Category: Advice for Players

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Does This Make Sense?

This is a column for “low intermediate” players and it involves 4-card inside straights in games where you get your money back for a pair of jacks or better, same payout for two pair, and 4-for-1 for straights. It also involves a paradox of sorts.

There are a lot of these games — Double Double Bonus, White Hot Aces, Triple Double Bonus, Triple Bonus Poker Plus, Super Aces Bonus, and others. What I’m talking about today does not work for games where you get double money for two pair (i.e. Jacks or Better or Bonus Poker), nor does it work for games where you receive 4-to-1 for straights (i.e. the best versions of Double Bonus.)

That last sentence should have caused many of you to do a double take. I said 4-to-1 rather than the more common 5-for-1. They are equivalent, but often players are a bit loose with their terminology. When a pay schedule lists numbers, the returns are always “for 1.”

Here’s the paradox:  Holding 4-card inside straights with no high cards (e.g. 4578 of mixed suits) is eligible to be held in these games.  (“Eligible” means better than throwing everything away. There may or not be higher paying options in the hand.) Assuming you’re playing dollar 9-6 Double Double Bonus, five coins at a time, holding this inside straight is worth $1.70. Holding 4-card inside straights with one high card (e.g. QT98 of mixed suits), worth $2.02 in the same game, is never held.

Both inside straight draws have four cards to fill them in. When there’s a high card involved, there are also three chances to pair up that high card. Of the 47 possible draws, three extra chances to get $5 (the payout in this game for a high pair), add 3 * $5 / 47 = 32¢, which is the difference between $2.02 and $1.70.

I call it a paradox because the greater of the two hands is never held and the lesser of the two hands is held sometimes (depending on the fifth card). So, what gives?

If you haven’t seen or heard this paradox before, I strongly urge you to see if you can figure it out for yourself before you read on. I’ll wait. No matter how many video poker paradoxes I write about, there are hundreds more that I will never get to. If you’re going to become a decent player, you’re going to have to learn to think for yourself.

The key to the paradox is using absolute values to deflect attention from relative values. The $1.70 and $2.02 numbers are absolute values — that is, what the position is worth on average if you play it out zillions of times.

What is important in video poker, however, are relative numbers. In the hand 4♠ 5♥ 7♣ 8♦ 2♠, we’ve already said the value of holding 4578 is $1.70. The important thing is that the value of throwing everything away is $1.62. Those are the best two choices, and the better of these two is to hold the 4-card inside straight.

From Q♥ T♥ 9♣ 8♦ 3♠, we’ve said the value of holding the 4-card inside straight is $2.02, but the value of holding the queen by itself is $2.12, and the value of holding the suited QT is $2.23. Relatively speaking, the value of $2.02 is less than the value of holding either the single high card or the high card with a suited ten.

Every time there is a 4-card inside straight with one high card, there is necessarily a high card by itself in the same hand — and sometimes a high card with a suited ten. So, we’re never going to hold this inside straight.

The fact that holding this inside straight is better than throwing everything away is interesting, perhaps, but irrelevant. We’re looking for the play with the highest EV, and throwing everything away isn’t going to qualify when there’s a high card in the hand.

Once you realize that we’re comparing one inside straight to throwing everything away, and the other inside straight to something else entirely, the paradox disappears.

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Which is the Better Place?

I received an email asking which of two casinos was the better choice for this player.

Casino A had 9/6 Jacks or Better with a 0.1% slot club with no multiple points ever. Casino B had 8/5 Bonus Poker with a 0.25% slot club, and he only played when there were triple points. He said the food comps at Casino A were better, but he wasn’t there for eating. He was there for making money.

He told me he played both games perfectly. This is extremely unlikely. Although 9/6 Jacks or Better is one of the easiest video poker games to memorize, 8/5 Bonus Poker isn’t. I would estimate fewer than one in a thousand 8/5 Bonus Poker players play the game perfectly. But letting that assumption slide, let’s see what we have, assuming perfect play.

 

Casino A:      9/6 Jacks                   99.54%

Slot Club                   00.10%

Total                           99.64%

 

Casino B:      8/5 Bonus                  99.17%

Slot Club                   00.75%

Total                           99.92%

 

The obvious answer, then, is that Casino B is considerably better. For a dollar player who plays 600 hands per hour, Casino A is $8.40 per hour more expensive than Casino B.

The obvious answer is incorrect, however. For this player, it is not the case that Casino B is better. Why not? Because his stated goal is to make money and that means that both casinos are TOTALLY unacceptable. Not less acceptable; TOTALLY unacceptable.

A return of 99.92% is not “close enough.” It’s impossible to end up a long-term winner when the casino has any advantage at all.

If the casinos had other promotions, however, that could change things. Perhaps one or both send periodic checks in the mail on the order of “come in during the first two weeks of the month and we’ll give you $50 just for showing up.” Or perhaps they have regular drawings and the player has a decent shot at winning something valuable. Either or both of these promotions could make the casinos potentially profitable. But without such promotions, the house has the edge.

For most players, this would not be an insurmountable problem. Few players demand that casinos be potentially profitable. (No slot player, for example, has any realistic expectation of being an overall winner. They hope to win THIS TIME, but they know that in the long run the casino will most likely win from them.)

Many players value the gambling experience and count the free meals and rooms as part of the deal. For players like that, both casinos offer an excellent gamble which is better for the player than can be found in many casinos. Which casino is better might well depend on how much better the food is at the casino with the lesser game and how important that is to the player. To some people having a quality meal is extremely important. Others don’t care that much.

Or perhaps how nice the rooms are. Or maybe how smoky the casino is. Or possibly “easier to get to.” All kinds of solid reasons exist for choosing one place over another.

What should this particular player do then? The choice is between either not playing, or lowering his expectations about whether or not this game will be profitable. It would not be terrible should he decide to play anyway because he really enjoys it. After all, people pay to do many pleasurable things. And if gambling is pleasurable, it’s okay to pay for that too. But I encourage you to be realistic about whether you are playing for profit or playing for pleasure.

In similar cases, I ALWAYS choose not to play. I’ve played video poker for close to 25 years and it’s isn’t a “special treat” to me. I enjoy it. But I can go without playing if the odds aren’t there.

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Comparing Two “Super” Games

Super Double Bonus (SDB) and Super Aces Bonus (SAB) are both variations of Double Bonus. In “regular” Double Bonus, four aces get paid 160 for 1, four 2s-4s get paid 80 for 1, and four 5s-Ks get paid 50 for one.

Each of the variations we’re looking at today keeps that basic structure for the quads, with one exception each. In SDB, four Js-Ks receive 120 for 1 rather than 50 for 1 (and you receive more for the straight flush as well). In SAB, four aces receive a gigantic 400 for 1. In both games, the amount for the full house and flush is adjusted downward until it gets into the “acceptable” range. This means the pay schedule returns enough to attract the players, but not so much that the casinos are afraid of it. The two pay schedules discussed in this article are the highest allowed for these particular games. In many casinos, you’ll find lower pay schedules than these, but that won’t affect the discussion that follows.

 

9/5 Super 8/5 Super
Double Bonus Aces Bonus
Royal Flush 800 800
Straight Flush 80 60
Four Aces 160 400
Four Js-Ks 120 50
Four 2s-4s 80 80
Four 5s-Ts 50 50
Full House 9 8
Flush 5 5
Straight 4 4
Three of a Kind 3 3
Two Pair 1 1
Jacks or Better 1 1
Return 99.69% 99.94%
Variance 38.0 63.4

 

The strategies for the two games are very similar. This is largely because they receive identical amounts for flushes, straights, and two pair — which are the three pay-schedule categories that matter most when it comes to strategy.

In today’s column, I’m going to present four hands that are played differently in the two games. Your job is to figure out both plays. Even if you have never played either game, you have two important clues to help you out:

  1. The plays are different. This is a HUGE clue.
  2. The plays are different because of the pay schedule.

 

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

 

Where dollar and cent amounts are indicated, it assumes you are playing for dollars, five coins at a time.

 

  1. There are only two reasonable plays here. The “chickens” keep the straight and the “gamblers” go for the straight flush. The different returns for quads has no bearing when you hold at least four cards of different ranks, so the determining factor must be that SDB returns more for the straight flush. In SDB, ‘5678’ is better by $2.87, and in SAB, 56789 is better by $1.39. Obviously neither play is close.
  2. With three unsuited high cards including an ace, the “standard” play in both Jacks or Better and Double Bonus is to discard the ace and hold the other two high cards. That’s the correct play in SDB by 10.6¢. In SAB, the much greater return for four aces means that you go for them more. In SAB, holding the single ace is the better play by 20.6¢.
  3. This is very similar to the last hand. In SDB you hold AQ by 2.6¢. In SAB, you hold the solitary ace by 19.6¢. And the reason, again, for the difference is the large amount you receive for four aces in SAB.
  4. This last hand is intentionally tricky, in that there are more than two choices. Holding ‘KT’ is obvious. Holding the inside straight, T876, is also an eligible choice. It takes some experience to know that inside straights with no high cards are worth considerably less than either single high cards or a single high card with a suited ten. Perhaps the hardest option to see is holding the king by itself. Some players can’t bring themselves to break up royal combinations no matter what the pay schedule. Once you realize that the king by itself is a viable option, then since SDB pays more for four kings, holding the single king in that game is the better play by 2.8¢. In SAB, the “normal” play of ‘KT’ is better by 3.0¢.

 

So how did you do? As a test, this wasn’t too difficult. But as a learning experience, there were some important things to remember. First of all, each game has its own strategy and those of you who use more-or-less the same strategy for most games are taking the worst of it. Second, sometimes the reason for the differences in the strategies is obvious once you closely examine the idiosyncrasies of the pay schedule.

Finally, I want to leave you with a hand that’s played the same in both games, assuming you are playing with the best pay schedule. K♥ K♠ 9♥ 9♦ 3♣. Although many seat-of-the-pants players will just hold the kings, in SAB, holding KK99 is better by 79¢. In SDB it’s a closer play because four kings pay so much, but KK99 is still better in that game by 19¢. If you find yourself playing a version of SDB where the full house pays only 40 or less instead of 45, that’s enough to change the correct play to KK.

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Interesting Promotion at the M

I received a postcard from the M where they are trying to get new players. The promo was:

  1.         I get $100 in free play right away for bringing in a new player,
  2.         The new player also gets $100 in free play — plus a kiosk spin (usually $5 in free play, I think, but it could be more),
  3.         For every point the new player earns in the first day, I get 10x points, up to a total of 50,000 points,
  4.        Good (if you got the postcard and the new player has NEVER had a card at the M) from June 1 to July 31.

The slot club is 0.3% (slightly more, actually, because they give you $3 for $999 coin-in rather than $3 for $1,000 coin-in). 50,000 points is worth $150 of free play — which is way more than the house’s expected win if you’re playing the best machines.

The loosest game is $2 9/6 Jacks or Better. There are two such machines — newly installed — in the high limit room. There is no choice as to the denomination and no telling how long they’ll last. 10x points (which is worth 3%) on top of a video poker game returning 99.54% seemed possibly like a mistake, except that it was limited to $150 max which might be a reasonable cost for a new player.

I don’t actually know if this was a mistake or not. I hooked up with a player friend, “Kevin,” who lives near Aliante — which makes the M geographically undesirable for him. Which is why he didn’t already have a card. I know some non-players for whom I technically could have played the free play, but that’s strongly against the rules there and I’m well known. No thanks. If I had to use a non-player, I would have let them play and talked them through their $105 in free play — which we would probably have played on 25¢ 8/5 Aces Bonus. If they were a non-player, any possible W2G could have been a problem for them.

As it happened, June 1 was a normal free-play pick-up day for me (they have 6 to 7 such days per month). Kevin and I agreed to go in and play the promotion on the first day it was active.

We were certainly not going to ask for clarification as to whether the 10x points included video poker or not. The booth personnel (who are also the cashiers) would likely have said, “I don’t know. Let me make a phone call.” If they did that, it’s possible that signs would have been posted saying “slots only.” If we could arrange it, we didn’t want such signs posted until after we played.

Our deal was, we would play the promotion and also play an additional 850 points which entitled us to a “free” lunch buffet. Other than the amount of my free play, we split everything based on my $850 worth of play and his $5,850. Whether this split was overly generous or not didn’t concern me. Kevin is a friend. And enjoying lunch together was part of the attraction of the “date.”

I often play for a buffet on my free -play pickup days there. There have been incidents where players who only picked up free-play without any additional play were punished for this. As a known professional player, I am hyper-sensitive about creating situations where it would be easy for them to justify restricting me.

The $205 in free play we got between the two of us more than covered the expected loss of playing $5,850 for him and $850 for me. If we got the additional $150, great, but it was still a decent play if we didn’t. (And yes, we could have lost, but the decision beforehand is made based on EV, because you don’t know what your actual result is going to be.)

I had him play $5,850 rather than just $5,000 because the M usually doesn’t allow you to “double dip.” If there’s a gift of the day you can get for 800 points and you also want the free buffet, it takes 1,650 to earn both. We only had one shot at this and if they decided to give us 10x points on only 4,150 points (which would be 5,000-850), that would cost us $28. No thanks.

We didn’t split the $150 on the day we played because I wasn’t certain whether or not we were going to get it. It could be that they “intended” it to say “slots only,” but they didn’t put that in writing. How it would be enforced down the road was an open question.

I hadn’t decided how aggressively to pursue the 10x points if they denied that it applied to video poker. It was “only” $150 (split between two of us) and you need to pick your battles. In a somewhat similar situation at the Silverton I wrote about a few months ago, we were talking about an $8,000 difference between getting the multiple points or not. I’m willing to fight a lot harder for $8,000 than I am for half of $150.

Eight days after we played, I received an email saying that 50,000 points had been placed on my card, so I sent my friend an email saying that I owed him $75 next time we saw each other.

I never had to decide how hard to argue for this. It’s possible that future players will be told “slots only” when they sign up. I don’t know. But this was a case of taking advantage of the situation before they made changes to it. If they keep the promotion “as is,” then whether we did it early or not doesn’t matter. If they restrict it later to slots only, it matters $150 worth. For me it was a no brainer to do it as early as possible.

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You’re Not a Poker Player

In early June, Bonnie and I were at a square dancing workshop and there was this guy, Scott from Alabama, who showed up. He had played a few days before at the Colossus event in the World Series of Poker, did well enough to get his money back plus $500, and was killing time before his flight back home. He had arranged his stay through the last day of the Colossus in case he made it that far. He hadn’t, but that was why he was still in town. Square dancing events are publicized if you know where to look, so he found us and danced. He was very welcome.

The Colossus is a $565 buy-in tournament with starting flights over several days. Re-entries are allowed. He was very proud of the fact that he cashed in his first WSOP event, which gave him the confidence to come back next year. He had to tell me, of course, about the hand he blew out on and that he was ahead until his opponent paired on the river.

I asked him if he had considered re-entering and he said, “No.  If I’m not a good enough player to win on my first try, I’m not going to throw good money after bad.”

I told him that I didn’t know anything about his personal bankroll, but that didn’t make any sense to me. He probably had $500 in expenses to get to and stay in Vegas for five days. That made his first entry cost $1,065. His re-entry would cost “only” $565, or basically half price since he was already in Vegas. If the first one was a good deal for him to enter, re-entry must be a great deal. Why come back next year and pay another $1,065 and not get the same equity right now for only $565?

In any tournament with several thousand entries (there were 18,000+ entries in this year’s Colossus), there is a considerable amount of luck insofar as how long each player lasts. The hand where he blew out (in 400th place or so) could have easily happened much earlier and he would have gotten nothing at all. No less skill on his part. Just the luck of the draw.

You can’t conclude, I argued, that just because you cashed this time that you are a good player or just because you didn’t cash any particular time that you’re a bad player. No player cashes every event. Your record over a whole lot of tournaments says a lot about your skill. Your result in a single tournament says very little.

He asked if I was a poker player. I told him no, that I was a video poker player, but that I’ve been a successful gambler for several decades and believe I have some knowledge and experience about how it all works.

He informed me that since I wasn’t a poker player, I really didn’t know what I was talking about and he didn’t want to discuss it anymore. Okay. A square dancing event is mostly a social activity and if he didn’t want to “talk shop,” that was fine with me. I went over and spoke to someone else. Whether or not I could get him to agree with me was not something I cared about very much. He had never heard of me and self-professed video poker experts are not people he considers worth listening to.

But you, my reader, I do care whether you agree with me or not. I assume you accept that I am generally knowledgeable about these things or you wouldn’t be reading this blog.

This is another case of paying undue attention to short term results. This example looks a bit different in live poker than it does in video poker, but the principle is the same. Perhaps this example is easier to understand than in the ways I have expressed it previously.

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Who Cares?

I was out walking for exercise and my iPhone rang. Had I looked at the caller ID, I would have seen “UNKNOWN,” usually a tip to avoid answering, but I was busy doing nothing at all important so I hit the green button and heard a recorded voice saying, “Now is the time to refinance your home because . . . ” I never found out what the specifics of the offer were. I hung up after nine words.

I find such calls mildly irritating. They take up a few minutes of my day, but to me they’re not a big deal. However, I’ve been around other people who slam down the phone in anger and loudly curse the machine making the call, “Why don’t you take your &%#!@& offer and shove it up your dial tone?” Or something like that. As though the machine making the phone calls cares.

The machine is dialing numbers according to a list, or perhaps according to a formula. When the last person hangs up, for whatever reason and with whatever emotion, the next one is called. Whether the current person places an order or not, the next call will be made as soon as the current one hangs up or perhaps is transferred to a real person. The machine will keep on calling as long as it has numbers to call and it’s within the hours prescribed for it, which might be something like 10 a.m. through 8 p.m.

A video poker machine is like that. When a new hand is triggered (which might be by hitting the deal button), the machine looks at its internal clock (in nanoseconds), checks one other “seed” (which is required for a random number generator to work, varies by manufacturer, and isn’t important to this discussion), and deals the cards. Sometimes people will say, “The machine is in a cold streak.” Nonsense. The machine is just dealing cards. The fact that you haven’t won in a half hour is totally irrelevant to it. One lady I knew said things like, “Sixes are running today,” and usually when she played accordingly, it didn’t help.

Others will say, “I hit two royal flushes yesterday so it’s making up for it now.” Nonsense. The machine is just dealing cards. Or, “Because I’m (pick one or two: on a winning streak, on a losing streak, fat, Armenian, over-drawn at the bank, using a slot club card, divorced, voted for Trump), the machine is . . . ” Nonsense. The machine is just dealing cards.

I think that people ascribe human emotion or motives to video poker machines because these people are trying to understand their results. They lost today and they won yesterday so it must be because . . .   They’ve lost six times straight, so the reason must be because . . .  Or perhaps they use the machine’s “behavior” as a good reason to change machines, or denomination, or change games within a machine. Or instead of trying to understand their results, perhaps these people are attempting to assign blame. Such as, “It was not really my fault. The machine was colder than a witch’s elbow. Nothing I could do about it.”

Perhaps surprisingly, the last explanation above is one that I might use. AFTER a session is over, it is possible to assign descriptive terms to that particular session. You can say it was “hot” (meaning that you won), “cold” (meaning that you didn’t), “so so” (meaning it was so so), or whatever. MIDWAY though a session, you can describe what the session has been so far, but there’s no way in the world to predict how the rest of the session is going to go. The “best guess” of what the future will bring is the average of what this type of machine under these particular conditions (i.e., dollars, NSU Deuces Wild, at a casino that pays .25% cash back, on a day when double points are being offered, during a month when you get a jacket if you hit a royal flush) typically offers over a million hours of play, given your particular skill level. You ARE PRETTY SURE the “best guess” will be high or low this time. You just don’t know which (i.e., Will it be higher or lower than normal this time?), and by how much, until after you are finished.

To make your next year of play better than your last year of play, you can choose better games (e.g., if one returns 98.9% on average and another returns 99.6% on average, the second is “better” than the first), stick to the good game once you’ve identified which one is best, practice that game on a computer or by studying a Winner’s Guide for the game, play at casinos with good slot clubs, and do most of your play only during good promotions. Doing these things will help you. Believing in such things as “The reason this machine started to pay off is because it was on a dry spell and the dam finally broke,” won’t.

 

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A Look at a Wheel Spin

Today’s column isn’t specifically about video poker, but it concerns a gambling situation that video poker players encounter in a casino. And most video poker players don’t care whether a $1,000 prize comes from a jackpot, a casino drawing, or a tournament.

Assume a casino is giving away money. If your name is called, you get to spin a fair wheel, where the possible prizes range between $5 and $1,000 in the following ratios:

 

Number of Prize
Occurrences Amount
1 $1,000
1 $500
4 $250
4 $100
5 $50
10 $20
15 $10
20 $5

 

If you add this all up, you’ll see there are 60 slots on the wheel, and the sum of the prizes adds up to $3,600. This makes the spin worth $60 on average ($3.600 / 60 slots = $60 / slot).  A few of the prizes are quite a bit larger than the average, and three-fourths of the prizes are $5, $10, or $20. To make the problem more interesting, assume the casino offers a $50 buyout. This is less than the $60 average, of course, but it’s a lot better than 45 out of the 60 prize and equal to another five out of the 60 prizes.

If somehow you were in the enviable position of being allowed to spin the wheel 400 times, you’d be a fool to take the buyout of $20,000 (400 * $50 = $20,000) rather than the average of $24,000 ($400 * $60 = $24,000) that would come if you spun the wheel every time. Spinning 400 times is close enough to the “long run” that you figure to hit the $1,000 and $500 enough times to make spinning pay off more than the buyout. It doesn’t HAVE to work out this way, of course, but the odds are in your favor.

The more interesting case is if the spin is “maximum once per person.” Now if we choose to spin and end up with a lousy $5, we have forever lost the $45 we could have gotten from the guaranteed $50. We will never get it back from this promotion simply because we wouldn’t be allowed to spin again, so the results could never average out. In this case, is it better to take the guaranteed $50 or spin for the prize with a bigger average (but a significant probability for a smaller result)?

To my way of thinking, whether we get the opportunity once or 400 times is not an important distinction.  I believe spinning is correct in either case. All of us have MANY gambles, and we are NEVER in balance in all of them. To the smart gambler, we take the advantage every time we can and trust/hope that it all balances out in the end.

If the numbers were “large” (which is personally defined), then it can certainly make sense to take the “bird in the hand”. For example, if we were guaranteed $5 million or could spin the wheel and get an average of $6 million, I would take the $5 million in a heartbeat.

Even though the math is the same, $5 million is such a potentially life-changing amount that there is no way I can feel comfortable gambling with it. But $50? For me that’s pocket change and I’m going with the math.

It’s possible that $50 is not ‘pocket change’ to someone in this position. If that’s a large amount to you, by all means take the sure thing if that will make you feel better.

Also, please note that I’m stipulating that the wheel is fair — meaning each of the 60 positions are equally likely to come up. In the real world, that’s assuming away part of the problem. You have to use your judgment here. In Nevada casinos, I’m going to assume the wheel is fair. I’m not sure I’m going to make the same assumption everywhere.

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Learning from Munchkin

My co-host on the Gambling With An Edge podcast is Richard Munchkin, a table games player who’s been successful at gambling for several decades.

We often answer listener questions on the show and if anyone asks about a table game, Richard is the go-to guy. Sometimes I’ll have a bit to add, but mostly what Richard says covers the subject very well.

He has used one particular phrase in his answers over and over again. The questions vary, but part of the answer stays the same.

For example, some blackjack player is using one particular count and is considering learning another count because it’s more powerful. Richard will discuss the features of each count, but say, “You’re stepping over dollars to pick up pennies. A slightly better count is NOT where the money is in blackjack. There are far more important things to spend your time learning.”

I’ve heard him say variations on this numerous times and I started to wonder if the way I tackle video poker makes me guilty of stepping over dollars to pick up pennies?

As many of my readers know, I try to learn most video poker games at the 100% level. In NSU Deuces Wild, for example, letting a W stand for a deuce, I play W 4♠ 5♠ 3♥ J♥ differently than I do W 4♠ 5♠ 3♥ J♦.

For the five-coin dollar player, if he holds W 4♠ 5♠ both times he is making a quarter of a penny error half the time. If he holds just the W both times he is also making a quarter of a penny error half the time.

I avoid this small error. I learned the game this well when I was playing $25 games so the error every other time is 6¢ rather than a quarter cent. I still have that play memorized even though the larger games aren’t available, insofar as I know.

Although this particular distinction is one of many many I have memorized, it is safe to say I’ve spent dozens of hours, probably more, learning these exceptions in the first place and reviewing them often enough to keep them memorized.

Have I gained enough to make the difference between learning these things worth more than even an additional $2 per hour over all the hours I’ve spent studying? Probably not.

Without spending this time learning these exceptions, could I have played games worth substantially more than $2 per hour and been better off financially? Definitely yes, insofar as finding games worth more than that.

So, is this a case of stepping over dollars to pick up pennies? Have I been violating Munchkin’s advice (never mind that I spent most of those dozens of hours studying that game before I ever heard Richard give that advice)? Maybe, but if so, as
they say in Traffic Court, I plead guilty with an explanation.

Although in the Dancer/Daily Winner’s Guides for both NSU Deuces Wild and Full Pay Deuces Wild, we distinguish between penalty cards and “power of the pack” considerations, for the sake of simplicity today I’m going to include both of these into the term “penalty cards.”

The underlying assumption behind the question “Is learning penalty cards worth it?” is that without studying the penalty cards you can play the penalty-free strategy perfectly. For me, at least, that assumption wouldn’t track with reality.

Just the study and practice I undergo to learn the penalty cards causes me to be practicing the basic strategy simultaneously. For example, the difference between W J♦ 9♦ 5♣ 6♣ and W J♦ 9♦ 5♣ 7♣, which is a basic strategy play, is probably ignored by all players who have not also made a serious attempt at learning all the exceptions. Even though this play is clearly shown on the Dancer/Daily Strategy Card and Winner’s Guide for this game, I suspect most players simply ignore it or don’t understand why the two hands are played differently.

So, while learning the penalty cards might only return $2 an hour on my study time, I also gain considerably more than that because I learn the basic strategy better during the process.

For me personally, since I’ve chosen a teaching career and a how-to writing career, there are additional income streams available to me for learning this stuff that wouldn’t be available to most others.

Plus, I like being a student. I was good at school and continue to try and learn new things. So even if learning penalty cards doesn’t make great financial sense, it brings me pleasure. Can you really put a price on that?

I’m going to conclude that Richard’s “stepping over dollars to pick up pennies” warning doesn’t apply to me in this particular case. And I make this conclusion knowing full well that others may disagree with my conclusion. That’s okay. I’ve made my own bed here and I’m perfectly happy sleeping in it.

Yes, I know I mentioned that certain hands were played differently than others, but I didn’t explain what the differences were. If you want to know, you’re going to have to look up the information for yourself. If that annoys you, so be it, but the learning process isn’t easy and you need to go through it to become a strong player.

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When 9/5 Was Better than 9/6

One of the very first lessons taught by virtually all video poker teachers, including me, involves the game Jacks or Better. We explain how the game pays 25-for-1 for all 4-of-a-kinds, 2-for-1 for two pair, and the difference between the good version and the bad version depends on how much you get for a full house and a flush.

The best reasonably common version is 9/6, returning 99.54%. The game in second place is 9-5, 98.45% requiring a similar but not identical strategy.

If you don’t know what I mean by 9/6 and 9/5, compare the two pictures at the bottom of this page. The one on the top is 9/6 and the one on the bottom is 9/5. The key numbers used in naming the games are shown in red.

Under normal circumstances, because of the approximately 1.1% difference in the returns, any player who played 9/5 when 9/6 was available is a player without a clue as to the winning process.

And, yet, for a couple of years ending a few years ago, I personally played millions of dollars of coin-in on a 9/5 game when 9/6 was available. As did many other knowledgeable players. What gives?

It had to do with “theoretical.”

Theoretical is the hold the casino expects to make from players as a whole. If a game is rated with a theoretical of 2%, it means that for every $100,000 coin-in the machine gets, on average the casino expects to hold $2,000.

The 9/6 JoB had a theoretical in this casino of approximately a half percent. For that same $100,000 coin-in, the casino expects to make $500. The “perfect” 9/6 JoB player only loses $460 for that play.

This casino had a policy that if you agreed to earn $5,000 in theoretical, they would give you $3,500 in free play as front money. If they figured the theoretical correctly, this would give them an expected profit of $1,500 on this much play to cover their expenses and profit margin. On the 9/6 JoB, this was no bargain for the player. Your expected loss was $4,460, even if you played perfectly, so while getting $3,500 back was certainly better than nothing, you were still in the hole.

For whatever reason, the 9/5 JoB game was assigned a theoretical of 4%. This meant that it took $125,000 coin-in to generate the $5,000 in theoretical. And playing that much on a 98.45% game meant that you expected to lose a little less than $2,000 on average if you played perfectly.

Losing $2,000 is no fun, of course, but the casino was giving $3,500 to ease your pain. That meant that you had a net expected profit of a little more than $1,500 each time you did it, plus your points were worth something, and there were significant other goodies as well, including a couple of free room nights. We could do this at least once a month, and sometimes twice a month. This was an inadvertent mistake by the casino. We hoped it would be several years before the casino fixed it.

Sometimes I’d lose $8,000 or so “earning” this EV, but other months I would win. Looking at individual months, you could sometimes question whether this was a good deal or not, but over time, it became clear that this was a moneymaker for the players who knew about it and exploited it.

I learned about it from someone who swore me to secrecy. I had to promise not to write about it. I honored that while that situation was still in effect. Now that it’s been over for more than a year, I believe it’s okay to shine a little light on it.

Eventually, the casino figured out that a 4% theoretical for this game was inappropriate and changed it to about 1.6%. Now it costs you almost $5,000 to earn $5,000 in theoretical, and if you get “only” $3,500 back, it’s no bargain. So, knowledgeable players don’t play that game anymore.

I used a 4% figure. Actually, it was slightly different than that and it varied slightly from machine to machine. And it could be “fixed” by the casino at any time. So after we played, we went to talk to a host and asked what our theoretical was. If it was under $5,000 we played some more. We wanted to get the theoretical high enough so that we’d keep getting the offers.

The time it came back as a theoretical of $2,000 for the normal amount of play, players knew that this particular party was over. Disappointing, but all good things end eventually. Calls went all over the player grapevine, and within a few days most of the players who played this promotion were notified.

I’m not mentioning the name of the casino where this took place. There will be many readers of this blog who know whereof I speak. Should any of them choose to comment on this article, please leave the casino name unspoken.

 

 

Royal Flush 250 500 750 1000 4000
Straight Flush 50 100 150 200 250
4-of-a-Kind 25 50 75 100 125
Full House 9 18 27 36 45
Flush 6 12 18 24 30
Straight 4 8 12 16 20
3-of-a-Kind 3 6 9 12 15
Two Pair 2 4 6 8 10
Jacks or Better 1 2 3 4 5
Royal Flush 250 500 750 1000 4000
Straight Flush 50 100 150 200 250
4-of-a-Kind 25 50 75 100 125
Full House 9 18 27 36 45
Flush 5 10 15 20 25
Straight 4 8 12 16 20
3-of-a-Kind 3 6 9 12 15
Two Pair 2 4 6 8 10
Jacks or Better 1 2 3 4 5

 

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Paying to Avoid Royal Flushes

Assume you are a 5-coin dollar player playing 9/6 Jacks or Better and are dealt 3♠ A♥ K♥ T♥ 5♥.  The only two plays to consider are holding three hearts to the royal flush and holding all four hearts.

If we check out EV, we find holding three hearts is worth $6.43 and holding four is worth $6.38. That nickel’s worth of EV has always been too much for me to ignore and I go for the royal every time.

BUT, I file as a professional player and get lots of W-2Gs. Let’s say you don’t get a lot of W-2Gs. In that case, each one that you do get has some serious tax consequences. What if you held the four hearts in order to prevent the W-2G?

Once every 1,081 times on average, AKT turns into a royal flush. If you gave up a nickel each of those 1,081 times and ended up getting one fewer royal flush, it would cost you $55 (rounding slightly).

This is probably not too high a price to pay because a $4,000 royal has far more than $55 worth of tax consequences.

AKT (and AQT and AJT) are the weakest 3-card royal flush draws for two separate reasons. First, the presence of the ace eliminates all straight flush possibilities and reduces straight possibilities. Second, the presence of a ten reduces the chances for a high pair.

If we compared the preceding hand to 3♦ A♣ K♣ J♣ 5♣, holding this 3-card royal flush is better than the 4-card flush by a little more than 17¢ and avoiding the $4,000 royal flush over 1,081 opportunities will cost you $185. That’s quite a bit more than the $55 we were talking about earlier.

Going for the flush from 3♥ K♠ Q♠ T♠ 5♠ costs us $683 over the 1,081 draws, and from 3♣ K♦ Q♦ J♦ 5♦, it sets you back $770. Finally, from 3♠ Q♥ J♥ T♥ 5♥ you’ll lose a whopping $1,095 over the 1,081 hands by going for the flush every time.

So where do you draw the line? I’m not sure. I go for the 3-card royal on all of these hands. You’re going to have to decide for yourself what avoiding a W-2G is worth.

Other factors: If it were a multiple point day and/or there was another juicy promotion which gave me a considerable advantage playing this game, I would be more inclined to go for the flush. After all, time is money and it could easily take 5-20 minutes to be paid.

If I were playing in a state where royals were penalized (say Mississippi which has a 3% non-refundable tax on W-2Gs), that would make going for the flush mandatory in our first example and a closer play in the others.

If I were playing near the limit of my bankroll — either actual or psychological — I would tend to go for the flush, which is a play with a much lower variance.

On the first hand, you get skunked about 70% of the time going for the royal and “only” 68% of the time going for the flush.  If I were someone for whom today’s score mattered, I might go for the flush.   I certainly don’t recommend that you worry about today’s score, but some players just can’t help themselves.

This wouldn’t happen to me because I don’t do this, but if you were picking up someone else’s free-play and a royal flush would be awkward and you insisted on playing dollars anyway because you were in a hurry, I would go for the flush every time on these hands.

There are other hands in this game and every other game where it could make sense to avoid the possibility of a royal flush if it could be done at a low cost. But you should look at them one-at-a-time BEFORE YOU PLAY so you know which “inferior” plays are cost-effective. Trying to figure it out at the machine is very difficult. It’s easy to over-compensate when you’re doing this without study beforehand.