Tag: video poker

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Learning a Second Game — Part I of II  

A few weeks ago, I wrote some articles about making adjustments to a strategy based on the pay schedule. The purpose of those articles was for the situation when you were attempting to “fake it” reasonably well. You already knew the strategy for one game and were attempting to play another similar game.

Today’s article, which will continue next week, is somewhat related, but with a different emphasis. Today’s article assumes you already know one game and are trying to learn an unrelated game — and you don’t want to keep getting the two games mixed up.

The first thing to know is that some of my readers will not be able to do this very well. It takes a certain amount of the right kind of intelligence to do this. Many people are plenty smart enough in other areas, not nearly smart enough in this one.

That’s not necessarily a showstopper to playing video poker successfully, because we are starting with the assumption that you play one game well. So long as you can find that game for the stakes with which you are comfortable, everything is all right in your world.

Today’s article, however, is for players who are capable of learning at least two games well. Perhaps they play at two different casinos and the casinos differ on their best games. Perhaps they are ready to move up in denomination and the casino doesn’t offer the same games in both denominations.

Hopefully, it’s not because they are bored playing the game they already know how to play. Video poker is basically a boring game. There are occasional exciting hands (like drawing to three aces or perhaps four to the royal), but most are rather mundane. Unless you can concentrate on playing these mundane hands correctly, you will probably end up earning much less than the expected value. Unless you can deal with this boredom (or, perhaps, even not be bored!), you will never be successful at this game.

So, to flesh out the example, let’s assume you already play 9/6 JoB and are trying to learn NSU Deuces Wild — which is the version where the pay schedule at the lower end is 16-10-4-4-3-2-1. The methodology I’m going to explain works on all games, but I’m just mentioning these for convenience.

The first step is to have good strategies for both. I recommend the Dancer/Daily strategies, but there are several other sources as well. Some are free (such as the ones on wizardofodds.com) and some are “free” if you already own software that computes it for you (e.g. Video Poker for Winners).

The next step is to learn how to read the strategies. In NSU, for example, you’ll see WW45, which you’ll never find on a JoB strategy. Looking at the notes that come with the strategy, you’ll see that the W refers to a deuce of any suit and the 45 refers to a 4 and 5 that are suited with each other. You’ll also see that hand referred to as a 4-card straight flush, with certain attributes.

You’ll see that WW45 is less valuable than WW57 and more valuable than WW46. The reasons behind this are all explained in the Dancer/Daily Winner’s Guide or in my classes, but if this is the first time you’ve tried to play NSU competently, the first sentence of this paragraph just might contain rather surprising information.

The next thing to notice about an NSU strategy is that it’s divided by the number of deuces dealt. That is, the rules for the 3-deuce section are different than the rules for the 1-deuce section. I think of these five sections as making the strategy easier — because you can instantly find the right section of the strategy simply by looking at the number of deuces. And each section is relatively small.

Probably the part of the strategy that will be the most difficult for you is the no-deuce section — because this is the part that compares directly to JoB and the basic concepts of the games are different. In JoB, K♠ K♥ 9♥ 7♥ 3♥ is played differently than T♠ T♥ 9♥ 7♥ 3♥. In Deuces Wild, they are always played the same, depending on how much you get for the flush. In NSU, you hold the hearts both times, but in certain other versions of Deuces Wild you hold the pair each time. It’s going to take a while before you get the concept that there are no high cards in Deuces Wild because you don’t get your money back unless you get 3-of-a-kind.

A related place where the games have different concepts has to do with the value of Q♣ J♣ versus Q♦ T♦.  In JoB, the clubs are more valuable because both the Q and the J are high cards, meaning you get your money back if you get of pair of either of them. In NSU, the two hands have identical values.

You’ll also need to learn the difference between the way straight flush draws are evaluated. In JoB, 4♥ 5♥ 6♥ is equivalent in value to 5♣ 6♣ 7♣ and A♦ 3♦ 4♦ is worth about the same as 5♣ 6♣ 8♣ and more than 3♠ 4♠ 7♠. In NSU, none of these relationships are the same as they are in JoB. You need to be able to change the way you evaluate combinations of cards while still retaining the old evaluation methodology for when you are playing the original game! It’s not a trivial task!

I’ve gone over a few of the things you need to know. There are many more — but this is not supposed to be a “how to play NSU” article. It supposed to be a “how do you learn to keep both games in your head at the same time” article.

We’ll continue this discussion next week.

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Ignoring Kenny Rogers

I’ve listened to Kenny Rogers’ song The Gambler a zillion times. Since I’m not a live poker player, the advice he gives seemed to make sense. After all, how bad can “You’ve got to know when to hold ‘em and know when to fold ‘em” actually be?

Whether the preceding line of the song is correct or not, I noticed there’s one line of advice in that song that has to be very wrong for many poker players — but largely correct for video poker players. So, I said to myself, “Self, there’s a column there!” So here goes.

The offending line is, “You never count your money when you’re sitting at the table.”

Since I’m not a poker expert, you’re well advised to take everything I say here with a grain of salt. But if the standard is being more accurate than a Kenny Rogers song, I’m confident I can clear that bar.

In no-limit hold ’em, among others, a major goal is to stack your opponents. That means, however many chips he has, that’s how many you’re trying to get.

For any given stakes, say $2-$5, your decisions are made relative to the amount of money in the pot. If there’s $20 in the pot and everybody at the table has $200, you need to play your cards fairly straightforward. The stacks are only 10 times the amount in the pot.

But if everybody has $2,000 in front of them, you can play much more speculatively, because if the right cards come in, you can collect 100 times what’s in the pot rather than only the 10 times in the previous example.

So far, I’ve been talking about how much money your opponents have, but the amount of money you have matters too. If you have $20 in front of you and your opponents all have $2,000 — then from your point of view, all your opponents have is $20 each. They can have side pots amongst themselves, but that doesn’t affect you financially. For you to stack somebody, you need at least as many chips as he has. (Being short-stacked definitely affects your strategy — where you’re basically “fold or all in.” Consult poker experts for more complete advice on this.)

With this in mind, it’s clear that, at least approximately, you need to know how much you have and how much your opponents have. This is counter to Rogers’ “You never count your money when you’re sitting at the table” advice.

In video poker, however, Kenny Rogers’ advice is generally spot on. If you’re trying to decide whether to hold three, four, or five cards from AAA33, there is no line on the strategy card that says, “Check the amount of money in your wallet first!” Players who adjust their strategy based on their bankroll are giving up EV every time they do so.

It definitely is important to consider your bankroll before you sit down to play and choose the particular game and denomination you’re going to play. But once you’ve made that choice you should make the highest EV play at all points.

One exception to this would be if you’re playing Ultimate X and you’re running out of money. If you’re playing the Ten Play version, you should never play a 100-coin hand when you have less than 145 credits (or more money in your pocket or otherwise close at hand.)

Why 145? It starts with knowing that if you play five credits per line (50 credits total), you can play off any existing multipliers without creating any new ones.  

If you play 100 credits and don’t earn any credits (i.e., you drew no paying hands), you left no multipliers on the game.  So, you take your 45 remaining credits and go home. If you play 100 credits and earn at least five credits, you will have at least 50 credits to play off all the multipliers on the game, again leaving no multipliers on the game.

So long as you earn at least five credits, you will have earned multipliers for the next hand — and you want to play those off five-credits per line, meaning 50 coins, before you abandon the machine to others. There are “fleas” who go around checking if you’ve abandoned any multipliers and you don’t want to be the person to feed those fleas.

There are a number of areas where video poker and live poker are played differently. In my just-completed video poker semester, there were several poker players who attended regularly. Comparing a draw to an unsuited KQJT with QJT9, I would explain the first had eight cards to complete the straight and nine cards to give you a high pair. The second hand also had eight cards to complete the straight but only six cards to give you a high pair.

“Aha!” one poker player would translate into a language she understood, “17 outs versus 14.” Sort of, but not really. In poker, an “out” is a card that will beat another player. In video poker, a card to give you a straight (paying 20 coins) is four times as valuable as a card that gives you a pair of queens (paying 5 coins.) All outs are not created equal.

I still enjoy hearing The Gambler occasionally whether it gives good advice or not. Bonnie and I dance the Texas Two Step and this song has a good beat for that. I never look to popular music of any decade to teach me to play games — professionally anyway. There are a number of songs through the years that have provided “words to live by.” But not “words to gamble by.”

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It’s How You Approach It — Part II of II

Beginning in last week’s blog, I discussed my thought processes for using a fairly large food comp intelligently. If you didn’t catch the start of this discussion, it’s available a few clicks away.

The next question was whether the $250 could be spent anywhere other than in a restaurant? Maybe a gift shop, spa, gaming, or whatever?

Yes, it could be spent at the gift shop — but the gift shop had very modest offerings. Still, at the end of our stay if it comes down to “spend it or lose it,” Bonnie might well decide that one of the purses wasn’t too bad. Or maybe she could get something there as a gift. Bottles of alcohol would have been okay. Yes, the cruise ship would lock them up for the duration of the cruise (they want you to pay shipboard prices for your booze), but we’d get the bottles back. As it turned out, bottles of alcohol were not sold at the gift shop.

Next, while dining at Slack’s, was it possible to buy a bottle of wine without having it opened? Bottles that have been opened will be confiscated by the cruise ship and not returned. Some restaurants will leave the bottle totally unopened for you. Many won’t. Sometimes a small tip will get them to bend the rules for you. (And it’s easy to over-tip here. A bottle you can buy for $20 in a liquor store might well sell for $60 in a casino restaurant. Tipping $10 might make sense if it were really worth $60, but that’s a huge tip for something worth only $20.) You don’t know until you ask.

And I certainly wouldn’t ask at the start of the first meal. When restaurant employees are dealing with strangers, they are more likely to follow the rules to the letter. But on the first night, if we spend five minutes talking to the manager about the various places on Cape Cod that would be good for a day trip the next day, and came back the second night thanking him profusely and telling him how his advice really made our trip, we then are no longer strangers. We are “friends.” And sometimes people do favors for their friends.

(I’m actually writing this after our first night at the restaurant and before the second. I have no idea how the conversation will go and it’s better to leave some things unsaid. This is more about the methodology of how I address this situation than it is about whether I was successful at getting an unopened bottle of wine this particular time.)

(A side issue that interests me is when cruise ships confiscate alcohol while you are boarding for a 7-day cruise is that they typically return it to you on the evening of the night before you disembark. For passengers who are remaining on the ship for 14 or 21 days, do they still give it back to you on the night before the first 7-day cruise is over? Or is their system sophisticated enough to keep it until the very last night of your multi-week cruise?

I’ve decided that if I don’t get the unopened bottle from Slack’s, I’ll stop at a liquor store and buy a bottle of wine to take on the ship as an experiment — because we’re no strangers to back-to-back cruises. It’ll be nice information as to whether we are able to enjoy our wine onboard during our second week aboard the ship in these situations.
Another option, whether we’re back-to-back or not, is to buy a bottle of wine off the ship and pay the $7.50 corkage fee. A $12 bottle of wine on land costs $30 on board. Paying the corkage fee is the better choice.)

I was interested in whether comp dollars could be used to buy free play in the casino. I was told that none of the $250 could be used for that, but any additional comp dollars I had can be redeemed for play-it-through-at-least-once free play at a 2-for-1 rate. That is, I could redeem up to $1,000 comp dollars a day for $500 free play. Playing a 99% game, this has an EV of $495 (with some variance). Would I rather have $1,000 in future meals at the M or $495 in cash? This is not an option available (so far as I know) in Las Vegas at either the M or the Tropicana, which are the two Penn National properties there.

I really didn’t know which was worth more to me, but I decided to exchange $1,000 worth of comp dollars for $500 in free play. On another day, I might have decided to keep all my comp dollars.

(The $1,000 in comp dollars I redeemed had nothing to do with the $250 in spend-it-or-lose-it comp dollars I was given as part of my Icon rewards. But they both happened on the same trip at the same place, so I decided to discuss them in the same article.)

Finally, we could let part of the $250 go unredeemed. It’s not the worst thing in the world. We are neither starving nor destitute. It goes against my grain to leave benefits on the table, but sometimes you have to. Sometimes you do this for strategic reasons. This time we’d do it because there was nothing we could get that we really wanted.

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It’s How You Approach It — Part I of II

I earn a number of “free” cruises for play at various casinos. One casino where this happens is the M Resort in Las Vegas. Icon members ($800,000 video poker coin-in per calendar six months), earn one 7-day Norwegian Cruise Line balcony cabin cruise for two people per six-month period — plus periodically they have extra cruise giveaways as well. Any cruises I earn from Caesars Entertainment are also on NCL.

In addition, Icon members receive $500 annually towards travel to get to their cruise and a 2-day trip to any Penn National resort including $250 in food credit. These are actually two separate benefits, but you can use them on the same trip.

Since Bonnie and I enjoy dancing and relaxing, cruises are pleasant vacations — and we’ve been to all the ports. Once or twice each year, we have enough offers for cruising two or three weeks in a row, but one of the concerns is getting to the cruise locations inexpensively. All the credit card discounts talked about by Jimmy Jazz or Eric Rosenthal are in play, of course, but an extra $500 off is always welcome.

As it happens, Plainridge Park casino is a harness racing racino, part of the Penn National chain, and very near the Foxborough part of greater Boston. If we can find interesting cruises out of Boston, then part of our transportation expenses will evaporate.

For much of the year, they have 7-day Bermuda cruises out of Boston, where the ship docks in Bermuda for a few days and doesn’t move. You have 24-hour on-and-off privileges. It’s a different sort of cruising experience compared to having a ship arrive at a port at 8 a.m. and you must be back on board later that same day.

In the fall, they have “fall colors” cruises for seven days north out of Boston, along the New England coast, and then down the St. Lawrence River (a key part of the St. Lawrence Seaway) to Quebec City. The following week, the ship returns to Boston, stopping at primarily different ports. So, if you plan your dates right, you can have three consecutive weeks where there is a different itinerary each week. Plus, if you stay in the same stateroom, you have an extra day to explore Quebec City or the nearby countryside.

That’s what we did. The last week of the Bermuda cruise season was September 7-14 and the first week of the fall colors cruise was September 14-21, followed by the return to Boston on September 21-28. A key part of making this work for us was to start the “fall semester” of video poker classes at the South Point on July 3 which would allow us to finish up on September 4 and get on a plane to Boston on September 5.

I was certainly willing to play at Plainridge were the pay schedules are “interesting.” They didn’t have much video poker, but the best games were actually better than I expected. The loosest I found was $1 Triple Play 9/6 Double Double Bonus, which is worth a tick under 99%, and the machines were busy enough that I couldn’t do an exhaustive search. They had no table games.  And even though this 99% game is less attractive than I normally play, it was plenty good enough to play some — which I’ll discuss in next week’s blog.

There is no hotel associated with the casino, so they put us up at a nearby Holiday Inn Express. Acceptable. They have nicer places in the area, and if they believed we’d be big players at the casino I’m certain a higher-end hostelry could have been arranged. But we probably weren’t going to play that much, and this was fine.

Arriving at the casino at 7 p.m. on a Wednesday, Bonnie and I had $250 to spend food-wise before Friday 9 a.m., which is when we’d leave the area to travel back to Logan Airport from where we had a shuttle reservation to get to the ship. They have Slack’s, which is an oyster bar and grill restaurant, and Flutie’s, which is a sports pub. They also have a food court, but $250 is simply too much fast food for two people to consume in two days.

The first thing we had to figure out was whether we were able to use the $250 over more than one meal? Although there’s a wine list at Slack’s which would allow us to easily surpass the $250 threshold, the surf-and-turf special ran only $30 apiece — meaning that running a tab of $250 over two days for two people without a significant amount of alcohol would be difficult. Food “to go” was of little interest because we were just about to spend three weeks on all-you-can-eat cruises. Still, we had a refrigerator in the room, so having a bit leftover for “midnight snacks” wasn’t all bad.

Next, we needed to determine what would happen to any part of the $250 that wasn’t spent? Was it placed in my “comp dollar” account — meaning that maybe we could spend it back in Las Vegas or at other Penn National properties? If that was the case, the “How do you spend it all right now?” problem disappears.

I was told by the only host on property Wednesday night that this, however, was not the case. The money wouldn’t “evaporate,” but could only be spent at Plainridge Park. I would have liked to ask this same question to a more senior host, but there was nobody available.

There were more things to consider in how to spend these comp dollars, but I’ll leave the discussion for that until next week.

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Figuring Out a New Strategy on the Fly — Deuces Wild Version

Last week I listed some rules about when you should make strategy adjustments based on pay schedules for games without wild cards. Today I’m doing the same thing for Deuces Wild games.

Again, I strongly recommend knowing the strategy for at least one game ‘cold.’ This game could be Full Pay Deuces Wild, NSU Deuces Wild, pNSN (called Airport Deuces by some), or some other variation, but if you don’t know at least one game, these rules will be of marginal value.

To the abbreviations I used last week, add W which stands for a wild card in general or, in this game, a deuce.

A key part of knowing Deuces Wild is knowing how 3- and 4-card straight flushes rank. Here I’m including a list I use in my classes. Even if you’re not familiar with Dancer/Daily notation, you should be able to understand the relative values of these combinations. Not all of these categories are eligible to be held in all games, but you should be aware of the relative ranking in the game they are held.

Summary of categories of SF3 and SF4

SF3 -2 = double inside; SF3 -1 = single inside; SF3 +0 = non-inside;

SF4 -3 = triple inside; SF4 -2 = double inside; SF4 -1 = single inside;

SF4 +0 = non-inside;

 

0-deuce SF3

SF3 [A-low]           [A34; A35; A45]

SF3 -2                     [includes 346 and 356; excludes any A-low]

SF3 -1                      [includes 456; for strategy purposes, includes 345]

SF3 +0                    [567 – 9TJ]

 

1-deuce SF3

SF3 -1                  [W57 – W9J > W56 > W45]   

SF3 +0                [W67 – W9T]  

 

1-deuce SF4

SF4 [A-low]        [WA34; WA35; WA45]

SF4 -2                  [W346; W356; W347 – W9QK]

SF4 -1                   [W345; W456; W457 – WJQ]

SF4 +0                 [W567 – W9TJ]

 

2-deuce SF4

          SF4 -2      [WW34 = WW35 = WW46 = WW47 – WW9Q]

          SF4 -1      [WW45 = WW56 = WW57 – WW9J]

          SF4 +0    [WW67 – WW9T]  

 

  1. K♥ Q♥ J♥ T♥ 9♥
  2. K♠ K♥ 3♠ 3♥ J♠  
  3. A♦ A♠ K♠ 7♠ 3♠
  4. A♣ 3♣ 4♣ 5♥ 9♠
  5. K♥ Q♥ 9♠ 8♥ 5♦
  6. J♠ T♠ 9♠ 7♠ 8♦
  7. Q♦ J♣ T♦ 8♠ 3♠
  8. K♠ Q♠ T♥ 9♣ 2♦
  9. W 7♠ 8♠ 9♠ A♠
  10. W 8♠T♠ 4♥ 5♥
  11. W W W T♠ T♥ versus W W W 4♠ 4♥

 

Now let’s look at how changes to the pay schedule will affect these plays. Note that my statements are strong tendencies, but exceptions may be found sometimes. I’m using the following notation here:

2P — two pair

3K — three of a kind

ST — straight

FL — flush

FH — full house

4K — four of a kind

5K — five of a kind

SF — straight flush

RF — royal flush.

 

When flushes pay 15 on a 5-coin basis, I’ll say FL pays 3-for-1. I went back and forth about whether to say “pay” or “pays.” I can argue persuasively against either way of doing it, but I had to pick one. So, I did.

 

Also, I am not including Ultimate X strategies here. I am only discussing strategies where there are no multipliers earned.

 

  1. You ALWAYS throw away the 9. It’s on this list more for completeness because in games without wild cards you ALWAYS keep the 9 when the royal pays 4,000 coins. Not all players go back and forth between games seamlessly
  2. Whether you hold one pair or two depends on how much you get for the FH. When FH pays 3-for-1, hold one pair. When FH pays 4-for-1, hold two pair. When you hold one pair, if all 4K pay the same and all 5K pay the same, it doesn’t matter which pair you hold. In a game like Bonus Deuces where five 3s pay more than five Ks, if the FH pays 3-for-1, just hold the 3s.
  3. Hold the pair when FL pays 2-for-1. Hold the spades when FL pays 3-for-1.
  4. Hold the A-low SF3 when the sum of FL and SF pays 12 or more. That is, in FPDW, FL pays 2 and SF pays 9 — so you throw everything away. In pNSU, where FL pays 3 and SF pays 9, hold A34. Do not even think about holding A345. That has only half as much value as an inside straight draw and is never held.
  5. If FL pays 3-for-1, hold KQ. If FL pays 2-for-1, throw everything away. In games where FL pays 2-for-1, you probably hold KQ if none of the remaining three cards are 9 or higher (i.e. a straight penalty) and none are suited with the KQ (i.e. a flush penalty).
  6. Hold all five cards when ST pays 2-for-1. Just hold the spades when ST pays 1-for-1.
  7. When FL pays 3-for-1, hold QT.  When FL pays 2-for-1, hold QJT8.  If the J were a 9, sometimes you hold QT even if the FL pays 2-for-1 — depending on how much the SF pays.
  8. Hold KQ if ST pays 1-for-1. Hold KQT9 if ST pays 2-for-1.
  9. Hold all five cards if FL pays 3-for-1. Just hold W789 if FL pays 2-for-1.
  10. W8T is ALWAYS preferred to W45 (see the chart prior to the list of problem hands), although sometimes both W8T and W45 are inferior to holding the W by itself. You’ll prefer W8T to just the W if the sum of the FL and SF add up to 12 or more.
  11. When 4K returns 5-for-1, hold the quints when they include TT, JJ, QQ, KK, or AA and otherwise just hold the deuces. It’s a close play and the reason for the difference has to do with the possibility of getting wild royals. In the more common situation where 4K returns 4-for-1, hold the quints when 5K pays more than 12-for-1.
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Figuring Out a New Strategy on the Fly

There are a LOT of video poker games out there. Sometimes you come across one that you haven’t studied before. There are some rules of thumb that can get you pretty close. This week we’re going to talk about doing that in games without wild cards where you get your money back for a pair of jacks or better. Next week we’ll talk about doing the same thing for Deuces Wild variations.

The first step of the process is the most critical. If you skip over that, your results down the road won’t be as good as they otherwise could be. And that first step is to know the strategy for at least one game cold.

This game that you know cold could be Jacks or Better, Double Bonus, Double Double Bonus, etc. But you need to know instantly how to play the following hands correctly. None of these are particularly difficult for an intermediate level player, but beginners will miss a goodly percentage of them.

  1. K♥ Q♥ J♥ K♣ 3♦
  2. A♠ K♠ J♠ 5♠ 2♥
  3. A♦ K♦ T♦ 4♦ 3♣
  4. 4♦ 4♠ 5♥ 6♣ 7♦
  5. 9♦ T♠ T♥ J♣ Q♦
  6. J♠ T♠ 9♠ 8♠ 7♦
  7. J♠ T♠ 9♠ 7♠ 8♦
  8. Q♦ J♣ T♦ 8♠ 3♠
  9. K♠ Q♠ T♥ 9♣ 2♦
  10. A♦ 2♠ 3♥ 5♣ 9♦
  11. A♠ Q♥ J♣ 5♠ 2♥
  12. 2♣ 4♠ 5♥ 6♠ 9♥
  13. A♦ K♦ J♣ 4♦ 6♠
  14. K♠ J♠ 3♥ 4♥ 5♥
  15. Q♥ J♥ 2♠ 3♠ 4♠
  16. A♠ A♥ 3♠ 3♥ J♠  
  17. K♠ K♥ 3♠ 3♥ J♠  

Now let’s look at how changes to the pay schedule will affect these plays. Note that my statements are strong tendencies, but exceptions may be found sometimes. I’m using the following notation here:

2P — two pair

3K — three of a kind

ST — straight

FL — flush

FH — full house

4K — four of a kind

SF — straight flush

RF — royal flush.

 

When flushes pay 30 on a 5-coin basis, I’ll say FL pays 6-for-1. I went back and forth about whether to say “pay” or “pays.” I can argue persuasively against either way of doing it, but I had to pick one. So, I did.

 

  1. When FL pays 5-for-1, KK is always correct. When FL pays 6-for-1, KQJ is correct if 2P pays 1-for-1, and KK is correct if 2P pays 2-for-1. If FL pays 7-for-1, KQJ is correct.
  2. When FL pays 6-for-1 or less, hold AKJ. When FL pays 7-for-1, hold AKJ5.
  3. When FL pays 5-for-1, hold AKT. When FL pays 7-for-1, hold AKT4. When FL pays 6-for-1, it depends on how much you get for 2P. When 2P pays 2-for-1, hold AKT. When 2P pays 1-for-1, hold AKT4.
  4. Hold 44 when ST pays 4-for-1 and 3K pays 3-for-1. If either ST pays 5-for-1 or 3K pays 2-for-1, hold 4567.
  5. If 2P pays 2-for-1 and ST pays 4-for-1, hold TT. If 2P pays 2-for-1 and ST pays 5-for-1, hold QJT9. If 2P pays 1-for-1, hold QJT9 unless 4K pays more than 50-for-1.
  6. Hold JT987 if SF pays 50-for-1. If it pays more than that, hold JT98.
  7. I don’t know of any games (other than special cases with progressives on the straight flush) where you don’t hold all five cards.
  8. Hold QJT8 when 2P pays 1-for-1. Hold QJ when 2P pays 2-for-1.
  9. Hold KQ by itself always.
  10. Hold A by itself unless ST pays 5-for-1, in which case hold A235.
  11. Hold QJ in every game except Triple Double Bonus and Super Aces Bonus, in which case you hold the ace by itself.
  12. Hold 2456 when 2P pays 1-for-1. Throw everything away when 2P pays 2-for-1.
  13. Hold AK when FL pays 6-for-1 or less. Hold AK4 when FL pays 7-for-1.
  14. Basically, always hold 345 unless you’re dealing with a progressive. How high the progressive must get to justify holding the KQ depends on the game.
  15. Basically, always hold QJ. Comparing the last two hands, 234 is significantly less valuable than 345 because of its nearness to the ace.
  16. Hold AA33 unless 2P pays 1-for-1 and four aces pay 160-for-1 or more.
  17. Hold KK33 unless 2P pays 1-for-1 and four kings pay 120-for-1 while FH pays 8-for-1 or less.

During my classes, I frequently give out this kind of information when it is relevant to the game I’m teaching that day. One of my students asked me to put it all down in one place, so that’s why I wrote this article.

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A Certain Kind of Approach

A month or two ago, I mentioned on the Gambling with an Edge podcast that I have a buddy with two kids — “Jack,” 12 years old and “Mary Ann,” 10 years old — who are becoming fascinated with the game of backgammon. I’ve agreed to provide them with some backgammon instructions, and I’m enjoying the process of teaching them. I’ve taught adults for years but have had limited experience with teaching children.

The lesson on this particular day was about the doubling cube.

“Let’s say,” I began, “that from a certain position, your opponent will win 26 times out of 36 and you will win 10 times out of 36.” Backgammon players will have no trouble constructing one or more positions that meet this criterion, but I want today’s column to be understood by those readers who do not understand backgammon as well as those who do.

“Let’s say that you are playing for $1 and your opponent,” I continued, “offers you the doubling cube.  What this means is that you have the choice of accepting the cube and playing out the game for $2 or passing the cube and conceding $1 right now. What would you do?”

Both kids are pretty bright and are in STEM schools, which specialize in science and math, but the boy is two years older.  When it comes to figuring out mathematical problems (which is what I thought this was), those extra two years make a difference.

At this point in time, neither knew how to figure this out (I hoped that this would be different by the end of the lesson), so both went with instinct. Jack could see that he was a big underdog to win, and he’d much prefer to lose $1 rather than $2, so he announced that he would pass the double.

Mary Ann wasn’t interested in the math at all. Her goal was to beat her brother. Since she knew she couldn’t beat him by going with the same answer he gave, she announced she was going to take the double.

Then I went through the math so they would know how to solve these “take-or-pass” backgammon problems in the future.

If they passed the double, like Jack wanted to do, they would lose $1. That much was clear to everybody.

But if they took the double, how do you figure that out?

Well, 10 times out of 36 you win, which would put you ahead $20 on those rolls. Twenty-six times out of 36 you lose, which would put you down $52 on those rolls. Your net loss in 36 rolls is $32, so the average loss is $32/$36 which comes out to 89¢. Since 89¢ is smaller than $1, the correct play is to take the double.

The acronym “QED” comes from the Latin quod erat demonstrandum and means I have shown that which was to be demonstrated — or, basically, this math proves my case. Neither child, however, was impressed by what I had done.

Jack assured me he understood the math, but he would still pass the double. He simply didn’t want to risk losing the extra dollar most of the time.

Mary Ann cared even less for the math. The important thing to her was she got it right and her brother got it wrong! What could possibly be a better result than that? “That was fun! Do you have another puzzle for us, Bob?”

There was nothing more for me to say. In my opinion, playing games successfully depends on understanding and following the math. They both rejected the math. I was out of ammunition.

I spoke to their father, a successful gambler, a few days later about this. I think he took the right approach. He said, “I really don’t care if they become professional gamblers or not. But if they do, I want them to know the math backwards and forwards. They certainly don’t need to know this math when they are pre-teenagers — and who knows what their aptitudes will be in a decade or more? Later, if and when they decide that playing games competently is what they want to do, that’s when it’s important that they learn this stuff.”

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Getting It Straight

Every now and then I share results with somebody in a drawing or tournament. Sometimes, other people do it to lower the fluctuations in their bankroll. That is, they would much prefer to get half the amount twice as often. Assuming they are playing with an edge, this smooths out the swings. One can think of it as getting to the long run more quickly.

That’s not the primary reason I share results. I share results for social reasons. Simply put, it’s more fun to do things with your friends.  Sometimes the decreased bankroll variance is important to the friend with whom I would share. Sometimes not.

Once you’ve agreed to share, only half the work is done. You need to carefully lay out what is and is not included in the agreement. For example, is this agreement for one drawing only? Is it always in effect unless otherwise specified? Is it never in effect unless explicitly specified?

If the award is in free play, do you share in cash? (That is: Let’s say one of the players earns $1,000 in free play. When it plays it through, he runs salty and only collects $900. Does he owe his partner $500, $450, or some other number?)

If the prize is in cash, are 1099s to be issued? If the prizes are $1,000 or less, the tax implications are fairly minor. If there is a rare $50,000 prize, the tax implications are not minor at all. Issuing a 1099 for $25,000 is the cleanest way to handle it, but if this isn’t agreed upon up front, hard feelings will abound.

Several years ago, Jamie Gold won the World Series of Poker main event for $12 million. He had a partner putting up some fraction of his entry fee, and possibly the partnership wasn’t thought through clearly enough. There was a major disagreement as to how the tax liability would be handled. The poker community generally appeared to be against Gold. Eventually it got settled and Jamie resumed his career — probably because he was wealthy and willing to play in games with significantly stronger players. But there were hard words and angry feelings until it got resolved. I’m not involved in any sharing opportunities where a jackpot anywhere near that large is possible, but that incident offers a lesson nonetheless.

At a recent Big Draw lottery at the M resort, most people earned zero, but you could earn $50, $200, $1,000, $10,000, or (with a less than 1-in-50 million chance) $250,000. The lower amounts were in free play and the largest one was in cash. The deal I had with another player was all prizes would be settled for the full 50% amount in cash, and if lightning struck and one of us got $250,000, a 1099 would be issued for half that amount.

Was that the best way to do it? I don’t know. But it was agreed upon up front and both of us thought it was fair. So that means it was fair.

Sharing isn’t always symmetrical. In a slot tournament where it’s just “hit the button as fast as you can,” everybody has more-or-less an equal chance and you can share with anybody who’s not completely senile.

In a video poker tournament, it’s a different situation. Some players are simply much faster than others, some can make better decisions than others in a split second, and some can correctly adjust their strategy in the middle of a round when it’s appropriate to go for a “royal-or-bust” strategy. You need to be very careful with whom you partner.

I recently shared in a video poker tournament with someone who I later discovered was a slightly faster player than I was. However, I probably made better decisions than he did because I’ve been doing this a couple of decades longer than he has. Neither of us know this for sure. It was close enough to being fair that neither of us were worrying about it.

Sometimes there are drawings where once you’re selected as one of the winners, you have an equal chance at each of the prizes. In these circumstances, if you’re one of the winners and want to make a deal with another of the winners, it’s fair. However many tickets you had going into the drawing no longer matters. At this point, you’re both in there and have equal chances.

If you have unequal numbers of tickets in the drum, it isn’t easy to come up with a fair system for sharing — simply because you usually cannot win more than one prize. For that reason, if I have 1,000 tickets and you have 500, giving me 2/3 of the prize money would be unfair to you unless there is only one prize. I have twice the chances as you to be called first, but then the rest of my tickets are dead while yours are still alive.

Still, if there’s enough goodwill between the players, usually players would go with a 2/3 and 1/3 split in this example. It’s “close enough,” and you’re friends. If there wasn’t sufficient goodwill, normally no split is done.

Finally, some people can be trusted with money and some can’t. Whenever I’ve felt I’ve been intentionally shortchanged by a player, I let others know — sometimes by an article in this blog. Once somebody shows he will steal from or shortchange me, I never will give him a second chance.  

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Looking at 9-5 Double Double Bonus Poker with Multiple Progressives

The Vegas Stats & Information Network radio studio is located in the middle of the South Point casino floor, and periodically I’ve been a guest of the early morning show hosted by Paul “Paulie” Howard and Mitch Moss. Paulie mentioned that he found the DDB progressives interesting and wanted me to talk on the show about when you should get on the machine.

Such numbers do not make for good radio, especially since some of the listeners are probably driving to work and can’t take the time to write down anything. When I was last on the program on June 29, I gave some numbers and said that I’d be going into greater detail in my July 17 blog. And here we go!

If you’re serious about progressives, you should get Frank Kneeland’s “The Secret Guide to Video Poker Progressives.” That has by far more useful information on progressives than you’ll find anywhere else.

For today, I’ll assume you’re just going to be playing the game occasionally — and basically want to know how to figure the return on the game.

The game in question at the South Point contains a number of progressives, but does NOT have a progressive on the straight flush. Today I’m going to assign a number to the straight flush progressive because this same progressive is found in numerous casinos — sometimes with a progressive and sometimes without.

In addition to telling you how to evaluate the game, I also want to explain how I came up with the numbers. That way readers who are interested can apply the same technique to other progressives.

You’re going to need computer software to analyze progressives. I’m going to use Video Poker for Winners and WinPoker as those are the ones I use regularly and know well. If you have Wolf Video Poker, that can work as well. While it’s not quite as user-friendly, the wizardofodds.com has a free calculator you can use online. For many, it’s hard to beat free.

To start with, we need the base return of this dollar game, which is 97.87%. We’re going to be coming back to this base game over and over again.

To see how the progressive on the royal increases the return, I’ll set the royal on the game to 8000 coins. When I do this, I see the return is close to 100.13%. Assuming the return increases linearly (not completely accurate, but close enough for the analysis we’re going to be doing today), this means that when the royal increases $4,000, the value of the game increases 2.26%. Dividing by 4, when the royal increases by $1,000, the return on the game increases 0.56%. Once we have this multiplier, we can figure it out for any royal. Say the royal is at $7,356. That is 3.35 “$1,000 increments” more than the base game, and 3.35 * 0.55% adds 1.84% to the game.

Those who have actually followed along with the math will have noticed that I have rounded downward. The reason for this is that there are strategic changes to be made as each of the progressives change in value and it’s virtually impossible to get them all correct. By lowering the estimates of what the return will be, we somewhat take this into account.

Now we look at aces with a kicker. This jackpot starts at $2,000. So, we return to the base game and enter $3,000 for aces with a kicker. This gives up a return of 99.23%, which is an increase of 1.36% over 10 $100 increments, or 0.13% for every $100 (again rounding downward)

For aces without a kicker, this starts out at $800. Increasing that to $1,800 from the base game gives us 101.37% — an increase of 3.50% over ten $100 increments. So, whenever this progressive increases by $100, I add 0.35%.

For four 2s, 3s, and 4s with a kicker, this starts out at $800. Increasing that to $1,800 gives us 101.11% — an increase of 3.24% over ten $100 increments. So, whenever this progressive increases by $100, I add 0.32%.

I’m looking now at the straight flush, even though it does not have a progressive on the South Point machines. Sometimes, it does elsewhere. I’ll set the straight flush to $1,250 to get a return of 100.61% — an increase of 2.74% over ten $100 increments. So, whenever this progressive increase by $100, I add 0.27%.

The other two progressives, 2s-4s without a kicker along with 5s-Ks with or without a kicker, turn over fairly rapidly. These add some value, as you might collect $403 or $256 instead of $400 or $250 respectively, but these never get high enough to make that much of a “sit down and play or not” decision.

I assign 0.13% as the sum of these no matter how high they are. Why? Because that makes the base game an even 98% instead of 97.87%. This is a much easier number to work with, especially if I’m doing this in my head rather than with a calculator or some other means.

The final question you need to address is, “How high does it need to be before it’s worth playing?”

This depends on you. Since they have a number of 9/6 DDB games in the casino, which return 99.0%, the minimum sum of the progressives that you need is this figure. For players who wish to play a winning game, however, this isn’t nearly high enough.

You need 99.7% to make it an even game with the 0.3% slot club. Actually, that makes it slightly positive because you will also receive mailers and be able to participate in promotions while playing this game.

I can tell you I’ve seen it above the 99.7% level frequently. This is a decent game for dollar players to add to their repertoire at a casino with a number of good choices.

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If It Looks Too Good to be True . . .  

I just finished a two-part analysis of Maria Konnikova’s The Confidence Game where one of her warnings was (paraphrased) “If something looks too good to be true, it probably is. Very likely there’s something fishy going on.” Soon thereafter, a friend, “Sam,” who’s a knowledgeable video poker player, sent me the following pay schedule on a Bonus Poker game in the Palms High Limit Room:

(The numbers on the left represent the “new” pay table. The numbers on the right represent “standard” good Bonus Poker which is worth almost 99.2% if you play it appropriately. Compare the two sets of numbers and you’ll see why Sam was excited about the new game).

Royal Flush 800    800
Straight Flush 50    50
Four Aces 80 80
Four 2s-4s 40 40
Four 5s-Ks 25 25
Full House 9 8
Flush 7 5
Straight 5 4
Three of a Kind 4    3
Two Pair 2 2
Jacks or Better 1 1

The new game returns 111.2% and it can apparently be played from 25¢ through $5, Triple Play through Ten Play. My my!

Except, this was not a standalone pay schedule. It was on Dream Card.

Dream Card is a 10-coins-per-line game where you periodically get a Dream Card on the draw and that card turns into the best available card to go with the other four cards in the hand.

On Bonus Poker games, the occurrence of Dream Card has historically been 46.7%. If that same frequency is in effect on this game, that would turn this game into a 112% monster, or thereabouts.

Sam generously said that in exchange for my analysis of the game, I could play it, but I should please try not to kill it. After all, games this good don’t come around very often.

I told Sam that I wouldn’t play it at all. Although I’m allowed to play at the Palms now that Station Casinos owns it (and made it worse, in my opinion), I am severely restricted in the benefits I receive. The net effect is that I voluntarily stay away.

Still, on a 112% game where I could play up to $500 per deal, it wouldn’t matter much if I got benefits from the slot club or not. I would have major paydays as long as the machine and my welcome lasted.

The problem is that many of the slot department employees who now work there are the same employees who worked there back in the “good old days” and would instantly recognize me on sight. If I started hammering a machine, word would get to management within a few minutes.  If the game were really a mistake, either the machine would be pulled off the floor or I would be pushed out the door. So, it wouldn’t do any player any good if I tried the game at all. If it was a mistake, all my presence would do is help the Palms identify a problem. No thanks.

But I suggested to Sam that he play 100 hands on the game for the lowest possible stakes (which is 25¢ Triple Play costing $7.50 per deal) and keep track of the occurrences of the Dream Card. If it’s close to 46, which would be standard for Bonus Poker Dream Card, then he should go ahead and play it for the largest stakes he could afford. But if it’s a lot lower, we should do further research.

He did this. He actually played 200 hands and got 40 Dream Cards — which is less than half of the 93 or so he would get under the “normal” Bonus Poker Dream Card frequency. Whether playing 200 hands was statistically significant or not, he became convinced that it was and didn’t want to continue.

I told him I could contact a source I had at IGT — who is the guy both Michael Shackleford (the “Wizard of Odds”) and I use to get accurate information we can publish about games. But, I told Sam, if the game really was a mistake, likely my friend at IGT would notify the casino and that would be the end of it.

Sam said he wanted to know. He was likely done playing it and he didn’t see anybody else knowledgeable playing it, so almost certainly it wasn’t a mistake. Just “misleading,” because it would mean the frequency of Dream Cards wasn’t fixed for a game type.

It turns out that the game is worth 98.6%.

One of the unusual things about the game is that when you play five coins, the game is 7-5-4-3 Bonus Poker (returning 98.0%), but when you play 10-coins, it is 9-7-5-4. In the past, the Dream Card pay schedule was the same on the 5-coin and 10-coin versions, at least in my experience. Many of us would see the 7-5 Bonus pay schedule and not look any further.

Keep in mind that if the Dream Card frequency were zero, the return on this 111.2% game would be 55.6% (illegal in Nevada and many other places) because you’re betting 10-coins per line. I do not know the actual dream card frequency here, but it’s clearly lower than the normal Bonus Poker frequency, and higher than zero. Once I found out that the game is worth 98.6%, that’s all I needed to know.

It could well be that this is the best game in some casino someday where they have suitable-enough slot club and/or promotions to make this playable. Which is why the 98.6% number is important to me and may be useful information at that time. But until that time, it’s just a curiosity.

This again was a case of it looked to good to be true, and indeed, it wasn’t nearly as good as it looked. But we couldn’t know for sure until we did some further research.