vpFREE2 Forums

Is this article by Dr. Gordon accurate, or obsolete and in error?

#1

I came across the following article by Dr. Edward Gordon, who did an analysis of VP some time ago, including the calculations of Dan Paymar and several other notables: http://tinyurl.com/itc5

He states that according to his calculations, JOB 9/6 full-coin has a slightly higher EV than what has typically been attributed to it, and he also goes on to indicate that the proper hold when presented with a suited Ace and Ten, with no penalties, is to keep both rather than just the Ace as other strategies typically indicate. He claims that those programs and strategies have failed to properly consider the penalty costs in discarding the Ten.

Winpoker indicates that the Ten should be discarded, and I think I can see where Dr. Gordon has possibly made an error in his assessment, but I'd feel more comfortable -- and will remain more confident about the accuracy of Winpoker -- if I can get some confirmation from my friends here on these groups, such as Harry Porter.

If some of you will please take the time to focus your attention on the article, a little more than half way down, under the heading "Can Discard Affect Choice?" -- it seems to me that Dr. Gordon is overlooking that the computed EV for the Ace without the suited-Ten already does take into consideration the cost of discarding the Ten. It seems to me that this is evident if one would look at a 'details' screen in WinPoker for a hand such as this: As-Ts-9c-8c-6h

The top line of that detail screen clearly assigns a value of zero under the Royal column, whereas the next line which calculates the value of the Ace-Ten clearly includes the possibility of a Royal.

My impression has always been that WinPoker is 100% accurate, and the methods it uses for calculations and comparisons seem logically to lead to that result. Anyway, I don't know if this was work that was done by Dr. Gordon before the advent of WinPoker; I can't tell from the web-site when the article was written, but 1996 is referenced for other purposes in the body of the article.

Any comments or discussion of that article would be appreciated.

I'm cross-posting this to FrugalVP as well because I'm interested in whether that program comes to any different results.

Thanks.

Bill Velek

#2

Jim Wolf wrote:

snip

From the help file...

When a Ranked Hand Will Not Occur

This is an advanced topic on showing hands in the chart that would not
otherwise appear.

With most strategy charts, a situation will occur where a strategy
combination will have a ranking, but will not actually occur with strategy
play. This is due to another strategy hand combination taking precedence
over this strategy combination, and is noted in the strategy statistics as
'WNO', or 'Will Not Occur' .

Thanks, Jim. Now I understand perfectly. I've designed my own personal strategy card which works a little bit differently and contains no 'rankings'. Instead, you just read down the card until you find the line in which all criteria have been met; such lines are, by default, the higher ranking hands, and there is no need to read any of the lower lines. Accordingly, my card ranks the J-Ts higher than a single Hi-card (which includes a lone Jack), but unless all of the criteria is met, those lines are skipped and you then end up holding the lone-Jack and discarding the Ten. It is actually much easier and more functional than it sounds from the description I just gave, especially with indentations and some color-coding that can't be shown here. Anyway, using that technic permitted me to combine 6 different JOB pay-tables onto a single pocket-sized card that I take to the casinos, with absolutely perfect play -- not a single concession whatsoever for even a single penalty. I have also made slightly simpler cards for the JOB's with a flush value of 5 (7/5, 8/5 & 9/5), and another for flush=6 (7/6, 8/6 & 9/6).

Here are the last lines from my combined strategy card so you can see what I mean.

29 JT-s when FL=6 ... AND no Flush-Pen ... AND no '9' except 7/6 no '7'
30 JT-s in JOB-7/5 or JOB-8/5 ... but only when no Penalties at all.
31 1 Hi-Card - including Jack split from ineligible JT-s
32 3-STFL 0-Hi 2-Gaps

You will note that lines 29 and 30 split the strategy according to flush values of either 5 or 6, so when playing JOB-9/6, line 30 doesn't apply at all. And because line 30 pertains only to JOB-7/5 and 8/5, neither lines 29 nor 30 apply when playing JOB-9/5, so you would _never_ keep the Jack-Ten in that game during short-coin play, even when there are no penalties at all.

Here are some example hands and how the above-lines would be scrutinized during various JOB games, SHORT-COIN:

Jh Th 9c 6d 5s -- the presence of a '9', without any other straight or flush penalties, disqualifies the JT-s /line 29 for JOB-9/6 and -8/6; incidentally, if the '9' was also a heart, then several different lines which are higher on the chart and pertaining to 3-STFL hands would apply. The result is not the same for JOB-7/6 because there is no '7' for the required double-straight penalty, as specified in line 29, so for JOB-7/6 you would keep the Jh-Th, even despite the '9' penalty.

Jh Th 9c 7d 6s -- same hand as above except there is now also a '7', which is a second straight penalty with the '9'; the '7' is specified here because there is no other card that could make a second straight penalty and still make it down to the bottom of the strategy chart to these lines. I.e., an A or K would make 2-Hi cards; a 'Q' or an '8' would make a 4-Straight, and cards below a '7' are simply not a straight penalty. This hand is to show you that with both a '9' and a '7', the Ten is now also eliminated in JOB-7/6 -- i.e., in ALL flush=6 games.

Jh Th 8c 7d 6s -- even though both the '8' and the '7' are 'straight' penalties when holding a J-T, they are NOT a 'flush' penalty, therefore line 29 is NOT eliminated and you WOULD hold both the Jack and Ten despite the double-_straight_ penalty. This is true for all three pay-tables where the flush is worth 6 [7/6, 8/6, and 9/6]. On a short- coin bet in 9/6, the difference in the Return for the two hands is less than .0001 betting units, but I wanted to make my strategy 100% accurate just for the challenge.

Jh Th 6h 5c 4s -- because the '6' is a heart, it is a _flush_-penalty; line 29 is therefore eliminated for all FL=6 games, and line 30 is also eliminated for all FL=5 games because this _flush_ penalty is "_a_" penalty, and none whatsoever are permitted in line 30. You would then proceed to line 31; the correct strategy, then, is to discard the Ten and keep the lone Jack for this hand.

I know that bothering with such precision doesn't save me much money, but it's nice when I'm playing WinPoker [haven't tried yours yet] and I manage to play sessions with over a thousand hands and not even make a single 'minor' error. When I do find an error, I check and it is always the result of carelessness on my part -- not my strategy. I get a lot of self-satisfaction from this.

Am cross-posting this to a couple of other groups in case anyone there finds this useful.

Cheers.

Bill Velek

#3

I can't speak directly for any of the commercial VP programs, but I
know this -- my own program takes no shortcuts, computes the exact
optimal strategy for maximizing EV, and gives 99.5439044% which I
believe compares exactly with several other independent efforts. That
number is not the number that Dr. Edward Gordon quotes.

JOB 9/6 is probably among the most widely analyzed games on
the planet. Is it possible that all of these independently developed
programs happen to have the same bug which gives the same
wrong answer? Yes, that is always possible, but it just doesn't
seem likely. Is it likely that Dr. Edward Gordon has produced a
correct number even though NOBODY else has reproduced his
results? Extremely unlikely. The whole reason for comparing
results with independent researchers is to validate those results
and gain confindence that the method used was correct. There
are many different ways to compute the correct numbers, and I
have total confidence that my algorithm is vastly different than
any other out there, yet the numbers agree.

I'm not very interested in spending a lot of time figuring out
what Dr. Gordon did wrong, but I think perhaps he made some
assumptions about how others had computed the results, and
then "corrected" figures that inherently needed no correction.

If any VP authors get a different number than the one quoted
above, based on an exact analysis, I would suggest that we
work together to find out why our numbers disagree.

ยทยทยท

On Saturday 02 August 2003 01:49 am, Bill Velek wrote:

I came across the following article by Dr. Edward Gordon, who did an
analysis of VP some time ago, including the calculations of Dan Paymar
and several other notables: http://tinyurl.com/itc5

He states that according to his calculations, JOB 9/6 full-coin has a
slightly higher EV than what has typically been attributed to it, and he
also goes on to indicate that the proper hold when presented with a
suited Ace and Ten, with no penalties, is to keep both rather than just
the Ace as other strategies typically indicate. He claims that those
programs and strategies have failed to properly consider the penalty
costs in discarding the Ten.

#4

Steve Jacobs wrote:

snip

I can't speak directly for any of the commercial VP programs, but I
know this -- my own program takes no shortcuts, computes the exact
optimal strategy for maximizing EV, and gives 99.5439044% which I
believe compares exactly with several other independent efforts. That
number is not the number that Dr. Edward Gordon quotes.

snip

I'm not very interested in spending a lot of time figuring out
what Dr. Gordon did wrong, but I think perhaps he made some
assumptions about how others had computed the results, and
then "corrected" figures that inherently needed no correction.

snip

I believe that I had already found at least one error that Gordon made, which I had already noted in my original post; I believe he was counting the penalty for the discarded Ten twice. I think he was starting with other folks computed values, which has already corrected considered the full impact of the Ten-discard, and then he added an additional penalty of his own. I assume that from there, he calculated the increased frequency of Royals based on the erroneous holding of the suited Ace-Ten, etc., and came up with his elevated figure.

I also found a math error on one of his tables that I discovered by using my computer calculator. This could possibly help explain his erroneous conclusions, as well.

I'm now absolutely confident that your figure is the correct one.

Thanks for taking the time to comment.

Bill Velek

#5

Bill Velek wrote:

I believe that I had already found at least one error that Gordon made, which I had already noted in my original post; I believe he was counting the penalty for the discarded Ten twice. I think he was starting with other folks computed values, which has already corrected considered the

That should have said: "correctLY considered"

full impact of the Ten-discard, and then he added an additional penalty of his own. I assume that from there, he calculated the increased frequency of Royals based on the erroneous holding of the suited Ace-Ten, etc., and came up with his elevated figure.

snip

Sorry about having to correct myself again. I'll try to be more careful.

Cheers.

Bill Velek