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This is a strategy guide for connoisseurs of video poker; you know who you are. You want to get the absolute maximum out of every session. When faced with a hand that could be played more than one way, it bothers you if you do not know which way is best. You want to know what kind of return you are getting on your gambling dollar, and which types of machines are the best to play.
The good news is that you can have confidence that, in playing video poker, you are playing the best game in the casino. Sometimes it takes a little searching, but you can always find casinos whose machines' return is at least 99.5% (when played optimally!). Sure, you can get that return from craps or blackjack, but those are games where the bet is essentially even money. There is no possibility of a single large score. Elsewhere in the casino, games that have large potential payout for a single bet compensate by increasing the average house cut. For example, the cut in Keno averages about 25%! Video poker has a jackpot possibility of at least 800:1 (4000 coins for 5 coins bet), yet has a house cut more in line with the 1:1 table games like craps. In fact, in some places in Nevada you can actually find machines that are in your favor when you play them optimally.
Before we start digging into the nuances of the various games, it is important to stress the two basic rules. First, ALWAYS PLAY FIVE COINS. Second, ONLY PLAY MACHINES WITH THE GOOD PAYOFFS. Five coins are necessary to enable the full royal flush jackpot; even though you only hit the jackpot on average once every 30,000 or 40,000 hands, it still pays enough to make this about 2.5% of your total return. Straight flushes, in contrast, account for only about 0.5% of your total return.
The second principle, only paying machines with the correct pay table, cannot be stressed too strongly. Some casinos will set the payoffs on certain hands lower than the standard pay; this can increase their total take by up to ten times what it would normally average for the same amount of play. Of course, there is the rub: they risk the amount of play falling off if players refuse to play the lower-paying machines. Video poker payouts are shown on the front of the machine. Better-paying machines usually pay equal or better in every single category than the lower-paying machines. Players that ignore the payout tables are the greedy casino's legitimate prey. Do not be one of them!
One final rule is less significant than the first two but still worth observing: ALWAYS JOIN A SLOT CLUB if the casino offers it. These clubs are marketing tools that the casinos use to build loyalty and to identify their best customers. In return, they offer prizes which generally amount to about 1/5th of a per cent of the amount you gamble (more if you think things like logo'd coffee mugs and tee shirts are worth the prices you see in the casino gift shop). If you are willing to spend an entire trip gambling at a single casino, you may find you have triggered their often secret threshold that makes you eligible for much more significant freebies, like free rooms and/or meals, on that trip or the next. However, never stick with a slot club if it leaves you gambling on an inferior machine—the percentages do not justify it.
One author (Dan Paymar) reports that the machines can be jumpered to deal unfairly, presumably for use in those jurisdictions that do not have Nevada's scruples. He reports he has observed machines that apparently cheat even in Nevada, specifically in the case of drawing one card to a four-card straight. He reports finding machines that are much more likely to return a card of the same rank as he discarded than mere chance alone would suggest. In other words, if he discarded a single four, he found he would draw another four about 50% of the time. This is wildly more than the true odds, which are 3 out of 47.
"That happens to me all the time," I can hear you say. I know; it seems like it happens to me all the time, too. But when I actually measure it carefully, the results are always consistent with the true odds. I think the explanation is that when you play video poker, especially when you play fast, you enter a zone where you simply do not notice the normal events. Only the unusual things catch your attention. So when I measure it, I never write down a result either way unless I have picked up the pencil before I drew the card. Thus, I am not unconsciously biasing the results to the event I am more likely to notice—receiving a card of the same rank—rather than to the normal event that may escape my notice. I figure that if I had not noticed that I was drawing to a straight ahead of time and picked up the pencil, I may not have noticed the normal result afterward. But if you have measured it carefully, and still found a cheating machine, I would be interested, send me a note.
How exactly do the machines shuffle the deck? Many sources report that the machine is "shuffling continuously" (spinning a random number generator?) while you are dropping coins in it. When you press "deal" or when you drop the fifth coin (I hope it is the latter if you are playing by my first principle above), the entire deck's shuffle is fixed. There is general agreement that the shuffle remains fixed no matter how much time you take to figure out your discard. This does not necessarily mean that you would have received the same cards regardless of your discard, however. The rumor is that some brands of machines have fixed a different "draw" card under each card in the hand. You get that card "underneath" when you discard, rather than picking your discard from the "top of the deck".
One author, "Keno Lil", reports that in International Gaming Technology (IGT) machines a chip is used to "shuffle the cards" rather than the microprocessor. She reports that chip performs 1000 shuffles per second. This seems very slow; even a software-based random number spin would run tens to hundreds of times faster. Yet, she is adamant about the "once per millisecond" figure.
The first thing you need to know is the best card in the deck is not the ace. (I am assuming a game without wild cards now.) The best card is the lowest card that will make a winning pair—a jack in the jacks-or-better game or a ten in the tens-or-better game. The reason is simply that the lower cards have more possible straights they can participate in. And, of course, a pair of aces pays no more than a pair of jacks. Failure to realize this leads to a very common error: many players know (or guess) that if they have an ace-high hand with two other high cards all of different suits, the best play is to save only two of the three cards. However, they then wrongly save the two highest cards. The best play is to save the two lowest cards. There is a greater chance of drawing a straight that way.
The old saying, "never draw to an inside straight," can also mislead the video poker player. In deuces wild, you always draw to an inside straight in preference to drawing five cards. And in jacks-or-better, there are certain inside straight hands (three or more high cards) where drawing to an inside straight is often the best play.
One other big difference from the table game is the importance of two- and three-card royal flushes, and three-card straight flushes. These hands are of no consequence in regular poker, but learning to recognize them and play them correctly is the key to expert video poker play. Unfortunately, the rules for playing them correctly cannot be summed up in a single sentence; the different hands differ significantly in value based on a lot of factors. I will explain my "gap method" for evaluating three-card straight flushes later, but value of the two-card royal flushes can be pretty much understood by just remembering the principle that aces are not particularly good cards. Thus, the ace-king is actually a pretty bad two-card royal flush. The lowly jack-ten is has many more straights (and, of course, straight flushes) it can be part of. However, unless you are playing one of those rare machines that pay on a pair of tens, the ten is a liability; you are better off with the queen-jack, where either card can pair up to make a winner. In jacks-or-better, the absolute worst two-card royal flush is an ace-ten. In fact, you never save it, except in those few machines with the 4700 (rather than 4000) coin royal flush jackpot, and then only when there is absolutely nothing else to save in your hand.
How important is it to play correctly? Most hands have only one obvious correct play. My calculations suggest that any person with a normal ability to recognize poker hands and normal table-poker intuition would not suffer by more than 1% over a person playing perfectly. Yet, if you read annual reports from the larger casinos and game manufacturers, you gain the impression that the machines return about 2% more than what they would if everyone played perfectly. It is certainly true that people play the machines with wild cards more poorly than those without. This is the only reason that wild card machines can be found that are actually in the player's favor when played optimally.
|Royal Flush||4000||1.98%||1 in 40390|
|Straight Flush||250||0.55%||1 in 9148|
|Four of a Kind||125||5.91%||1 in 423|
|Full House||45||10.36%||1 in 86|
|Flush||30||6.61%||1 in 90|
|Straight||20||4.49%||1 in 89|
|Three of a Kind||15||22.33%||1 in 13|
|Two Pair||10||25.86%||1 in 7|
|Jacks or Better||5||21.46%||1 in 4|
In addition to the payouts, the table above lists the percentage return due to each hand, and the expected frequency with which the hands hit (when playing the optimal strategy). You can also use them to make quick estimates of the expected return of other machines with altered pay tables; for example, see below.
I think the term gap is more evocative. Gaps are bad. (In contrast, you have to think twice about inside and outside. Is it better to be inside or outside? It is warmer inside. But I digress...) After all is said and done, though, the telling characteristic is the number of possible straights you could make with the cards you hold. A 6-7-8 can make three different straights (8 high, 9 high, and 10 high); add one gap and only two straights can be made; with two gaps only one straight can be made. If your mental model is that a zero-gap three-card straight flush is three times better than a two-gap one, you would not be far wrong. This brings up the only trickiness in using the gap method for evaluating straights: if you are near one end or the other of the card ranks, you have to count extra gaps. For example, an A-2-3 is equivalent to a two-gap three-card straight flush because it can only make one possible straight. If you find this confusing, you can probably ignore this subtlety without affecting your bottom line more than 1/10th of a per cent.
By a serendipitous chance, having a high card in a three-card straight flush almost exactly cancels out the disadvantage of a gap, because it greatly increases your chance of ending up with a high-card pair. Of course, this is only important in games like jacks-or-better where high pairs pay. Thus, in these games, when counting your gaps, you should subtract one for every high card in the three-card straight flush. For example, a J-9-8 should be figured as a zero gap hand, the jack cancelling the 10 gap. This greatly reduces the number of hands that need to be listed in the tables. It also explains the one rule-of-thumb that is true no matter what variation of machine you are playing: when faced with a choice of a two-card royal flush or a three-card straight flush which contains the two royal flush cards, it is always better to save the three cards.
In the wild card machines, you should ignore wild cards for the purposes of counting gaps. For example, a Joker-6-7-9 would be a four-card straight with one gap. In a game where deuces are wild, assume any straight with a deuce simply does not exist. For example, 3-4-5 should be counted as having two gaps, not zero as it would be in any other machine. The reason is that a middle straight can be satisfied both by the missing straight cards and by deuces. However, when a missing straight card is also the deuce, you do not want to count your chances twice. Ignoring them entirely is also not precisely correct, but is a good first-order approximation.
By the way, it is relatively easy to get a quick estimate of what a pay table variation will do to the net return of a game. Start with the payout table given above. Working out the 4700 royal flush example, you can notice that royal flushes account for 1.98% of the total return when the payout is 4000. Thus, when the payout is 4700, they should roughly contribute (4700/4000 * 1.98%) or 2.33%. ("Roughly" because in this case you can adjust your playing strategy slightly to pick up 1/100th(!) of a percent.) Thus this machine should pay at least 0.35% more than the standard machine—and it does.
On the other hand, the common "greedy casino" jacks-or-better variation is to change the payout of a full house to 40 and a flush to 25. These machines are called "5/8" machines as opposed to "6/9" machines; the names come from the flush/full house payoff for a single coin. 5/8 machines give 2% or more back to the casino and should be avoided.
Some 5/8 machines will offer a progressive jackpot on the royal flush, one that starts at 4000 but then increases slowly until some player hits it. While it is true that if the jackpot gets high enough it can offset the disadvantage of a 5/8 payoff, I avoid progressive machines as a matter of personal taste. Saying that a progressive is occasionally in your favor is like saying that the state lottery is occasionally in your favor; it is true, but it requires you to actually hit the big payoff to realize the advantage. Also, my strategy was calculated for the 6/9 payoff, so your return will be off by a fraction of a percent from the optimal return if you use it on these games.
A relatively new gimmick used on 5/8 machines to make them more attractive is "bonus poker"—offering higher payoffs for certain fours-of-a-kind. It seems to be working; these machines are popular. Avoid them. The "bonus" only slightly compensates for the big disadvantage of the 5/8. On the other hand, "double bonus" poker is a good machine; its return is 100.17%, if you can find the full payoff version. There is a discussion of Double Bonus below.
A rare variation of jacks-or-better is tens-or-better. These machines pay on a pair of tens as well. These are actually "5/6" machines, as the payoff for a flush is 25 and for a full house is 30. Nonetheless, he average return for optimal play is almost exactly the same as the jacks-or-better machines. Yet it seems casinos steer away from them, and the few that offer them are exceedingly proud of it. I suspect that the problem with tens-or-better, from the casinos' point of view, is that it is less susceptible to bad play than other machines. Even people who have no idea what they are doing can apparently get a reasonable return on these machines. Anyway, from your point of view as an expert player, tens-or-better is neither better nor worse than jacks-or-better and can be played when you are looking for a change of pace. I have made up a expert strategy sheet for tens-or-better.
However, tens-or-better has a lower variance than jacks-or-better. Variance is a mathematical quantity with an important practical consequence. A high variance game will be much more "streaky" than a low variance game. You will find yourself alternately plummeting, then being treated to a flurry of wins that put you back up ahead (we hope). This streakiness is a quality of a gambling game that some people like and others do not. If you like playing a high variance game, bring more money. For example, if I am playing jacks-or-better, I figure that $100 stake should last for as long a session as I am comfortable playing (which for me is three hours), even if I am relatively unlucky. If I am playing jokers wild (the highest variance), $200 seems to be the equivalent stake. And this is true even though the return on jokers wild is better than jacks-or-better.
Sometimes you will find machines that pay only 5 for two pair instead of the normal 10. This is a complete rip-off, and should be avoided at all costs. Two pair account for 25% of your total return, and cutting that in half gives an enormous 12% extra to the house, an amount that cannot be compensated for by increases to the payoffs of the rarer hands.
|Royal Flush||4000||1.95%||1 in 41112|
|Five of a Kind||1000||1.87%||1 in 10706|
|Wild Royal Flush||500||1.04%||1 in 9604|
|Straight Flush||250||2.87%||1 in 1739|
|Four of a Kind||100||17.11%||1 in 116|
|Full House||35||10.98%||1 in 63|
|Flush||25||7.79%||1 in 64|
|Straight||15||4.98%||1 in 60|
|Three of a Kind||10||26.79%||1 in 7|
|Two Pair||5||11.09%||1 in 9|
|Kings or Better||5||14.20%||1 in 7|
Almost every payout is less than jacks-or-better, and it has the dreaded 5 coin payout for two pair, and yet this machine returns 100.6% for optimal play. If you can find a royal flush payout of 4700, the return increases to 100.9%, the highest of any machine I have found but one. It is also the highest variance of any machine. You can expect big swings if you play jokers wild.
|Royal Flush||4000||1.77%||1 in 45281|
|Four Deuces||1000||4.07%||1 in 4909|
|Wild Royal Flush||125||4.49%||1 in 556|
|Five of a Kind||75||4.80%||1 in 312|
|Straight Flush||45||3.71%||1 in 242|
|Four of a Kind||25||32.47%||1 in 15|
|Full House||15||6.37%||1 in 47|
|Flush||10||3.33%||1 in 60|
|Straight||10||11.30%||1 in 17|
|Three of a Kind||5||28.45%||1 in 3|
The high payoff for four deuces acts as a mini-jackpot, one that you actually have a reasonable expectation of hitting in a weekend of play. The average return for deuces wild is also above 100%. It has a noticeably higher variance than jacks-or-better, but not quite as high as jokers wild. You will find the key to deuces wild is how often you hit four-of-a-kind. Four-of-a-kind accounts for about 1/3rd of your total return, yet you hit it on average only 1 in 15 hands. That means about one four-of-a-kind for every two rolls of quarters. If you get three, you will be soaring; if you get none, you will be plummeting. Neither outcome is that unusual.
Both of these variations reduce the bread-and-butter payoff of deuces wild, the four-of-a-kind payoff, from 25 to 20. Not surprisingly, this also turns out to be the technique used by the many rip-off variations of deuces wild. You might think that if you reduce the four-of-a-kind payoff, but increase the payoff of the "more likely" hands like flush and full house, the net return would have to increase. The fallacy is that with four wild cards the normal hand frequencies are greatly distorted. For example, fours-of-a-kind are five times more likely than full houses.
Another interesting machine type is the five wild machine, which adds
a joker to the four wild deuces. The net return on these machines is 99.0%,
which is rather low. However, the five wild machines have a very low variance.
Thus, if you like the thrill of the inflated hands of the other wild card
machines, but do not like their high variance, you might enjoy five wilds.
I have a
expert strategy sheet for five wilds.
|Royal Flush||4000||1.66%||1 in 48048|
|Four Aces||800||3.18%||1 in 5030|
|Straight Flush||250||0.56%||1 in 8841|
|Four of a Kind (5-K)||250||8.03%||1 in 622|
|Four of a Kind (2, 3, 4)||400||4.19%||1 in 1908|
|Full House||50||11.18%||1 in 89|
|Flush||35||10.46%||1 in 67|
|Straight||25||7.50%||1 in 67|
|Three of a Kind||15||21.65%||1 in 14|
|Two Pair||5||12.46%||1 in 8|
|Jacks or Better||5||19.23%||1 in 5|
|Loss||1 in 1.7|
If you were to simply play the normal Jacks-or-Better strategy on a Double Bonus machine, you would be giving up about one half of a percent back to the casino. I have an expert strategy sheet for Double Bonus that has the complete strategy. Here is a summary of some of the differences between it and Jacks-or-Better:
Actually, if you are mathematically inclined, it is usually fairly easy to estimate the minimum value of promotions like these. For example, take the sequential royal flush promotion. The number of different ways you can order five things is 5*4*3*3*1 or 120 ways, so there are 120 different royal flush orders. Two of these are sequential. Thus, 1 out of 60 royal flushes will gain you the 50,000 coins. Thus you could estimate that the royal flush payout is actually increased to (50000 + 4000*59) / 60 or 4767 coins. For any game, you can use my tables to look up how much of your total return is from the royal flush payoff, and increase that by 4767/4000. You will get a figure 0.3-0.4%.
But this is a minimum, because it assumes you do not adjust your playing strategy for the promotional payoff. Playing slightly differently will nudge up the return a bit. So how should you adapt your play? You can pretty much be guaranteed that radical departures from your normal play is not a good idea. However, you can sometimes "hand calculate" some minor modifications. Again using the sequential royal flush example, you can observe that if you have four royal flush cards in the right place, your chance of drawing the fifth is 1 out of 47. Thus this hand is worth 50000/47=1067 coins, not even counting all the chances at flushes, straights, etc. that you have. Thus, if you had a wild royal flush with deuces, worth 125 coins, discarding the single deuce should be a no-brainer if you could make a sequential royal flush.
If you have three of the royal flush cards in the right place, your chance of filling them in is 1 out of 47*46=2162. (You also have a 1 in 2162 chance of getting them in the other order, for a normal royal flush.) You conclude that the promotional payoff is worth 50000/2162=23 coins for this hand. Thus you would break a pat straight in jacks-or-better (20 coins) to draw for the sequential royal. It turns out you break up a flush (30 coins), too, but that is a close call.
But enough calculations. The point is that these casino promotions are are like slot clubs: they are worth looking for for the additional (albeit small) extra return they give. This is true even if you do not bother to change the way you play. However, if you are able to figure out some small adjustments to your play on your own; so much the better.
Over the years I have tried many formats for the strategy sheets and finally settled on a format that lists the hands in the order in which you should save them, together with visual examples to illustrate the hand and the discard. The examples are picked to illustrate the particularly problematic hands.
To save space, the hand names are abbreviated. These abbreviations should be obvious: RF for royal flush, SF for straight flush, 4K for four of a kind, FH for full house, FL for flush, ST for straight, 3K for three of a kind, 2P for two pair, 1P for one pair, and HC for a hand with only high cards. Incomplete straights and flushes are indicated by number: for example, 4FL is a four-card flush, 3SF is a three-card straight flush.
My abbreviation for a wild card is "w". Thus, a 1w3K is three of a kind that includes one wild card; in other words, it is a pair plus a wild card. A 2wST is a pat (five card) straight with two wild cards (which, of course, you will not find in the strategy sheets because you should never save it).
The strategies contain some simplifications, but on the whole they are accurate to within 1/100th of a per cent. If you use the strategies when playing my program, the program will occasionally correct your choice. You will notice that this is always happens on hands that are very close choices.
Again, this is on average. So how long would it take so you could reasonably expect the good luck and the bad luck to "average out". 10 hours of play? 20 hours? 100 hours? The true number is much larger. You should play enough hands so that you have a good chance that the frequency of royal flushes you have hit is close to the expected frequency. You should expect to play enough to hit on the order of 100 royal flushes, about 4,000,000 hands, about 4667 high-speed hours, about 582 full 8-hour days—a good two years of full-time gambling with occasional week-ends off.
So, if you think of playing video poker as a career I think you are missing the point. Video poker is recreation, and by learning to play correctly you can make it very inexpensive recreation. Or to be precise, you can make it so that the probability is that it will be inexpensive over the long haul.
I wish you the best of luck and I hope you make money over the short haul, too.