A Look at SF3+1, SF3+0, SF3-1, and SF3-2 – Part II of II

Putting Bills Into a Machine

This is a continuation of last week’s discussion. You might want to check that blog out for context.

Consider the values of these combinations, playing 9/6 Jacks or Better for dollars, five coins at a time. Note that the value of these combinations can vary depending on the other two cards in the hands. In the examples so far, I’m considering the fourth and fifth card to be an unsuited 2 and 3.

SF3+1 SF3 2h1i QJ9 $3.70
SF3 1h0i JT9 $3.68
SF3+0 SF3 2h2i QJ8 $3.21
SF3 1h1i JT8 $3.20
SF3 0h0i 987 $3.18
SF3-1 SF3 1h2i QT8 $2.72
SF3 0h1i 986 $2.70
SF3-2 SF3 0h2i 874 $2.22

Within each of the four SF3 categories (SF3+1; SF3+0; SF3-1; SF3-2), you’ll see that each example is worth very close to the same amount, and that the difference in value between the categories is approximately 50 cents each time. In this particular game, adding (or subtracting) a high card is equal to almost exactly the same amount as subtracting (or adding) a gap, or inside.

With this information, it’s not hard to conclude that however you play, say, QJ8 in a hand, you’ll play 987 the same way. Figuring out which of these two examples of an SF3+0 is being discussed in a particular hand shouldn’t be confusing because in games without wild cards, it’s impossible to have two separate SF3 combinations in the same five cards.

And it shouldn’t be surprising that there might be hands where you’d play QJ8 differently than you’d play QT8, simply because QJ8 is worth about 50 cents more. 

Coming to these conclusions takes you a long way from treating all 3-card straight flush combinations the same. And having four SF3 categories (in the first column) is a lot easier to deal with than listing eight separate types of hands (in the second column). 

In addition to removing four lines of strategy from the basic strategy chart, using this notation provides part of a shorthand to discuss more complicated hands. While a complete discussion of straight penalties, flush penalties, and various other types of penalties is beyond what I want to talk about today, understanding the categorization of SF3s is the first step to being able to understand our advanced strategies.

Now consider 10-7 (or 9-7) Double Bonus. When we’re dealing with SF3s, the amount you receive for the full house is irrelevant because full houses only have two different ranks of cards in them and SF3s have three. While two pair as a final hand is definitely possible when starting from an SF3, the probability of ending up with two pair affects all these hands identically — so it doesn’t matter in ranking these hands whether we get paid five coins or ten for two pair. Compared to Jacks or Better, Double Bonus pays more for the flush and more for the straight. See how the values of our SF3s change in this game:

SF3+1 SF3 2h1i QJ9 $3.91
SF3 1h0i JT9 $3.95
SF3+0 SF3 2h2i QJ8 $3.36
SF3 1h1i JT8 $3.41
SF3 0h0i 987 $3.46
SF3-1 SF3 1h2i QT8 $2.86
SF3 0h1i 986 $2.91
SF3-2 SF3 0h2i 874 $2.36

In Double Bonus, all of the SF3s are worth more than they were in Jacks or Better and the SF3s in each category aren’t clustered so tightly. In these examples, you’ll see that when you reduce the number of high cards by one unit and increase the number of insides, the value of the SF3 goes up by about a nickel. 

Our SF3 simplification still works, but not quite so perfectly.

Another example is Triple Bonus Poker Plus. In this game, flushes get paid only 5-for-1 (instead of 6-for-1 in Jacks or Better and 7-for-1 in Double Bonus) but straight flushes get paid 100-for-1 instead of 50-for-1 in the other two games. Let’s see how that affects the value of our combinations.

SF3+1 SF3 2h1i QJ9 $3.83
SF3 1h0i JT9 $4.05
SF3+0 SF3 2h2i QJ8 $3.12
SF3 1h1i JT8 $3.33
SF3 0h0i 987 $3.55
SF3-1 SF3 1h2i QT8 $2.62
SF3 0h1i 986 $2.84
SF3-2 SF3 0h2i 874 $2.12

Here the combinations are not nearly so clustered as they were in the other two games. Getting paid twice as much for a straight flush adds a lot more to the value of an SF3 without insides than it does to an SF3 with one or more insides. Remember, an SF3 with two insides has the potential to become one straight flush only. An SF3 with one inside has the potential to turn into two straight flushes, and an SF3 with no inside has the potential to turn into three different straight flushes.

Because of this, in one case on the strategy for this game, we have to separate the two types of SF3-1. On a hand like “KQ” 346, hold 346. (346 has the same value as 875 in the previous chart. Both have no high cards and one inside.) On a hand like “KQ” A35, we hold “KQ”. A35 (one high card and two insides) is worth the same as QT8 and as our chart above says, A35 is worth 22 cents less than 346

In my personal Triple Bonus Poker Plus strategy, however, I still use the SF3 notation discussed in the last two weeks. But when it doesn’t fit (as in the hands discussed in the previous paragraph), I resort to the clumsier notation. There is value to use the same notation in all strategies — but I don’t force it when it isn’t a good fit.


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A Look at SF3+1, SF3+0, SF3-1, and SF3-2 – Part I of II

Putting Bills Into a Machine

When Liam W. Daily and I began looking at publishing strategy cards and later Winner’s Guides for a number of video poker games, we devised a terminology for discussing the various forms of 3-card straight flush combinations. We decided to start from zero, add one for every high card in the combination, and subtract one for every inside (which is usually, but not always, a gap).

Although the idea was original to us, in the sense that we didn’t read or hear about it from anybody, we later found out that other strong players were using very similar terminology among their teams. These notations weren’t published or otherwise publicized, so we hadn’t heard about them.

At the time (mid-1990s), I was a strong intermediate video poker player. Daily was much less of a player, but an Oxford-educated Ph.D. economist. He was a brilliant theoretician who had devised new ways of looking at a number of problems — including for the International Monetary Fund! By the time we finished the Winner’s Guides many years later, we could both call ourselves experts. Our expertise came from doing the hard work on so many strategies.

I was teaching and publishing articles (in Strictly Slots and Casino Player, at the time, plus a weekly blog that has morphed, more or less, into what you are reading now) which gave me a sort of trial by fire. When I published something that wasn’t quite right, there were a number of players who would trumpet the evidence that I wasn’t as good as I claimed I was. In addition to developing a thick skin, I learned from this. When the criticism was justified (sometimes, not always, and sometimes inconclusively), I improved my knowledge base.

I started to be recognized as an expert when Shirley and I had our $500,000 half-hour at the MGM Grand in 2001. Just hitting two big royals in short order didn’t mean I was a better player or any smarter than I was the day before (when I was $500,000 less wealthy), but there were a number of players who concluded that if I could hit such big jackpots, I must know what I’m talking about.

Enough of the background. Here is a complete list of 3-card straight flush combinations, and our terminology for them, for all games without wild cards where you get your money back for a pair of jacks or better:

SF3+1: SF3 2h1i QJ9 
SF3 1h0i JT9
SF3+0: SF3 2h2i KH9QJ8
SF3 1h1i QT9JT8J98
SF3 0h0i 34545656767878989T
SF3-1: SF3 1h2i KT9QT8Q98JT7J97J87, A23A24A25A34A35A45
SF3 0h1i 234235245346356457467568578, 67968978T79T
SF3-2: SF3 0h2i 236246256347,NO 357367458468478, 56957958967T68T69T

There are two combinations in the SF3+1 category — namely two high cards and one inside (QJ9) and one high card and no insides (JT9). These are the most valuable 3-card straight flush combinations in this type of game. While having three high cards and two insides would also qualify as SF3+1, such a combination is physically impossible. Having three high cards in a 3-card combination makes some sort of an RF3 combination, rather than an SF3 combination.

There are three combination types in the SF3+0 category — with more than one combination in each type. You can see the list above. For those unfamiliar with our KH9 notation, the H represents a high card lower in value than the first card listed. So KH9 represents both KQ9 and KJ9. These combinations have exactly the same value and can’t both co-exist in the same five cards (unless you had a 4-card straight flush draw) which is much higher on the strategy chart).

There are two combination types in the SF3-1 category. There are two unusual things here — both of which deal with insides. The combination 234 has an inside and is worth exactly the same as 235 and 245. Although 234 may look like it has no insides, the only straight flushes it can be part of are A2345 and 23456 – which are exactly the same two straight flushes which are possibilities for 235 and 245.

All six of the ace-low combinations listed have exactly the same value. Even though A23 has one gap and A45 has two gaps, the only straight flush either one may be part of is A2345. Sometimes players can understand that these combinations have equal value when they see a strategy listing something like SF3: A-low. But sometimes they need to be told explicitly,

It is my belief that understanding the previous two paragraphs, and applying the concepts to strategies, is a major difference between beginners and intermediate players.

The final SF3 category is SF3-2. These all have no high cards and two gaps. Sometimes they are the lowest valued category of cards worth holding. But in most games, you are better off holding them than throwing all of the cards away.

So far, we have just defined things. Next week I will show how these are used in strategies and show how they differ between games.


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Southwest 20% off fare coupon for points flights


I recently received an offer from Southwest via my Chase Rapid Rewards Priority Visa Card. I received two coupon codes which are good for 20% off the points needed for a flight, round trip or one way. The big catch is that you must travel within 14 days of booking the flight.

Anyone who flies Southwest even a little bit knows that SWA fares tend to increase as you get closer to the departure date. And they increase a LOT within a month of departure. So, this is one of those offers that sounds good but isn’t typically all that usable.

I booked a one way flight from Reno to Detroit on 7/24 for 33,879 RR miles. I checked the last week of June, and the flight was almost 50,000 RR miles. I figured I would not be able to use this offer. But in today’s email was a SWA flight sale notice. I get these regularly. So, I checked online, and my flight had decreased by about 400 RR miles. No big deal. However, I could use my 20% off coupon and now my flight is 7023 RR miles less. Using 1.5 cents per mile, this is $105 savings.

The coupon code I used is CMD2UHFDAK. I don’t know if that code is unique to me or not.

For future flights, if I get a SWA email announcing a fare sale and that email is within 2 weeks of my flight departure, I will check to see if I can save some miles. It is good to periodically check SWA to see if your flight cost has decreased but I typically do this at least one month out. Now, with this coupon offer, checking within 2 weeks could be a money saver, especially if SWA is having a fare sale (a pretty frequent occurrence).

I didn’t see a straightforward way to modify my flight to now include the coupon code. I ended up purchasing the new flight and then cancelling the old flight. A call to SWA may have allowed me to do the flight modification but hold times on SWA have been very long so I just decided to do it online.

One quirk about SWA is you can’t easily book a round trip, multi city flight online easily. You can book a one way flight with a stop in between but I haven’t found a way to make it work for a roundtrip ticket. We are going on a cruise out of Los Angeles in October. Our flight plan is DTW to LAX, then take the cruise, then LAX to LV for 2 days then finally to DTW. With the 5 day gap in the middle, plus the extra stop, I didn’t see a way to do this online. I am going to call SWA and see if it can be done. I’ll report out when I find more information.

As always, if you are interested in sharing a credit card referral, you can email me at [email protected]


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¿Están sus hábitos de juego cruzando una línea invisible?

Triple Corona y Los Apostadores en Recuperación

El Consejo de Juego Compulsivo de Florida (FCCG) desea aprovechar esta oportunidad para compartir cómo los profesionales ven y diagnostican las diferentes etapas de las apuestas. Las apuestas problemáticas y las apuestas compulsivas son sinónimos del término clínico “apuestas desordenadas”, que se clasifica como un trastorno relacionado con sustancias y adictivo en el Manual Estadístico de Diagnóstico 5 (DSM V) de la Asociación Estadounidense de Psiquiatría (APA).1  Por lo general, se ve y se trata como una adicción. Si alguno de los siguientes puntos le resulta familiar, Your One Sure Thing (su acción segura) es buscar apoyo llamando al 888-ADMIT-IT.

La APA define las apuestas desordenadas como un comportamiento de apuestas problemáticas persistente y recurrente que conduce a un deterioro o angustia clínicamente significativos, como lo indica el individuo que muestra cuatro (o más) de los siguientes puntos en un período de 12 meses y el comportamiento no se explica mejor como un episodio maníaco:

  1. Necesita apostar con cantidades crecientes de dinero para lograr la emoción deseada.
  2. Se pone inquieto o irritable si intenta reducir o dejar el juego.
  3. Ha hecho repetidos esfuerzos infructuosos para controlar sus apuestas, reducirlas o dejarlas.
  4. A menudo está preocupado por las apuestas (por ejemplo, tiene pensamientos persistentes que reviven experiencias de apuestas pasadas, haciendo cálculos o planificando la próxima oportunidad, pensando en formas de obtener dinero para apostar).
  5. A menudo apuesta cuando se siente angustiado (por ejemplo, indefenso, culpable, ansioso, deprimido).
  6. Después de perder dinero apostando, a menudo regresa otro día para vengarse (“perseguir”” las pérdidas).
  7. Miente para ocultar el grado de su implicación con las apuestas.
  8. Ha puesto en peligro o perdido una relación, trabajo u oportunidad educativa o profesional significativa debido a las apuestas.
  9. Depende de otros para que le suministren dinero con objeto de aliviar situaciones financieras desesperadas causadas por las apuestas.2

El término “apuestas problemáticas” es un término integral que se refiere a todos los patrones de comportamiento de apuestas que ponen en riesgo, interrumpen o dañan actividades personales, familiares o vocacionales y que dan como resultado la ruina financiera o problemas legales que pueden ir de serios a graves.

Tipos de apostadores:

  • Apostador de bajo riesgo:
    • Apostador social: Apuesta por diversión y entretenimiento, puede controlar cuánto gasta fijando un límite y apegándose a él, y puede retirarse con sus ganancias.
    • Apostador social serio: Apuesta regularmente con intensidad mientras aún está bajo control; podría detenerse, pero lo echaría de menos.
  • Jugador en riesgo: Responde afirmativamente a uno o dos de los criterios indicados anteriormente, comúnmente llamado Apostador de alivio o escape que podría convertirse rápidamente en un apostador compulsivo si ocurre algún evento traumático o circunstancias que le cambien la vida.
  • Jugador problemático: Responde afirmativamente a tres o cuatro de los criterios indicados anteriormente, comúnmente llamado Apostador situacional o compulsivo. Donde las apuestas ya no son divertidas, han comenzado a causar problemas.
  • Apostador compulsivo/desordenado: Responde afirmativamente a cinco o más de los criterios enumerados anteriormente.

Si usted o una persona que conoce podrían estar experimentando alguno de estos signos y necesitan hablar con alguien para encontrar ayuda y recursos, llame o envíe un mensaje de texto al 888-ADMIT-IT. Esta Línea de ayuda de Florida es gratuita, confidencial y multilingüe, está disponible las 24 horas del día, los 7 días de la semana, para apoyar a aquellos que luchan contra las apuestas compulsivas.

  1. “2021–2022 24-Hour Problem Gambling Annual HelpLine Report.” Florida Council on Compulsive Gambling, February 2023.
  2. Ibid.

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Putting credit cards to work.


My wife and I try to do one new travel location a year. This year, we picked Denver, Co. We timed the trip around seeing a Detroit Tigers game. We departed on June 30 and returned on July 4th. Here is how it played out.

We flew Southwest non stop for 28,000 Rapid Rewards points. My wife likes to get early boarding so we used 2 upgraded boarding vouchers we had via a Chase southwest card. We also used my companion fare so we both flew for the 28,000 miles. The flight would have cost $425 per person and that was booking way back in February. The month before we left the flight would have been $600 apiece.  Upgraded boarding costs $50 per person. If you get the upgraded boarding you can usually ( but not always) get the exit row seat that has no seat in front of it. I would happily pay $50 for that seat.

We booked 2 night at Hyatt House by the airport and 2 nights at Holiday Inn near Coors Field. We got a great deal on Hyatt, using 8,000 Hyatt points for each night. The rooms go for $450 a night so that is like 5.5 cents per Hyatt point. The Holiday Inn was about $270 a night and we got it for 41,000 and 43,000 IHG points, so about 0.6 cents per point.

We used Autoslash for the car rental and paid $220 for 4 days, which is pretty cheap for Denver. My chase sapphire reserve gives us primary rental car insurance, which is $25 – $30 a day. I won’t count this in the calculation

So, just purchasing the air and hotel, it would have cost about $850 for airfare plus $100 for upgraded boarding. Hotel would have been about $1450 plus tax. We aren’t sure if we have to pay parking ( $30 per night). So, instead of $2400 we just used up some points and miles.

I wanted to give a concrete example of how credit cards can greatly reduce travel costs. There are some annual fees involved so even reducing this by $200 or so, it was a great deal.

If you are interested in splitting a referral bonus for credit cards, please email me at [email protected]


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Are Your Gambling Habits Crossing an Invisible Line?

Triple Corona y Los Apostadores en Recuperación

The Florida Council on Compulsive Gambling (FCCG) would like to take this opportunity to share how the professionals consider and diagnose the differing stages of gambling. Problem gambling and compulsive gambling are synonyms for the clinical term, “disordered gambling”, which is classified as a Substance-Related and Addictive Disorder in the American Psychiatric Association’s (APA) Diagnostic Statistical Manual 5 (DSM V).1 It is typically viewed and treated as an addiction. If any of the below resonates with you, Your One Sure Thing is reaching out for support by calling 888-ADMIT-IT.

Disordered gambling is defined by the APA as a persistent and recurrent problematic gambling behavior leading to clinically significant impairment or distress, as indicated by the individual exhibiting four (or more) of the following in a 12-month period and the behavior is not better explained by a manic episode:

  1. Needs to gamble with increasing amounts of money in order to achieve the desired excitement.
  2. Is restless or irritable when attempting to cut down or stop gambling.
  3. Has made repeated unsuccessful efforts to control, cut back, or stop gambling.
  4. Is often preoccupied with gambling (e.g., having persistent thoughts of reliving past gambling experiences, handicapping or planning the next venture, thinking of ways to get money with which to gamble).
  5. Often gambles when feeling distressed (e.g., helpless, guilty, anxious, depressed).
  6. After losing money gambling, often returns another day to get even (“chasing” one’s losses).
  7. Lies to conceal the extent of involvement with gambling.
  8. Has jeopardized or lost a significant relationship, job, or educational or career opportunity because of gambling.
  9. Relies on others to provide money to relieve desperate financial situations caused by gambling.2

The term “problem gambling” is an all-inclusive term that refers to all gambling behavioral patterns that compromise, disrupt or damage personal, family, or vocational pursuits resulting in financial ruin and/or legal problems that can range from serious to severe.

Types of gamblers:

  • Low-Risk Gambler:
    1. Social Gambler: Gambles for fun and entertainment, can control how much they spend by setting a limit and sticking to it and able to walk away with their winnings.
    2. Serious Social Gambler: Gambles regularly with intensity while still under control, could stop but would miss it.
  • At-Risk gambler: Answers yes to one or two of the criteria listed above, commonly called a Relief or Escape Gambler who could quickly become a compulsive gambler if any traumatic event or life-changing circumstances occur.
  • Problem Gambler: Answers yes to three or four of the criteria listed above, commonly called a Situational or Binge Gambler. Where gambling is no longer fun it has started to cause problems.
  • Compulsive/Disordered Gambler: answers yes to five or more criteria listed above.

If you or someone you know might be experiencing any of these signs and need to talk with someone to find help and resources, call or text 888-ADMIT-IT. This Florida Helpline is free, confidential, and multilingual, available 24/7 to support those struggling with compulsive gambling.

  1. “2021–2022 24-Hour Problem Gambling Annual HelpLine Report.” Florida Council on Compulsive Gambling, February 2023.
  2. Ibid.

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Blackjack Xchange – Gambling With An Edge

Blackjack Xchange - Gambling With An Edge

This post is syndicated by the Las Vegas Advisor for the 888 casino group. Anthony Curtis comments on the 888 article introduced and linked to on this page.

AC says: Blackjack Xchange is one of many carnival, or “carney” games, in the market. You’ve probably never heard of it, but it’s been around a while. The reason it may sound new is because it’s dealt only in online casinos, due to the many rapid calculations necessary to offer the Xchange odds that you’ll read about. The big takeaway here is that there’s no reason outside of pure entertainment to ever make an Xchange, which might lead you to wonder why this game even exists. That question can be asked of many of the blackjack- and poker-derivative games that have worse odds than their traditional counterparts. The reason is that people will play them, either out of ignorance of the disadvantage they face or just because of an attraction to the action provided (video keno, anyone?). Those interested in the psychology, mathematics, and procedure for getting a new game into the casinos can find those details in our book The Essentials of Casino Game Design—From the Cocktail Napkin to the Casino Floor, by Dan Lubin, the only book on the market covering this topic.

This article was written by John Grochowski in association with 888Casino.

Blackjack Xchange

Imagine you’re dealt a stiff hand in blackjack such as 10-5 or 9-7 and the dealer has a 10 or an Ace face up. You’d love to exchange the lower card and take a chance at getting a 10 or Ace instead, wouldn’t you? Would you pay for the privilege?

Conversely, would you accept a fee from the house to exchange the higher card instead? Those are the kinds of situations that arise in Blackjack XChange, now carving out a niche at online casinos.

There are many player-attractive features to XChange, but the defining characteristic is the opportunity to exchange cards.

Mind you, paying the price to XChange doesn’t give you better odds than basic blackjack. At WizardofOdds.com, Michael Shackelford calculates that it’s best to skip the XChange feature and just take advantage of some favorable blackjack rules.

But for those looking for a little intrigue, it’s going to be awfully tempting to XChange when holding 10-6 and take a chance on improving on the 16, perhaps turning a stiff into a winner and maybe even creating a blackjack for a 3-2 payoff.

Click to continue reading …


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The Value of Creating Strategies

Putting Bills Into a Machine

In my opinion, much of the value of a strategy lies in the creation process — figuring out what makes this game different from the others; looking for the rare cases; figuring out how to transcribe those cases — not in using a strategy created by somebody else. 

When I’m looking for the rare cases, I’m learning all of the not-so-rare cases automatically along the way. So much of video poker is playing the mundane hands correctly. 

The reason I bring this up is that at one casino, the game I play depends on the promotions. One game pays slightly more percentage-wise but it tops out at a $5 denomination. The “lesser” game goes up to a $10 denomination. Normally playing at the $5 level is better, but fairly often the casino has four-hour promotions where some sort of point multiplier is in effect.  

During those four hours, the expected return from the $10 game (including multipliers) is higher than the expected return from the $5 game. During “non-promotion” times, the $5 game returns more. On one trip, where I’m going to be playing both when the promotion is going on and when it isn’t, I will play some of each game.

The games are similar but not identical, so in addition to having both strategies figured out, I’ve created a list of the “deltas.” That is, which hands are played differently between the games. Before I go to that casino to play, I study all three strategies. Sometimes it is several months between visits to this casino and, since I play these games nowhere else, my memory of the fine points deteriorates over time. So with the three strategies, I can get up to speed again fast.

So far, I’ve spoken a little bit in code. I could just tell you which casino I’m writing about, which games, and give you all three strategies. But while that gives some information to players, it also gives some information to casinos. Which I don’t want. Plus, relatively few of my readers play $5 and $10 games anyway, so I’m risking giving up a situation that isn’t relevant for most of you. If you think you can figure out which casino and which games, please don’t publish those things in the responses to the blog.

The same principles hold for lower denominations — whether it’s 25¢ games versus 50¢ games, $1 games versus $2 games, or whatever. While some of you only play one game, most of you play at least two — and making yourself a list of the deltas would be useful.

The games have to be similar to do this. Deuces Wild games are so different from Double Double Bonus games that the list of deltas would be longer than the full strategies! But Double Bonus versus Double Double Bonus (of whatever pay schedules you play) would be suitable, as would Triple Bonus Poker versus Double Bonus Poker. 

You’re going to have to decide for yourself how advanced you want these strategies to be. I want the strategies to be 100% complete and 100% accurate, but I’m sure I’m in the minority about that. A lot of you don’t play any game 100% accurately, let alone comparing the differences between two or more different games at that level.

So for many of you, what Liam W. Daily and I called “Basic Strategies,” which is as accurate as you can get without using penalty cards, would be suitable. 

If you were comparing 9/6 Jacks or Better (JoB) with 9/6 Double Double Bonus (DDB), you should include hands like A♠ J♠ T♠ 4♠ 5♦ on your list where with Basic Strategy you hold three spades in JoB but four spades in DDB. Unless you’re trying for 100% accuracy, you probably should skip hands like A♠ J♠ T♠ 4♠ T♦, where with Advanced Strategy the correct play is to hold four spades in both games. I’d certainly have that hand on my list, but it’s a fairly rare hand and not worth much if you skip it.

Many of you don’t want to do such hard work to squeeze every last penny out of a game. That’s your choice. I’m not putting you down. But for me this is both my vocation and my avocation and I want to do it as well as I can.


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Do Strong Players Ruin It for Everybody Else?

Putting Bills Into a Machine

I received an email from Deke Castleman with the Las Vegas Advisor asking me if I’d answer the following QOD (Question of the Day):

The QoD on Station Casinos giving zero player points on some video poker
machines generated lots of strong reader comments.  One opinion is that
Advantage Players are one contributing cause for lessening, even ending,
player points on VP machines.  As a big-time video poker advantage player,
might Bob Dancer have some cogent thoughts on this topic?

I definitely have some thoughts about this — people regularly disagree about how cogent those thoughts are. Since my answer was going to be long, I thought it more suitable for a blogpost rather than a QOD.

Local casinos often have slogans such as, “We Love Locals,” or “We You More,” among many others. These slogans are geared towards making you believe these are benevolent organizations run by grandfatherly types just looking for ways to make your life better.

In fact, casinos are money-making businesses — or at least they are trying to be. They are offering games that they hope will induce players to come in and leave some money behind.

In the slot department, which includes video poker and certain other games, machines are evaluated by daily hold. Let’s say in a particular casino that the average hold of machines is $100 per day. That’s not all profit, of course. Perhaps $80 of that goes for the various expenses necessary to run a casino.

Since Station Casinos was mentioned in the question, let’s look at the Double Double Bonus games they have. They have some 10/6 games returning a tick more than 100% to the perfect player, 9/6 games returning about 99%, 9/5, 8/5 and perhaps even worse. For a competent dollar player playing a modest 600 hands per hour, the 10/6 game will allow him to break even, the 9/6 game causes him to lose $30 per hour on average, the 9/5 game $70, and the 8/5 game about $100.

All of these numbers have big fluctuations. Sometimes the player hits one or more royals or aces with a kicker and wins several thousand dollars. Usually, he doesn’t hit one of those fairly-rare jackpots and loses. But on average, the amounts given are averages for strong players. Not-so-perfect players lose much more, of course.

The skill of the players is very important. Six hundred hands per hour means 600 decisions are required. There are occasionally hands where there are two plays returning the same amount, such as with 2♠ 4♥ 5♣ 6♦ 8♠ it doesn’t matter EV-wise whether you hold 2456 or 4568, but most hands have one best play. Even in the hand mentioned where you have two equivalent correct choices, a number of not-so-strong players throw everything away, which is quite a bit worse. 

On the 100% game, let’s assume it makes $50 a day for the house. There are enough imperfect players that the house still makes some money, but less than the house average and less than the break-even number the casino needs to survive. The casino now has a number of choices — of which there are basically an infinite number of variations:

  1. The casino can live with making less money on these games. They might figure that players who play these games also bring in friends who don’t play so well. Or these players might also bet on basketball while they’re there and the house makes money on that. Or maybe advertising these games as “loss leaders” can bring in players, not all of whom will correctly play the loose games.
  2. They can reduce the “extras.” Casinos offer slot club points. Often casinos have policies such as loose games take more coin-in to earn a point than tight games do. Or loose games aren’t eligible for point multipliers. Or loose games get points, but the players playing them get no mailers. 
  3. The games themselves are tightened. The 10/6 games become 9/6 games. These games have a 1% hold and the casino can make money on these games — IF players still play them. Players, of course, always have the choice of whether to play or not.
  4. Players who only play the loosest games and do so successfully are restricted. Lots of ways to do this as well, and there are mild restrictions and severe restrictions. There are temporary restrictions and there are permanent ones.

One could argue that if there were no strong players, the house would make plenty of money and not need to resort to any of the measures listed. And that’s probably true. (But not necessarily. Even if casinos could increase their daily hold to $150 per machine per day, most competent slot directors would be exploring ways to increase that to $200.) Just as the casinos are trying to make money, players have similar incentives. Players figure out that if they get good enough, they can support themselves playing in casinos. That’s a lot more attractive way for some of us to go through life than working at a of “regular job.” 

The players who aren’t so competent at the games can certainly bemoan the fact that good players force the casinos to take countermeasures. And these players can also blame people like me for teaching others how to do well playing these games. 

If skillful players didn’t figure out the game and some of us teach others, then it would definitely be much, much easier many more players to win in casinos. And that “easy money” would cause people to work hard to get that money. That’s the way capitalism works — and you can probably find similar incentives under other economic models as well. You find an area where you can make money and you go do that. If that doesn’t work, you try something else.

Complaining about those who are further along the “skillful player path” doesn’t do much good, however. The facts of life are that if you want to succeed at gambling (or anything else for that matter), you have to learn how to play the game, and then play what you have learned. If you’re not willing to do that, it’s much easier to resort to blaming others for your misfortune.

Whether it does them much good or not, there will always be players who play the blame game. That’s just the way some people are wired.


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This post is syndicated by the Las Vegas Advisor for the 888 casino group. Anthony Curtis comments on the 888 article introduced and linked to on this page.

AC says: The first step toward expert play in blackjack is learning basic strategy, which is the correct way to play your hands against all casino upcards, assuming there’s no additional information from using a count system or any other source. This article provides an interesting extension of learning basic by concentrating on just one dealer upcard. I’ve never thought about approaching the basic strategy learning process like this, but now that I see it, I like it. I suggest learning all of basic strategy first in the traditional manner, then rereading this article to lock in an even stronger grasp of proper play against a 9, especially the more obscure rules, like surrendering hard 16 except when playing a single- or double-deck game. I’m looking forward to additional articles from author Henry Tamburin that cover the other dealer upcards. Most important in this discussion is to understand that basic calls for hitting A7 vs. 9, which is a play that many don’t make. One correction: In the quiz, the answers to numbers 8 and 9 are switched — #8 should be Split and #9 should be Hit.

This article was written by Henry Tamburin Ph.D. in association with 888Casino.

How To Play Your Hands against a Dealer’s 9 Upcard

When a dealer shows a 9 upcard in blackjack, she has about a 77% chance of getting to a final hand that totals 17 through 21 and only a 23% chance of busting (depending on the number of decks shuffled).

A 9, therefore, is a strong card for the dealer, which means we have to be more aggressive when we’re dealt a stiff hand (hit rather than stand) and less aggressive when we’re dealt a two-card soft hand (hit rather than double down).

We also should surrender one hand, even when it means we forfeit half our bet. What follows is the accurate playing strategy for any hand when the dealer shows a 9 upcard.

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