Clearing.html

Preserved reference

Bob Dancer posted the following critiques to public forums, and has posted additional criticism of my work in his own web site. Comments are welcome (see below), and any rational comments from anyone, including from Bob, will be posted here.

Bob worked for me on the publication of Video Poker Times (VPT) for a few issues in 1993. When we parted company, we agreed that neither of us would ever fault the other's work. I have kept my side of that agreement. I have never faulted Bob's work. My only criticism has been to state my opinion that his strategies are fine for pros but some are too complex for most recreational players.

Bob has repeatedly made false claims about me and my publications in the online forums, in private e-mails to other players and even on his public web site, so I think it's only fair to review the facts objectively. Bob has not offered an opportunity for me to respond on his web site, but if he can find any errors in my responses below, or if he can document any of his other claims, I will publish them here with apologies to Bob and my readers. I also welcome readers comments in our VP forum.

The e-mail below was received from Bob Dancer on March 5, 1998. Yes, that's a long time ago, but in it he goes back to 1993, and Bob recently went back to 1993 yet again in an attempt to fault my work, claiming that I had recommended deviating from the correct strategy, when in fact I had stated that such deviation would only reduce the player's expected return. (It's worth noting that Bob has not specifically criticized anything I've written more recently than 1995.)

I have not previously published a response to the 1998 post because I was hoping that the controversy would fade out. Unfortunately, Bob is so desperate in his attempts to vilify me that he has continued to attack my work without letup, creating "errors" out of thin air, fabricating lies about me, and including repetition of some of these same claims in his web site and in online forums, so I feel it necessary to finally bring out the facts in a detailed response.

Of course, the e-mail addresses are no longer valid. I have made no changes in content or intent of any of Bob's comments. Bob's post is in red print, and my responses in black.

Historical contact information removed.

Dan - I originally sent this to you, Tabbycat and Joe C., but I had a typo in your e-mail address.

Alan, Dan, and Joe:

I spoke out strongly against a historical video-poker writer's work, and all three of you responded negatively to my outburst. I am sending you my reasoning concerning why I spoke out so loudly. I will not publish this on the mailing list unless there is sufficient demand for it.

Tabbycat and Joe C. are well respected in the world of video poker. I never saw their responses, but Bob's words above give an indication of what they thought of his "outburst." Bob never did publish his post anywhere, ignoring my requests that he do so. Now back to Bob's e-mail.

Joe, your point on Paymar's All American poker is well taken, except that it isn't Paymar's work. Paymar's original work on this game wasn't very accurate. The most definitive work that I know of was done by "The Fireman" who provided it to both Paymar and myself some time ago. Paymar published it, and credited The Fireman appropriately.

The old All American Poker strategy that Bob referred to was done before any VP analysis software was commercially available. I had to write my own computer programs to do the analysis, something that Bob has never done so he has no concept of the scope of such a project. I think The Fireman invested a lot of hours using Video Poker Tutor (VPT) when it first came out to generate the improved AA strategy. Prior to that, my AA hand rank table was the only strategy anyone had published for that game. It was obviously not perfect, but it was the best available at the time.

I have never suggested that Dan couldn't recognize good work done by others. Dan and I have feuded for years. I briefly worked for him (on the Video Poker Times) and made major (uncredited) contributions to his book between his 8th and 9th edition.

There never has been a feud from my side. All I ever wanted was for both of us to abide by the agreement to not fault each other's work.

Bob's "major contributions" to Video Poker - Precision Play were primarily to eliminate references to various perceived anomalies reported by readers. My conclusion about Bob's attitude is that he is very closed-minded, and even though it is known to be mathematically impossible for a digital computer to generate truly random numbers he refuses to consider any possibility that the games are not completely random. Bob also wanted to replace the "money management" section with a discussion of the Kelly Criterion. I felt then, and still do, that the Kelly Criterion is not particularly well suited for use with video poker. More recently, we have found that the jazbo/Sorokin formula for Risk of Ruin is by far the best tool for money management.

Bob first offered his "improvements" to me for $100, sight-unseen; when I hesitated, he said he would give me the changes, and I could pay what I thought they were worth.

After going over his proposed changes, and putting a few of them in the book, I didn't feel that they were worth much to me, but he reneged on the offer that I could pay what I thought they were worth and insisted I pay him $100. I was short of cash at the time, and asked if I could pay him $50 that week and $50 the following week. He agreed to that, but he again reneged on the agreement and withheld his column for the next issue of VPT until I paid him the full $100. He wrote in a hard copy letter (which I still have): "I understand that this is an ultimatum." It was right at my deadline for the issue, and I made the big mistake of giving in to avoid delaying the issue to write a column myself.

Only a few of his proposed changes were made in the 9th edition, and in the 10th edition nearly all of these changes reverted to my original. One need only compare the 10th edition to the 8th edition to see that there is very little in the book that can be attributed to Bob.

Also, contrary to what Bob says, he was listed in the credits in the 9th edition, and he is listed in the credits in Video Poker - Optimum Play.

As for the quality of my work, my strategies for Jacks-or-Better, Deuces Wild and Joker Wild (Kings) were developed on my own computer programs, and they were the most accurate available from January, 1992 (when the first edition of Video Poker - Precision Play was published) until Video Poker Tutor came out, whereupon several people who never did any programming themselves (including Bob) began refining the strategies. In spite of this, the Precision Play™ rules for Jacks or Better and Deuces Wild are virtually unchanged from the first edition and have served thousands of people very well. Bob's specific critique of those original Precision Play rules (see later in this document) show that they were very good indeed. I feel that these strategies are still the best available for recreational players, and especially for beginners. Now back again to Bob's e-mail.

I did not work on jacks or better, as I had not studied the game at that point. I believe this is in mid-1994 that we are talking about. I claimed on these pages that he made several major errors in his book on Jacks or Better, at least through the 2/1/95 version of the ninth edition, which is the latest I have. Tabbycat challenged me to identify them.

Paymar's Precision Play Rules are "top down", meaning that if a hand is described in two separate rules, the earlier mention takes precedence. Paymar's rules include regular Jacks or Better instructions, along with a few approximate references to Jacks or Better Progressive machines.

I am listing certain of his rules. Some are being paraphrased (to eliminate the references to the progressive game). In no case does my paraphrasing affect the accuracy of his chart. On the chart "BD" refers to my strategy, "DP" refers to a historical video-poker writer's Precision Play Rules.

I have provided a value of errors, assuming you are playing for dollars. Quarter players may divide by 4. Each hand (at dollars) stands to be a loser, on average, of about 2.4¢. Any of the errors listed above should be compared to that.

Rules 1 - 3: I have no quarrel at all with his first three rules.

Rule 4: Break a 4-card flush only for a 3-card royal

(BD comment - The errors in this section are truly minor. They are listed here for completeness. The bigger errors are coming.)

Hand a) Ah Kh 10h 6h 10s
BD: A-K-10-6
DP: A-K-10
Worth 0.5¢

Hand b) Ah Kh 10h 6h Qs
BD: A-K-10-6
DP: A-K-10
Worth 3.7¢

As Bob says, these "errors" are miniscule. Actually, I don't consider them to be errors at all. As stated in the book, my strategies are optimized; that is, they are intentionally simplified in cases where a situation occurs infrequently and the EV difference is small. This makes the Precision Play rules easy to learn, resulting in increased playing speed and fewer unintentional deviations from the strategy during play. For most recreational players (the obvious target audience of all of my publications), this maximizes the player's real expected hourly win rate (my definition of "optimum play"). I would be willing to bet that most players would go for the royal over the flush anyway, regardless of what the strategy said to do.

But let's see just how much this "error" really costs. A three-card royal flush with no higher draw (such as a high pair or 4-card straight flush) averages once per 91.65 dealt hands, and it contains both an ace and a ten in only three out of nine of those hands, or once per 275 deals. Fewer than two in 45 of those hands will also contain both a small suited card and a high unsuited card (required for Bob's 3.7¢ "loss"). Sorry, Bob, but I can't become very concerned about giving up 0.0074 of expected value one time in 6185 hands (about eight hours of play) in order to "perfect" my play. Bob's other example is even less frequent, and the long term "cost" is truly in the noise level.

Rule 5: If you have both a 4-flush and a 4-straight, go for the flush (and never draw to an inside straight unless it includes 3 honors)

(BD comment. He discusses inside straights before 3-card straight flushes. Later on, he gives erroneous rules for breaking A-K-Q-J hands, but he never discusses breaking A-K-Q-10, A-K-J-10, A-Q-J-10, or K-Q-J-9 hands. It is a confusing situation.)

Hand c) Ah Ks Qc 10c 9c
BD: Q-10-9
DP: A-K-Q-10
Worth 43.8¢

Hand d) Ah Ks Qs 10d 5h
BD: K-Q
DP: A-K-Q-10
Worth 28.4¢

It appears that Bob deliberately misinterprets the strategy. He says, "It's a confusing situation," but he seems to be the only one confused. Just before each set of Precision Play rules, the book says to "Follow the first rule that applies to the hand you've been dealt." At the beginning of his letter, Bob says "Paymar's Precision Play Rules are 'top down', meaning that if a hand is described in two separate rules, the earlier mention takes precedence." While this is basically correct, it is incomplete.

Bob also says, "In no case does my paraphrasing affect the accuracy of his chart," yet this does affect the usage of the rules, allowing him to find an "error" where none exists. Rule 5 does not mention SF3 hands at all, so it does not apply to example hand c. No one else is confused by this; anyone who is not just trying to find errors where none exist would simply go on to the next rule which covers SF3's, so there's no error here at all.

Figuring the frequency of a dealt hand such as example d is very complex, but it's clearly very rare that an inside straight draw is better than a K-Q RF2, so the cost this "error" is miniscule in the long run (see the Summary below).

Incidentally, even though it didn't cause errors being where it was, the discussion of inside straights was moved down to become Rule 9 in Video Poker - Optimum Play to make the rules even easier to follow.

Rule 6: Draw to any 3-card straight flush (even a double inside draw) unless it requires breaking a made pay, any pair, or any 4-card flush or open-end straight, except draw to one or two honors rather than a double inside straight flush with no honors

Hand e) Qh Jh 5d 4d 2d
BD: Q-J
DP: 5-4-2
Worth 55.4¢

Hand f) Ah Qc Js 10c 8c
BD: A-Q-J-10
DP: Q-10-8
Worth 4.6¢

For hand e, the last part of rule 6 clearly says to hold the Q-J, so Bob is creating yet another "error" out of thin air. Bob is such a stickler for accuracy, it's hard to believe that this was accidental. Did he intentionally misuse the rule that he had just quoted?

Hand f is another rare situation that was carefully contrived. Only about one in 232 dealt hands would be playable as a Straight 4 i (h3), and a SF3 di (h1) coexists in only one out of 112 of those, or about once per 26,000 hands. At 800 hands per hour that's about once per 32 hours of play. Net cost: about one-fortieth of one cent per hour on a dollar machine.

Rule 7: Break A-K-Q-J for suited Q-J or any three suited honors

Hand g) Ah Ks Qc Jc 5c
BD: A-K-Q-J
DP: Q-J
Worth 6.0¢

Hand h) Ah Ks Qc Jc 9s
BD: A-K-Q-J
DP: Q-J
Worth 1.1¢

This one was discussed in detail in an e-mail to Skip Hughes' on-line video poker forum, and in the section "Errors In Precision Play?" in Video Poker - Optimum Play. The net cost of this error in the long run is in the noise level. With more complex rules (e.g., Bob's) the majority of players would lose more through slower play and occasional misunderstandings of the strategy. Such extreme detail is of interest only to professionals and wanna-be pros.

Rule 8: Break any three of A, K, Q, and J for any two suited honors

Rule 9: Hold any one, two, or three honors, except discard A from A-honor-honor

Rule 10: Keep a suited ten when you have only one of K, Q or J and no discard is of the same suit

Hand i) As Jc 10c 5h 2h
BD: J-10
DP: A-J
Worth 15.2¢

Hand j) Jc 10c 6s 3s 2c
BD: J-10
DP: J
Worth 14.6¢

Hand k) Kh Js 10s 5c 3d
BD: J-10
DP: K-J
Worth 7.3¢

Hand l) Ac Qh 10h 5c 3s
BD: Q-10
DP: A-Q
Worth 6.1¢

Rule 10 had a genuine error, but note that Bob is referring to the 9th edition of the book, the edition that he claims contained his "major contributions." So why didn't he say anything about it at the time? Rule 10 (now 11 in Video Poker - Optimum Play) was revised, so the EV differences are much smaller. (Note: Before Bob takes credit for this, let me mention that the first manuscript of VP-OP, which included this change, was sent to ConJelCo in February, 1998. That was before Bob's critique.)

In the back of his book, his Table 2 (Pre-draw Hands - Jacks or Better (4000) has fifteen notes. Taken as a strategy chart, this is quite a bit better than his Precision Play Rules. For example, Hands c, d, e and g are given correct explanations here, but the other errors remain. He also introduces a new set of errors in Table 2. For example:

Note g says "Break a high pair to draw to K-Q-J suited." This error is worth 32.8¢ or 38.7¢ or 24.0¢ depending upon whether the fifth card is an A, a 10, or neither. He also says that "A-K-Q suited vs. a high pair is a very close call - so take your choice." It is not close at all. The error is worth up to 80.9¢, depending upon the discards.

Note m is particularly bad: "Don't hold a 10 with any high card if any discard is the same suit or a straight card." This leads the the following errors:

Hand m) Jh 10h 7s 5s 4d
BD: J-10
DP: J
Worth 19.5¢

Hand n) Jh 10h 5h 4d 3c
BD: J-10
DP: J
Worth 14.6¢

Note "g" was completely rewritten for Video Poker - Optimum Play (again, this was done before Bob's critique). I thought I had changed note "m" a long time ago, but somehow it slipped through the cracks. I wish to thank Bob for pointing out this error. In the second printing of Video Poker - Optimum Play, "any high card" was changed to "a king." Fortunately, the decision to hold Q-10 or J-10 does not occur very frequently, so the cost in the long run is quite small.

All of this discussion of the hand rank table notes is insignificant because most of my readers would be using the Precision Play rules, and they were always correct on this decision.

Are Paymar's Precision Play rules more accurate than those of Scoblete or Frome? Yes. Most definitely. But you don't see Scoblete or Frome going around advertising that their rules are "Highly Accurate." If they did, I'd jump all over them too. Paymar regularly advertises that his rules are very nearly as good as any other strategy - which presumably includes mine. Paymar know this is false, and yet he keeps on making these claims.

I am not going to publish this on the mailing list, because I am quite sure that everyone there is fed up with "Dancer-Paymar" sniping - from either direction. This will be my last "harangue" unless Paymar continues to publicly maintain that his work is of high quality.

It seems to me that both Scoblete and Frome did claim that their strategies were accurate. Frome claimed 99.6% payback for Jacks-or-Better with his hand rank table (0.056% more than the perfect play maximum), but Bob never criticized him for that. Of course, Bob claims 100.2% payback with his strategy for Double Bonus Poker in spite of the fact that the maximum with perfect play is 100.173%. I claim only 100.15% for my cue card. Just who is claiming more accuracy than is reasonable?

Summary:

After I posted my response to Bob's criticism of Rule 7 on Skip Hughes forum, Jazbo Burns did an analysis using his own strategy evaluation software and determined that my Precision Play rules would yield 99.5348% expected return. That's less than 0.01% below the game's theoretical maximum payback of 99.5439%. Jazbo obviously followed the rules logically. I had never promised more than 99.52% payback for the Precision Play rules, so contrary to what Bob says, I have never made any false claims. Actually, it seems I have always been more conservative than necessary.

As with so many of Bob's claims, it appears that he pulled the "2.4¢ per play" out of thin air. Even using his own figure of 0.0136%, he contradicts himself because 0.0136% of $5.00 is only 0.068¢ per play, and using jazbo's more objective 99.5348% figure it's only 0.0455¢ per play. Bob's "2.4¢ per play" claim is an exaggeration by almost two orders of magnitude!

The only objective measure of a strategy's accuracy is how close it comes to yielding the game's perfect-play expected return. By that criterion, I stand by my claim that my Precision Play rules are very nearly as accurate as any other strategy (yes, including Bob's), and for most players they are better. (By "most players" I mean the vast majority of all video poker players, of whom at least 99.99% are non-pros who would likely lose more through misunderstandings and loss of speed when attempting to use a more nearly "perfect" strategy.)

Some final comments:

Bob's own words ("outburst" and "harangue") illustrate his attitude and the merit of his remarks, which may be why he chose not to previously publish it in an on-line forum in spite of my repeated requests that he do so.

Before Bob gleefully points it out, I should mention that a typo error crept in to the first printing of Video Poker - Optimum Play. In the Precision Play™ rules for Deuces Wild (page 46), the third rule under one deuce should begin "Any 3-card royal..." (instead of 4-card). This was correct in all editions of Video Poker - Precision Play, and it was corrected in the second printing of Video Poker - Optimum Play.

Another "harangue"

Below is Bob's post to vpFREE and my response to it in June, 2006. Note that he's still going back 15 years to find faults. Apparently he's unable to find anything to attack in my contemporary publications.

First, I want to reiterate that I write for the vast majority of players, those who are not professional gamblers but who want to improve their skills and play at an advantage while earning comps to make their vacation more enjoyable. I have never claimed that my strategies are perfect; rather, I have always said that they are optimized for the majority of players to be able to achieve the best per-hour win rate (or smallest loss rate on negative games). This is done by simplifying in situations where the difference in EV is small and the occurrence is infrequent. This approach has been justified by Skip Hughes, showing that a penalty-card-free strategy can yield within 0.01% of perfect play for most games, and within 0.001% on Jacks or Better.

My strategies have been validated many times. Jazbo, well known in the online forums as an expert mathematician, has shown that following my Precision Play rules objectively will yield within 0.01% of perfect play. Before I could complete this and post it, Skip Hughes found that 1998 post and proved that Jazbo had, indeed, thus evaluated my rules. Although Bob has never developed a strategy on his own from scratch, he seems to think that he is a better strategist and mathematician than Jazbo or myself.

Bob didn't copy the old rules in his post, so I'll reproduce them here so that we all know exactly what we're talking about. Remember, this strategy is for 9/6 Jacks or Better, and also that there have been some improvements to this strategy since this early version, so although this strategy will get you within 0.01% of perfect play, the Precision Play rules in Video Poker - Optimum Play are even better but just as easy to learn and use.

1. Never break any made pay of two pair or better, except;
Break anything but a pat straight flush for any 4-card royal

2. Break a high pair only for a 4-card royal or any 4-card straight flush (including an inside draw); also for K-Q-J suited if a royal flush pays at least 4300 coins

3. Break a low pair only for K-Q-J-10, any 3-card royal flush, or any 4-flush or straight flush

4. Break a 4-flush or open-end straight only for a 3-card royal

5. If you have both a 4-flush and a 4-straight, go for the flush
(and never draw to an inside Straight unless it includes 3 honors)

6. Draw to any 3-card straight flush (even a double inside draw) unless it requires breaking a made pay, any pair, or any 4-flush or open-end straight, except draw to one or two high cards rather than a double inside straight flush with no honors

7. Break A-K-Q-J only for suited Q-J or any three suited honors

8. Break any three of A, K, Q and J for any two suited honors

9. Hold any one, two or three honors, except
Discard Ace from A-honor-honor (but keep A-honor if suited)

10. Keep a suited 10 when you have only one of A, K, Q or J, and no discard is of the same suit, except don't hold a ten with an ace if the jackpot is less than 4600 coins

Now on to Bob's post. I don't understand why Bob wants to make himself look ridiculous, but since he's a glutton for embarrassment, here goes. Again, Bob's post is in red, and my response in black.

I am surprised that Dan welcomed a chance to identify his errors. But he did, and he deserves a response. He invited me to "give it my best shot", and I intend to do that. Had he not made such an invitation, I would not have written this.

There's no reason for him to be surprised. I've made this invitation many times over the years, and this is the first time that Bob has dared to post his criticism publicly. I finally get a chance to make a direct response.

He says he didn't start this thread. Fair enough, but I didn't either. Someone else suggested that the reason I started writing about video poker is because opportunities were drying up, and I responded, truthfully, that the reason I started writing about video poker was that the current writers weren't very accurate. Dan said that the reason my Reports were so accurate was that I copied them from him. That is inaccurate and highly offensive. Had he not said that, this thread would not have started.

Bob always claims he didn't start a thread. He and many others know otherwise. In this case, on February 26, he posted on vpFREE:

My reports were first published in 1995, when I was barely into dollar stakes and still played mostly quarters. My writing was mainly inspired by the lack of good published information. I have a background in teaching various things, so teaching others about video poker came naturally. The only "reasonable" video poker writing I could find then was Bradley Davis, Frome, Paymar, and Wong. While Davis and Wong were accurate enough (but only about specific games I wasn't interested in), the other two weren't --- by a long shot.

That post is what started this latest thread, with Bob saying that my strategies were not as accurate as Davis or Wong "by a long shot." I had not posted anything mentioning Bob for several months prior to that. BTW, note that in this post, Bob said that my strategies were not as accurate as Frome's, but in his 3/5/98 post above he said: "Are Paymar's Precision Play rules more accurate than those of Scoblete or Frome? Yes. Most definitely." He can't make up his mind!

I am getting chastised on vpFREE for picking on Dan. In my opinion, he asked for it by accusing me of copying his work. I have stated many times that Dan's work is extremely sloppy and that people using it are making a large number of mistakes. I was not going to keep harping on that, but when Dan starts up and accuses me of plagiarism, he's asking for it, in my opinion.

If you will pick up any copy of my Precision Play rules, as far back as the first issue of Video Poker - Precision Play in 1991, you will see that my format and method of putting the strategy into a short set of rules instead of just a hand rank table was unique until Bob's "Reports" came out several years later in very similar form.

Dan suggested that his Precision Play for Jacks or Better was certified to be within 0.01% by Jazbo. I responded that this slandered Jazbo. I can't believe that Jazbo is so inaccurate that he would make such a miscalculation. I've always believed the error was considerably larger than that, but I never calculated it until tonight. My calculation tonight (shown below) shows that the error is actually 0.0136% --- although I was only working with 4-place numbers so that number might be off a bit. This is 40¢ an hour for the 600-hands-per-hour dollar player. Since I was planning on moving up to $5, I couldn't see playing a strategy that would cost me $2 an hour. This was hopelessly inaccurate for my purposes. If you count the error made by EITHER the Precision Rules or Table 2 in the back (they are NOT the same at all), the error is closer to .015%.

I have great respect for Jazbo, as do most people who are involved with video poker analysis. After Bob posted his harangue (his word), I was surprised and grateful when, unsolicited, Jazbo posted a comment that my rules would return 99.5248%, only 0.0081% off of perfect play. In response, Bob wrote, "Be careful, Jazbo." Clearly, Jazbo was much more careful than Bob. Prior to that I had only claimed that my strategy would yield within 0.02% of perfect, and here Bob inadvertently validates that claim by saying that the error is 0.0136%. Thank you, Bob. Even without going further in the discussion, you have shot down your own criticism. And Bob is right, that would be almost 41 cents on $3000 action. If you're a pro, this might be important to you, but most players would lose more due to loss of speed and unintentional deviations from a complicated "perfect" strategy.

I completed the following table in about an hour. I did figure out an error overnight (in counting the hands including "KT", a flush penalty, and a 9 penalty, I forgot to subtract out hands like "KT8"97, which is a 4-card straight and is handled correctly by Dan. It's possible that more errors exist. But it should be pretty close. And if I were going to publish this in a book, it would be checked three or four times. If anyone doesn't understand how a certain number was derived, feel free to ask.

Dan's Precision Play strategy misplays 22,500 different hands, listed below. (With a number like this it may appear to be rounded. But it's not. That's the number of hands I counted.) This is approximately 1 in 115 hands. The Advanced strategy I published in my reports misplays zero hands. It's hard to imagine how he figures I copied his work. If I had copied his work, I would have the same errors he did.

It doesn't matter how many hands are "misplayed" (i.e., not played for the absolute greatest EV) provided the end result is within acceptable tolerance. My rules were refined a bit for publication in Video Poker - Optimum Play (in part due to comments by Bob and others).

Also, I never claimed that Bob copied my work. Only the concept of putting the strategy in the form of a small number of rules that are much easier to remember than a hand rank table. Again, he validated my work by using the same form. What's that they say about the sincerest form of flattery?

Each of the hands has a number next to it showing the number of occurrences. To show an example of how this number was calculated, look at the first row. (This error in particular is one that Dan never attempted to play correctly. I'll discuss later which hands were because there were penalty cards and which ones were due to sloppiness. The explanation here is how the 288 figure is derived.)

This hand occurs when "AKT", "AQT", or "AJT" is combined with a card of the same suit in the range 2-9. Further this must be accompanied by an off-suit ten. There are four suits. So we multiply 4 (for the number of suits) * 3 (for the number of 3-card royals in the category) * 8 (number of different cards in the range 2-9) * 3 (number of suits possible for the off-suit ten). This comes out to 288.

The next column over is the size of error if you are playing five coins on a $1 machine. The error here of 0.0046 represents slightly less than a half-cent. (This number is five times as large as the 1-coin EV figure that Dan prefers to use. We each have our reasons for using the particular EV sizes we do, but there is a 1-to-1 correspondence between them and either can be used to do calculations.) There are several errors on this list in excess of 40¢.

The last column is an "extension" --- that is, the product of the previous two columns. I needed to do this in order to calculate the size of the total error.

There are more notes below the chart.
1 Ah Kh Th 2h Ts 288 0.0046 1.3248
2 Ah Kh Th 2h Js 576 0.0370 21.3120
3 As Ks 2h 3h 5h 108 0.3454 37.3032
4 As Ks 3h 4h 6h 288 0.2814 81.0432
5 As Js 7h 8h Th 24 0.3256 7.8144
6 As Qs 7h 8h Th 48 0.2516 12.0768
7 Ks Qs 2d 3d 5d 264 0.3627 95.7528
8 Ks Js 7d 8d Td 24 0.3972 9.5328
9 Ks Qs 7d 8d Td 24 0.3232 7.7568
10 Qs Js 2d 3d 5d 84 0.4539 38.1276
11 Qs Js 5d 6d 8d 24 0.4352 10.4448
12 Qs Js 6d 7d 9d 12 0.4145 4.9740
13 Qs Js 6d 8d 9d 12 0.3997 4.7964
14 Qs Js 7d 8d Td 12 0.4539 5.4468
15 Ah Js Qd Td 8d 48 0.0463 2.2224
17 As Ks Qh Jh 2h 288 0.0601 17.3088
18 Ah Js Ts 2d 3d 1008 0.contact information removed
19 Ah Js Ts 2d 7d 540 0.1323 71.4420
20 Ah Js Ts 2d 8d 540 0.1125 60.7500
21 Ah Js Ts 2d 9d 540 0.0928 50.1120
22 Ah Js Ts 2s 3d 720 0.0490 35.2800
23 Ah Js Ts 2s 7d 180 0.0095 1.7100
24 Ah Js Ts 2s 8d 180 0.0295 5.3100
25 Ah Js Ts 2s 9d 180 0.0095 1.7100
26 Ah Js Ts 8d 7d 108 0.0977 10.5516
27 Ah Js Ts 8d 7d 108 0.0780 8.4240
28 Kh Js Ts 2d 3d 1080 0.0731 78.9480
29 Kh Js Ts 2d 7d 540 0.0533 28.7820
30 Kh Js Ts 2d 8d 540 0.0336 18.1440
31 Kh Js Ts 2d 9d 540 0.0336 18.1440
32 Kh Js Ts 7d 8d 108 0.0188 2.0304
33 Kh Js Ts 7d 9d 108 0.0188 2.0304
34 Ah Qs Ts 2d 3d 1548 0.0607 93.9636
35 Ah Qs Ts 2d 8d 648 0.0410 26.5680
36 Ah Qs Ts 2d 9d 648 0.0212 13.7376
37 Ah Qs Ts 8d 9d 108 0.0064 0.6912
38 Kh Th 2h 9s 3d 1440 0.0077 11.0880
38 Jh Th 2h 3s 4d 972 0.contact information removed
40 Jh Th 2h 3s 7d 720 0.1317 94.8240
41 Jh Th 2h 3s 8d 720 0.1174 84.5280
42 Jh Th 2h 3s 9d 720 0.1031 74.2320
43 Jh Th 2h 7s 8d 180 0.1066 19.1880
44 Jh Th 2h 7s 9d 180 0.0923 16.6140
45 Qh Th 2h 3s 4d 2052 0.0764 156.7728
46 Qh Th 2h 3s 8d 1080 0.0620 66.9600
47 Qh Th 2h 3s 9d 1080 0.0476 51.4080
48 Qh Th 2h 8s 9d 36 0.0369 1.3284
49 Kh Th 2h 3s 5d 1080 0.0066 7.1280

22500 1766.5044

Rows 1 and 2 are legitimately omitted by someone developing a penalty-free strategy, although that wasn't part of the terminology in those days. I do not fault Dan for these particular errors, but many of Dan's errors were because he used the penalty card concept incorrectly. This wasn't understood by most players until my Reports came out --- which is one reason I find it so offensive that Dan keeps repeating that my Reports were basically a rehash of his Precision Play rules.

I haven't bothered to go over the gritty details. I included all of them above only to avoid any possible claim that I edited Bob's post and to show how concerned Bob is with "perfection." Bob may be 100% accurate in each of the above hands, but it's the end result, not the minutia, that's important.

No one understood penalty cards very well prior to the availability of Panamint Software's Video Poker Tutor. I had to write my own computer programs to analyze the games. Bob is comparing work that was first published in 1991 with later work using better tools. I guess he's afraid or unable to criticize current publications.

And I find it offensive that Bob never gave credit to me for developing the technique of reducing a strategy to a set of rules that are much easier to follow than a hand rank table when he used that same format in his "Reports."

Rows 3-14 are all cases where we have two suited high cards combined with a 3-card straight flush with no high cards and one inside. This was sloppy. This is hardly "optimal".

Bob confuses the word "optimal" with "optimum." I have never claimed "optimal" or "perfect" strategies. In fact, I have NEVER used the word "optimal." I have always said that my strategies were optimized for maximum hourly win rate by non-professional players. Bob finds fault by changing words and by (intentionally?) misinterpreting my rules.

Row 15 are cases where a 3-card straight flush with 1 high card and two insides is less valuable than a 4-card inside straight with three high cards. This is a case where there are an equal number of cases where the straight flush is better than the inside straight as there are where an inside straight is better than the straight flush. Any simplified strategy has to pick one way or the other. If you pick the way Dan did, all the errors are 4.6¢. If you pick the opposite way, the same number of errors are 2.8¢ apiece. This is hardly "optimal".

Row 16-17 are cases where AKQJ are superior to a suited "QJ". These are reasonable things to omit in a simplified strategy. I do not fault him for this.

Rows 18-27 are cases where he said an unsuited AJ is superior to a suited "JT". This is NEVER true in 9/6 Jacks. This is hardly "optimal".

Rows 28-33 are cases where he said an unsuited KJ is superior to a suited "JT". This is a case where errors were inevitable, whether he said KJ > "JT" or he said "JT" > KJ --- because sometimes it's one way and sometimes it's the other. This is something strategy-makers need to accept if they are going to produce a simplified strategy. Unfortunately, Dan chose the wrong one. "JT" > KJ is the better choice, with fewer (and smaller) errors resulting. This is hardly "optimal".

Rows 34-37 are cases where he said an unsuited AQ is superior to a suited "QT". The exact comments from the previous paragraph apply here, and again, Dan chose the wrong one. Again, he misuses the claim "optimal"

Row 38 is a highly penalized case that Dan willingly accepted. I do not fault him for this

Rows 39-49 are just plain sloppiness. His rule 10 said "Keep a suited ten when you have only one of A, K, Q, or J and no discard of the same suit . . ." This is an extremely sloppy penalty card rule. He's talking about flush penalties here, and there is only one case in 9/6 Jacks where this matters --- and it needs a straight penalty to boot. (That's the case listed in row 38.) Here again, his claim for "optimal" is misplaced.

Both the number of errors and extension were summed. To get the percentage error, I divided the sum of the error by ($5 * 2,598,960), which is the total amount of money spent when each of the possible hands are played for the stakes I'm talking about.

I haven't bothered to review on all this detail because, in the end, it all adds up to only 0.0136% according to Bob, or 0.0081%, according to Jazbo. I trust Jazbo's evaluation better because, as I understand his method, his program follows the rules to play every possible dealt hand and tallies the results. Either way, though, the expected return is well within my claims. Thank you, Bob, for validating what you've been trying to malign.

Dan's Table 2 is what I would call an Appendix. It is a hand listing for the same game. It corrects several of the errors Dan made in his Precision Play rules but makes some others.

Actually, of course, it's the other way around. The hand rank table was developed first, then the Precision Play rules were derived from it to provide basically the same strategy, but simplified by ignoring low frequency situation with small EV differences.

His note m says " . . . and don't hold a 10 with any honor if any discard is the same suit or a straight card." I'm assuming that he means this to mean what is today referred to as a flush penalty and a straight penalty. In rows 39-49 above, we've already shown the quantity and size of his "flush penalty" misstatement. There are NO cases where a straight penalty affects whether to hold to a KT, QT, or JT except the aforementioned case on row 38 where we have BOTH a flush penalty and a straight penalty.

This would include the following cases: "JT"9, "JT"8, "JT"7, "QT"9, "QT"8, and "KT"9 (where the last two cards are lower, and there is no pair, 4-card straight, or 3-card straight flush in the hand), all of which are misplayed by the rule. The reason I didn't count them all is because I don't know when he says one penalty OR the other does he really mean one penalty AND/OR the other. (Both interpretations are wrong.)

Yes, a penalty card by today's nomenclature. And, as noted above, penalty cards were barely recognized in 1991 when the above strategy was first published. The point that should be noted here is that Bob continues to criticize work that is 15 years old. Using better tools, he has improved on that, but obviously so have I. For example, note "m" now says, "Don't hold a suited 10 with an ace if the jackpot is less than 940-for-1, and don't hold a suited 10 with either an ace or a king if any discard is the same suit or is a ten or higher." Still not "perfect" or "optimal" by Bob's standards, but it's definitely optimized.

But how did note "m" get into this discussion anyway? We were discussing the Precision Play rules, and that note is related to the hand rank table.

As sloppy and as "unoptimal" Dan's Jacks or Better strategy is, his Joker Wild strategy is considerably worse.

One of my problems with Dan's writing is that since he defined Precision Play rules as "Optimal," as being, then the definition of "Optimal," basically, is whatever he said it was. He says he didn't change the strategies between editions 1-8 (I have no reason to doubt this), but I know he changed them in each subsequent edition --- each time changing the definition of "optimal". A far better definition of "Optimal" is "the best possible strategy with using penalty cards". Dancer/Daily Level 3 strategy, or the identical-except-for-format version produced by Frugal VP offer good example of this. Jazbo's strategies (which I last saw about five years ago) would meet this definition. Paymar's rules are sadly lacking.

Again, "optimal" instead of "optimum." Bob seems to equate "optimal" with "perfect." I'll leave it to Bob to publish such strategies for the few hundred pros (most of whom wouldn't be bothered buying a strategy), and I'll continue to publish strategies that are optimized for serious recreational players. And how did Joker Wild get into this? I thought we were discussing Jacks or Better.

I do owe Paymar two big thank yous. First, if his work hadn't been so bad, I wouldn't have ever begun this career. Second, although he used the term incorrectly and very sloppily, I didn't start thinking about penalty cards until I saw his reference to it.

Well, thank you, Bob, for unintentionally validating my Precision Play rules and for admitting that you were building upon my work, as I have credited Lenny Frome for the basics that I built upon. The difference is that we have taken different paths. I write for intelligent recreational players (the vast majority of players) who want to gain the skill to play at an advantage, while you write for wanna-be pros and casino management, and you continue to criticize stuff that is over fifteen years old!

But BTW, although I did discuss a few cases of discards affecting a play in those early strategies, I didn't call them "penalty cards." Credit for that probably belongs to Skip Hughes or Jazbo. In Video Poker - Optimum Play, however, I give a very clear definition of penalty cards.

Some other facts:

1. Lenny Frome was truly the father of good published information on video poker. Besides his own booklets, he had regular columns in Card Player and Gaming Today magazines. Shortly after Lenny died, Bob told several people that I had contacted Gaming Today claiming that Lenny had designated me to take over his column. The fact is that I have never talked to anyone at Gaming Today or contacted them in any way. TomSki called someone he knew there and verified that fact. Bob's claim was a complete fabrication.

2. In a post to the vpFREE online forum in June, 2006, Bob stated that some (unidentified) publisher had refused to publish my strategy for Double Bonus Poker because of errors. I suppose that's wishful thinking on Bob's part, but it's just another fabrication. The truth is that no one has ever refused to publish any of my strategies. I never even bothered to develop a strategy for Double Bonus for many years because I felt that the player advantage was too small and the strategy too complex for my readers, most of whom are low limit recreational players. I finally included a hand rank table for Double Bonus in the second edition of Video Poker - Optimum Play at the request of my publisher (ConJelCo) and several readers.