penalties are all there in those three charts.

    > 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).

    Must be a mental block: 12, 13, & 14!!

    > 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.

    How about all of the DD charts in chapter 10 of BJA. I'm beginning to get the sinking feeling that you don't have the book. I guess that is remotely possible! :-)

    > 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

    Certainly ballpark correct.

    > 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.

    Absolutely correct (he said, kindly, setting him up for the fall).

    > Subsequently, we will
    > be placing an average of 16.37 wagers, and
    > will make a minimum of 16.37 strategy
    > decisions.

    OK.

    > 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,

    Emphasis on the "per pack," he said, throwing out a clue as to your ultimate demise.

    > effectively replacing the "stolen"
    > 3% penetration, improving expectation on
    > that note, though obviously detracting from
    > expectation due to misplay.

    Much more than you might ever imagine.

    > 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, you may be underestimating somewhat, glancing at my BJA numbers. But, I guess you threw out the most damaging plays v. the ace, as per above. No matter.

    > 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.

    Per PACK!!!! And, head-on, at roughly 200 hands per hour (16 hands per pack), or at least 12 packs per hour, we're looking at a loss, for the $5 player, of 12 x $1.80 = $21.60 per hour!!!!! (Note that, from p. 128 of BJA, simply adding all the losses and dividing the $100 wager by 20, to get a $5 wager, I get an hourly dollar loss of about $365/20 = $18.65.) I wouldn't expect a perfect agreement for many reasons, which I won't bother to enumerate here. But, the order of magnitude is what is important.

    > Now we compare this to our prior
    > stated increase in expectation, to determine
    > if I'm totally nuts or not;-).


    I'll be polite here! :-)

    > 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_%

    I'll see that and raise it to double the increase: I'll give you an extra 25% in hourly dollars won; how's that?

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

    Are you sure you want to do this? It could get messy? :-)

    > ___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%___

    Here, I miss something. If all figures assume a $5 minimum bet, heads up, just how are you figuring to win $60 an hour, exactly?? But, I digress. Let's say with a bold spread you might win $15 or $20 per HOUR. And, let's say that with the extra 3% pen, you will increase that hourly win by, say, $5. Hey, what the hell ... let's make it $10. Do you see that the entire gain is more than doubly wiped out by the mistakes in play??

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

    Bzzz. Sorry.

    But, don't get me wrong; I like the way you think.

    Don

  6. #6
    Adam N. Subtractum
    Guest

    Adam N. Subtractum: Don...

    ...you'll forgive me for not commenting immediately, I must reprimand myself for making such a horribly ploppy-like and obvious mistake...a night at the Mohegan Sun would be sufficient punishment, perhaps. What do you think? :-) Thanks for taking the time to check it out.

    ANS

    ps: in my defense, I was on about 1 1/2 of sleep.

  7. #7
    Don Schlesinger
    Guest

    Don Schlesinger: No apology needed

    > ...you'll forgive me for not commenting
    > immediately, I must reprimand myself for
    > making such a horribly ploppy-like and
    > obvious mistake...

    No apology needed. As I said, I very much enjoy your posts, and I like the way you think.

    > a night at the Mohegan Sun
    > would be sufficient punishment, perhaps.
    > What do you think? :-)

    Never having had the "pleasure," I wouldn't know. But, I've been told the games are pretty gruesome.

    > Thanks for taking the
    > time to check it out.

    You're welcome.

    > ps: in my defense, I was on about 1 1/2 of
    > sleep.

    So, there is a lesson there. Best not to post if not clear-headed. Also, best not to play BJ, either, under those circumstances. :-)

    Don

  8. #8
    Sun Runner
    Guest

    Sun Runner: ANS

    > Now we compare this to our prior
    > stated increase in expectation, to determine
    > if I'm totally nuts or not;-).

    Nuts? Not by a long shot.

    Not many would have waded on to this public forum with that detailed of an anlysis.

    Excellent effort.

    SR


  9. #9
    SnoopDarr
    Guest

    SnoopDarr: Re: And the moral of this story?

    And the moral here? If it sounds too good to be true, it probably is... or maybe, ANS needs to get a 2ed job to take care of some of his "free time" problem

    BTW, i wonged out of the first post soon after you mentioned wonging out, because I was also on 1 1/2 hours of sleep. What i'm saying is that this is a nonsense post

    > Nuts? Not by a long shot.

    > Not many would have waded on to this public
    > forum with that detailed of an anlysis.

    > Excellent effort.

    > SR

  10. #10
    Adam N. Subtractum
    Guest

    Adam N. Subtractum: Thanks SR *NM*


  11. #11
    Adam N. Subtractum
    Guest

    Adam N. Subtractum: Thanks Don, lesson learned *NM*


  12. #12
    Parker
    Guest

    Parker: Agree with Don

    I greatly appreciate your taking the time to attempt to quantify this.

    I must confess that, when I read your post, I also overlooked the error (even after repeated readings), which is why I called in the "big gun." :-)

    Thanks in part to your post, I think we can now safely conclude, beyond any reasonable doubt, that this is not a viable method of attacking a "blind pitch" game.

    . . . um, which is what I've maintained all along, but nevermind, let's not go there :-)

  13. #13
    Adam N. Subtractum
    Guest

    Adam N. Subtractum: Parker...

    > I greatly appreciate your taking the time to
    > attempt to quantify this.

    It's my pleasure.

    > I must confess that, when I read your post,
    > I also overlooked the error (even after
    > repeated readings),

    Sure you're not just sayin' that to make me feel better? ;-)

    which is why I called in
    > the "big gun." :-)

    And he fired away with precision, as always.

    > Thanks in part to your post, I think we can
    > now safely conclude, beyond any reasonable
    > doubt, that this is not a viable method of
    > attacking a "blind pitch" game.

    Undoubtedly.

    > . . . um, which is what I've maintained all
    > along, but nevermind, let's not go there :-)

    If you know me Parker, I'm the type of guy to explore all possible avenues before taking directions. Alot more time consuming, and sometimes costly...but I enjoy the ride.

    ANS

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