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Dancer's Answers We publish a brand-new video poker article from Bob Dancer every Thursday in this section. These columns are called "Dancer's Answers". Click on any of the links below for more Dancer's Answers: Bob Dancer Articles - Main Page Vicksburg Video Poker - May 8, 2008 Vicksburg, MS Video Poker - Part 2 - May 15, 2008 Vicksburg Casino Video Poker - Part 3 - May 22, 2008 Common Deuces Wild Mistakes – Juan or the Other – May 29, 2008 Figuring Out Quick Quads - June 5, 2008 Breaking Full Houses in Quick Quads - June 12, 2008 A Quick Quads Puzzler - June 19, 2008 Let’s Go Scouting - June 26, 2008 When You're Not Sure of the Game - July 3, 2008 Can it be Right to Play Hunches - July 10, 2008 Good Hearted Woman in Love With a Good Timin’ Man - July 17, 2008 One-Way Versus Two-Way Straight Penalties - July 24, 2008 Effectual versus Ineffectual Straight Penalties - July 31, 2008 Unusual Dealt Royals - August 7, 2008 Learning from a Horse Handicapper - August 14, 2008 When Bad Is Good - August 21, 2008 I Live For These Moments - August 28, 2008 Las Vegas Do It Different - September 4, 2008 Figuring the worth when there are Multiple Progressives - September 11, 2008 Which is the Better Play? - September 18, 2008 How Much is Too Much? - September 25, 2008 Evaluating a Promotion - October 2, 2008 Sometimes the Jack, Sometimes Ace-Jack, Never the Ace by Itself - October 9, 2008 Why I Don't Play Poker - October 16, 2008 What is a Royal Flush Cycle? - October 23, 2008 A Logical Puzzler - October 30, 2008 Another Look at Changing Machines - November 6, 2008 Testing Matters - November 13, 2008 Next Dancer's Answers column coming on November 20, 2008! |
Effectual versus Ineffectual Straight PenaltiesIn the last column, I defined a straight penalty as a card in the original five cards that reduces the chances for one of the combinations in the hand becoming a straight.
When we discuss straight penalties, we need a term to indicate whether the straight penalty changes the correct play on this particular hand. When it does, I call the straight penalty “effectual.” When it doesn’t, I call it ineffectual. To show you what I mean, let’s look at 9/6 Jacks or Better, played for dollars, five coins at a time. Let’s look at three hands in this game, and then later we’ll look at the same three hands in other games.
In all three hands, the decision is whether to hold the ‘QJ’ or the AKQJ. The AKQJ is worth $2.979 in all three cases. In (a) the ‘QJ’ is worth $3.002; in (b) ‘QJ’ is worth $2.982; and in (c), ‘QJ’ is worth $2.967. In (a) the seven provided no straight penalty to the ‘QJ’ so ‘QJ’ was 2.3¢ superior to AKQJ. In (b) the eight IS a straight penalty but ‘QJ’ is still superior by 0.3¢. I’m calling this an ineffectual straight penalty. Even though the ‘QJ’ was reduced in value by this straight penalty, the ‘QJ’ is still the preferred play. In (c) the nine is a stronger straight penalty, which I’m calling an effectual straight penalty, and in this case AKQJ is preferred by 1.2¢. The reason WHY the nine is a stronger penalty than the eight is because the nine penalizes both the KQJT9 straight AND the QJT98 straight. The eight only penalizes the QJT98 straight. That explains why the nine is a stronger penalty. It does NOT explain why the nine is effectual and the eight isn’t. The reason the nine is effectual and the eight isn’t is simply that the value of AKQJ is lower than the value of the nine and higher than the value of the eight. The fact that the nine is a stronger penalty than the eight is a necessary condition for the nine to be effectual and the eight to be ineffectual, but it is not sufficient. There are numerous cases where we have two penalties, one stronger than the other, and BOTH are effectual or BOTH are ineffectual. Now let’s look at the same three hands in 8/5 Bonus Poker. Would you guess that the nine and eight are effectual or ineffectual? Before we address that question, it’s probably appropriate to note that AKQJ in this game is worth the same $2.979 as it was in 9/6 Jacks. After all, starting from AKQJ, the only possible outcomes are a straight or a high pair and both 9/6 Jacks and 8/5 Bonus have the same values for these pay schedule categories. To my mind, it’s pretty obvious that both the 8 and 9 are ineffectual straight penalties here. The reason they are ineffectual is that the value of ‘QJ’ is reduced by 5.6¢ relative to 9/6 Jacks because a flush pays $25 in this game rather than $30. Since the value of AKQJ didn’t change and the value of ‘QJ’ went down by quite a bit, we hold AKQJ even in case (a), where there is no straight penalty at all. And since we already know the value of ‘QJ’ will be lower in (b) and lower still in (c), it’s obvious that we’ll hold AKQJ there as well. Let’s try the same thing in 9/6 Double Double Bonus. Would you guess the nine and eight were effectual or ineffectual in this game? The value of AKQJ will remain the same as in the other two games, but what about ‘QJ’? While the value of the flush stays the same as in 9/6 Jacks, two other categories are different. The relevant quads are worth $250 rather than $125, but these only come around one time in 8,000 (approximately). Two Pair gives you $5 rather than $10, and these come around once every 22.8 hands on average. It may not be obvious, but the total reduction from Two Pair is MUCH bigger than the total increase from quads, so in all three of the cases, ‘QJ’ is worth 20.4¢ less in 9/6 Double Double Bonus than it is in Jacks or Better. I have identified one situation where a straight penalty is neither effectual nor ineffectual. It is a case where it is arbitrary whether or not to change the play, because the Expected Value of both plays is the same. The example I’ve come up with comes from Full Pay Deuces Wild, or any other Deuces Wild variation where straight flushes return 9 for 1 and flushes return 2 for 1. In this game, if we have a 3-card straight flush with two insides, with a straight penalty, it doesn’t matter EV-wise whether we hold the 3-card straight flush or the 4-card inside straight. There are dozens of examples of this, but I’ll choose 4h 6h 8h 7c Kd for illustration. Both ‘468’ and 4678 are worth $1.702 assuming you can find the game for dollars (good luck!) A case can be made in this case that holding 4678 is superior to ‘468’ because it has a lower variance. What this means is that you have a very slightly lesser chance of going broke if you play 4678 rather than ‘468’. If we make this argument, then the seven is an effectual straight penalty. If we deny the relevance of the argument, then the seven is “arbitrarily effectual” or “arbitrarily ineffectual” depending on the player. I think the idea of effectual versus ineffectual straight penalties is interesting and helpful. I’m not crazy about the word “effectual.” I tried “potent” and “impotent” and I wasn’t crazy about those terms either. Bob Dancer is America's best-known video poker writer and teacher. He has a variety of "how to play better video poker" products, including the software "Video Poker for Winners," Winner's Guides, strategy cards, his autobiography Million Dollar Video Poker, and his two novels, including Sex, Lies, and Video Poker. Dancer's products may be ordered at www.bobdancer.com or by telephone at 1-800-244-2224 M-F 9-5 Pacific Time.
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Classic Dancer We republish a classic Bob Dancer article every Sunday - often these articles are updated with new insights from Bob Dancer, the master of video poker writing. Video Poker Questions and Answers - May 4, 2008 More Answers to Questions About Video Poker Machines - May 11, 2008 Losing is a Major Part of Winning at Video Poker - May 18, 2008 Video Poker VS Blackjack - May 25, 2008 The Art of Tipping Slot Personnel - Part 1 - June 1, 2008 The Art of Tipping Slot Personnel - Part 2 - June 8, 2008 Putting Your Ducks In a Row - June 15, 2008 Luck and Skill in Video Poker - June 22, 2008 Strategy Adjustments in Video Poker - June 29, 2008 One Coin vs Five Coin - July 6, 2008 Video Poker Progressives - July 13, 2008 High Pairs versus Three Cards to a Rolal in Kings or Better Joker Wild - July 20, 2008 The Double Up Feature - Does It Ever Make Sense? - Part 1 - July 27, 2008 Doubling Up - Does it Ever Make Sense? - Part 2 - August 3, 2008 Did I Quit at the Right Time? - August 10, 2008 Money Management: What Does and Doesn't Work - August 17, 2008 "I'm Playing The Wrong Game" and Other Video Poker Fallacies - August 24, 2008 You Use To Be Such a Cheapskate - August 31, 2008 Is This a Good Promotion? Part 1 - September 7, 2008 Is This a Good Video Poker Promotion? Part 2 - September 14, 2008 More Video Poker Fallacies - September 21, 2008 Not All Proposals Should be Accepted - September 28, 2008 An Opportunity Too Good to Pass Up Part 1 of 2 - October 5, 2008 An Opportunity Too Good to Pass Up Part 2 - October 12, 2008 Predicting Your Future Results at Video Poker - Part 1 of 2 - October 19, 2008 Predicting Future Video Poker Reulsts - Part 2 of 2 - October 26, 2008 Moving Up in Denomination - Part 1 of 2 - November 2, 2008 Moving Up in Video Poker Denomination - Part 2 of 2 - November 9, 2008 A Letter from a Non-Believer - Part 1 of 2 More Classic Dancer coming Sunday November 23, 2008. |
