Bob Dancer responds – 8/5 Bonus

(This guest post has been kindly written by Bob Dancer. It has been posted with no edits, except for converting it from its original format to HTML.)

Filius Bruce sent me his analysis of the Dancer/Daily 9/6 Jacks or Better card (which he found excellent) and the 8/5 Bonus Poker (which he found to be generally good but imperfect.) Which, frankly, is not too surprising. Strategies for that return 5-for-1 for the flush are MUCH more difficult to play accurately than strategies for games that return 6-for-1 for the flush — especially if you want to get into the Advanced Strategy.

First of all, my co-author for the card, Liam W. Daily (an anagram of William Day, his real name) passed away a number of years ago. His input in the cards defense would have been useful. I’ll do the best I can.

The card should be properly referred to as the Dancer/Daily card rather than the Dancer card. Yes, I know I’m the surviving partner and as an author and teacher far more famous than Daily ever was in this field (but not in Economics, where his Ph.D. dissertation as used by international agencies), his contributions were major and should be acknowledged.

When I am quoting Bruce, I will use italics.

  1. The main problem I have with the Beginner strategy is a printing error: all the suits (♠♥♦♣) are missing from the strategy card:

    Yes. That happened on one printing batch. We changed printers and the font used by the new printer did not include the symbols for the suits --- which was unfortunate. Several of these cards were sold before we noticed this omission. That has been corrected and today’s cards include the suits. If you have one of these cards, it only affects the Beginner strategy, which is probably avoided by most readers of this post.

  2. There is no mention of KH being preferred to AH in these strategies.

    While this is fine at a Beginner or Recreational level, I think this should have been caught and corrected for the Basic and Advanced strategies. The authors could have simply written "KH > AH" and all would have been well. But the way the card is printed, the Advanced strategy is far from computer perfect, despite the hard work the authors have put in figuring out many of the edge cases.

    (Interestingly, the strategy generated by the Video Poker by Winners software for 8/5 Bonus Poker has a very similar problem! It lists "AH; KQ" in a single line, while KQ is definitely more valuable than AH and they can indeed appear in the same dealt hand.)

    We actually consider this to be a feature rather than a problem. The reason the strategies say KH, AH is there are no hands that are less valuable than KH while being more valuable than AH. This is done because we believe that fewer instructions are better than more instructions — partly because we can use a larger type face on the cards. By the time many of our readers get enough money to gamble with, their eyesight is going!

    The hand AKQJ is specifically listed, as is KQJ, and there’s a footnote that says: “Prefer HH to AHH.” Keeping all of these statements in mind, the line KH, AH is not ambiguous, because KH and AH cannot be in the same hand without it being either AKQJ or AHH, which are explicitly covered.

    Bruce spends quite a bit of time talking about this situation, so clearly he thinks it’s not clear. But I do. But I also agree with him that writing this KH > AH could have been clearer.

    Bruce also mentions the AH; KQ notation in the Video Poker for Winners strategies. That project was after Liam W. Daily’s death and all the credit/blame for the notation falls on me. The Dancer/Daily strategy cards were one of my resources when I put together the VPW strategies, but the VPW strategies did not include all of the footnotes and the associated Winner’s Guide. In the VPW strategy, KQ > AH would have been better than AH; KQ. In the strategy cards for Jacks or Better and Bonus Poker, I think it’s implied.

  3. A♣ 2♥ 3♣ 4♣ T♥: Correct hold is A♣ 3♣ 4♣ (SF3 -1), but the strategy card recommends A♣, since there is a straight penalty (2♥) unsuited with the ace and no high cards other than the ace. (The book's strategy is identical here. In the detailed explanations for the strategy, the book claims "the straight penalty must be external to the to the SF3 -1 to avoid creating a more valuable 4-card open-ended straight”. In this case, that 4-card straight, A♣ 2♥ 3♣ 4♣, is never held, since it's still an inside straight with just one high card. I believe that "must" is a part of the analysis, not the strategy, so I don't consider the book's strategy to be correct in this case either.)

    As Bruce mentions, in the Winner’s Guide we mention it must be an external straight penalty. There cannot be an external straight penalty to an A-low 3-card straight flush. These are: A23, A24, A25, A34, A35, and A45. Since the only straights or straight flushes any of these can be part of is A2345, any external penalty card must be a six or higher, which can’t be a straight penalty.

    I don’t remember why we didn’t specifically include the phrase “except A-low” when we referred to that particular strategy rule. Perhaps it was because we knew you could never have an external straight penalty to an A-low combination. Perhaps it was just an oversight.

  4. Q♥ J♣ 10♣ 7♣ 6♥: Correct hold is J♣ 10♣ 7♣ (SF3 -1) but the card recommends Q♥ J♣. This is probably because of a typo in the card, since the book's strategy is different.

    Correct. This is a typo. The card actually reads (using bold italics for suited combinations):

    QJ ........ (< J97 with no 8p; < J97 or J87 only when Ap)

    The first J97 should be JT7.

  5. Q♥ J♣ 9♣ 7♣ 6♥: Correct hold is Q♥ J♣ but the card recommends J♣ 9♣ 7♣ (SF3 -1), since there is no 8-penalty. This is probably because of a typo in the card, since the book's strategy is different.

    This is the same typo as the previous one. We intended J97 to only appear once. Unfortunately, it appeared twice, with one the existing ones supposed to be JT7. Bruce caught both halves of the same typo.

  6. J♠ 8♣ 6♣ 5♣ 4♥: Correct hold is J♠ but the card recommends 8♣ 6♣ 5♣ (SF3 -1). This is one of the simplifications the authors refer to when comparing SF3 -1 to a jack. The table in the book's appendix mentions the correct hold for this case.

    Bruce is correct here. The strategy card says: “This is a simplification of a complex relationship. For the precise conditions, see the Appendix of the Dancer/Daily Winners Guide to Jacks or Better.

    As Bruce says, the book’s appendix gets it correct. For the 5-coin dollar player, this error is worth about 0.6¢. We wanted this strategy to be able to be memorized and used in the casino. That required a few simplifications. This is one of them.

    Bruce includes this same hand twice, the second being in his discussion of the 8/5/35 version of Bonus Poker. In this game, the error is much larger, namely 1.8¢. This is NOT what I consider to be a minor error that should be swept under the carpet.

    My excuse is weak, but here it goes. At the time we published, the 8/5/35 game was brand new — and obscure (as opposed to today when the game is not so brand new, but still obscure.) We did not spend the time and energy on examining this game as we did 8/5 Bonus. This is a difference between the games that we missed.

  7. A♣ Q♥ 10♥ 7♣ 6♠: Correct hold is Q♥ 10♥ but the card seems to imply that A♣ Q♥ may be the correct hold. It says: "AH < QT with neither fp nor sp" but since the ace is a straight penalty to the QT, the exception can never hold:

    The detailed explanation in the book mentions that such a straight penalty can only be a 9 or an 8. The authors probably had every intention of excluding the ace as a potential straight penalty to QT, but literal interpretation of the card would consider the ace a straight penalty. The strategy should probably say something like “AH < QT with no 8p, 9p, or fp”. (I wondered if a “penalty card” is defined as any card that is not mentioned in any of the options. But the information sheet that comes with the card says: “A penalty card for one option may also be part of an alternative option”.)

    This hand is discussed in Bruce’s 8/5/35 section of his critique. In regular 8/5 Bonus, QT is NEVER superior to AQ.

    That said, his discussion brings up what we mean for penalty cards. We exclude as a penalty card, any card that makes a higher-ranked combination. For example, one (truncated) rule says JT   (< KJ when fp ...)

    We don’t consider an ace or queen suited with the JT to be flush penalty because that would mean that there is a 3-card royal flush in the hand, which is higher on the strategy list. 

    Another implied rule with penalty cards and their documentation is that we’re only talking about cards that are not mentioned in the rule. That is, in this case where we say “AH   (< QT with neither fp nor sp)” we are NOT considering the ace as being a penalty to the QT. It IS a penalty, of course, but we’re looking for additional straight penalties. Our card would have been much longer and more complicated if instead of saying “sp” we felt we had to say “sp in addition to the ace that is already listed in the rule.”

    Did we specify this anywhere in the cards or Winner’s Guides? I don’t remember. But we think it’s a reasonable, intuitive rule.

    It’s possible one can find exceptions to the “reasonable, intuitive rule” I just mentioned. In 9/6 Jacks or Better we discuss (truncated),
         “KQJ9 (< SF3 -1 with no sp)”
    In this case, on a hand like K J Q98, we definitely consider the jack to be a straight penalty to Q98.

    How can I reconcile the two cases? In the first case, on the A (< QT with no sp . . .), there is no reason to list the rule if we considered the ace a penalty card. We have a logically consistent system without extraneous, unnecessary rules. In the second case, KQJ9 (< SF3 -1 with no sp), this was the most efficient way to write it. 

    There are LOTS of cases where AHHT or KQJ9 intersect with a SF3 -1 in the same five cards. Our rule allows you to 100% accurately determine which ones call for the 4-card inside straight to be held and which ones call for the SF3 -1. If we used a slightly different definition of penalty cards to make it work, that’s the price of the simplification.

  8. J♥ 6♣ 5♣ 3♣ 2♥: Correct hold is J♥ but the card recommends 6♣ 5♣ 3♣ (SF3 -1). This is one of the simplifications the authors refer to when comparing SF3 -1 to a jack. The table in the book's appendix mentions the correct hold for this case.

    Yes, this is a simplification. Our goal was to present strategy rules that were able to be memorized and could fit on a strategy card. This particular error costs about 0.6¢ for the dollar five-coin player and occurs once every 217,000 hands, which, for reference, is three times as frequently as a dealt royal flush. And it is one of several similar cases. The rule we have is, however, the best simplified rule which is consistent with our goals.

    In the Winner’s Guide, however, we’re not limited for space. We can list all the exceptions, even though we believe that very close to zero humans would ever memorize all the exceptions to this game. We didn’t have this problem in 9/6 Jacks or Better because that strategy, even at the advanced level, is very simple. If you value your time as worth anything, it’s not cost effective to memorize every rare exception.

  9. A♥ J♠ 5♣ 4♣ 2♣: Correct hold is 5♣ 4♣ 2♣ but the card recommends J♠, since the ace is a straight penalty unsuited with the jack. This is one of the simplifications the authors refer to when comparing SF3 -1 to a jack. The table in the book's appendix mentions the correct hold for this case.

    This is NOT a simplification. This is NOT a Dancer/Daily error. On the top of the second side of the card devoted to the Advanced Strategy it says: “When either AH or KJ is present, it is the relationship of SF3 -1 to either AH or KJ that is relevant, not the relationship with A alone or J alone.”

    I don’t think we hid that rule, but I agree it’s easy to miss (as Bruce did.) Our attempt on this card was to present the advanced strategy as succinctly as possible with limited space. To my knowledge, no other author has presented an accurate advanced strategy for this game on a card.

    Yes, the Wizard of Odds presents an accurate and free strategy (two very difficult things to compete with!), but his strategies list individual hands which are impossible to memorize. If Dancer/Daily gives something as AH > xxx, WOO will present three lines in his exceptions list of AK > xxx, AQ > xxx, and AJ > xxx. And he won’t tell you what category xxx falls into (say SF3 -1 with such and such penalties either present or absent). He will just list the hands and let you make sense of it.

  10. Q♠ 7♣ 6♣ 4♣ 3♥: Correct hold is Q♠ but the card recommends 7♣ 6♣ 4♣ (SF3 -1). The book is also incorrect here. Neither the card nor the book mention that a queen could ever be better to hold than SF3 -1.

    Again, this is listed as part of 8/5/35 Bonus rather than the “regular” 8/5 Bonus. And Bruce is correct. We missed all of the cases where the solitary queen is superior to SF3 -1.

    This particular error on our card is worth a quarter of a cent and occurs every 108,000 hands. This falls in the range of “no financial import.” Possibly there are other Q versus SF3 -1 hands we missed as well. I didn’t know that then and I’m not going to look for them now. Should there be “many” of these hands we missed, it could add up to being worth creating a rule.

  11. For the Basic and Advanced strategies, which I assume most of the readers of this post would be using, the card should be corrected to say "KH > AH". With that correction, the Basic strategy would only leave an extra 0.002% on the machine. The Advanced strategies need some fixes to the exceptions, apart from the AH vs KH issue. But after correcting "KH, AH" to "KH > AH", the 8/5 strategy would only differ from computer perfect by 0.0010%.

    And I believe that, considering the card as a whole, KH > AH is definitely implied. The only time it matters is AKQJ, AKQT, AKJT, AKQ, and AKJ and every one of these cases is explicitly covered in either the card and/or the footnotes.

To get the most out of any card, you need to have the card in front of you while you practice on a computer. Whenever you miss a hand, look at the card to see what is correct. After a while, you’ll begin to understand the card author’s notation and start to become a better player.

I appreciate Bruce’s work here. The biggest disagreement we appear to have is the “AH, KH” rule as opposed to KH > AH. I believe the latter is implied by the totality of the work. Bruce probably accepts this too. But he argues that some readers won’t catch this subtlety.

And he is probably correct. A lot of users look at the card for the first time while at a machine in a casino. They have not taken the time and effort to master the card in its entirety before they attempt to use it.

Daily and I, on the other hand, spent several hundreds of hours on the combination of Winner’s Guides / strategy cards. The two of us (especially Daily) started off smarter and more dedicated that a large percentage of our users. So we assumed things that might not be true.

I have heard through the years that some players find our cards incomprehensible — meaning we wrote them for smarter people than are attempting to use them. I suspect this will always be the case when you’re attempting to document an advanced strategy. The subtleties are much more complicated than many players can get their heads around.

Finally, this is my second draft of my response. On my first one, Bruce wrote back and explained I had misunderstood some of what he had written, and where he considered I might want to rephrase things. For this I thank him.

I’ve found his work to be thorough and respectful. And if we still disagree — well, it is his website and within pretty broad limits he can write what he pleases.