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What are the odds of getting a Royal Flush on a video poker game by holding two cards and drawing three to make the royal flush? From Laguna Niguel, California The number of ways to draw 3 cards out of the 47 remaining in the deck is combin (47,3)=16,215. One of those will be the three needed for a royal so the odds are 1 in 16,215. Let us assume that a hand of video poker takes 5 seconds to play. You would then be able to go through 12 hands every minute and 720 hands every hour. If you keep this up you would be expected to get your Royal Flush after playing straight for two days and 7 hours as the chance of hitting one is approximately 1 in 40,000 hands. Video poker may be a card game that cannot be played at a table, but this doesn’t mean the odds and probabilities involved and strategy that can be applied to them are any less important. Here is a runthrough of the probabilities and house edge in Video poker and tips and strategy that you should bear in mind when playing.

Video poker odds are very similar to those of regular draw poker in that the probability of receiving a particular hand is the same. Video poker is also like straight poker in that there are many variants found. So what are the main factors that determine whether or not you will walk away a winner? First, like in blackjack, you must play perfect strategy. The strategy you would employ for a jacks or better video poker machine is different from the strategy you would use for a deuces wild game, and so on. If you are already an avid player, and are interested in becoming better, try picking up a book that specifically deals with all the various video poker games found in casinos today.

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Payout Ratios Odds of Hands

The second main factor that figures into your expectation for winning in video poker is the game's payout schedule. This is the table you see on machines displaying how many credits they return based on credits bet and winning hand combination. Another important factor is the house edge in video poker. The return to player is one of the highest of all casino games. With the house edge very small to begin with, you can easily try to play for demo mode and see for yourself that the payouts are good opportunities. If you didn't already know, just like slot machines, some video poker games offer a much better return rate than others. However, unlike their one-armed counterparts, it is easy to spot which machines are high-paying thanks to the conveniently placed pay table displayed on each game.The chart below shows you what to look for.

Video Poker Odds Between Different Games

While browsing the video poker choices at a casino, either land based or online, be sure to keep an eye on the pay schedules. Here's what to look for: on the chart to the right, the numbers in the first column represent the payout rates for Full Houses and Flushes at one unit bet. If you see a Jacks or Better game that shows a Full House pays 9 units, and a Flush pays 6, then you know the return rate for that particular game is approximately 99.5%, making it a solid bet. Ideally, finding a machine that is 10/7 or 9/7 is the best bet, because these machines have a payout percentage over 100. Does that mean they actually pay out more than they take in? It's pretty unlikely. Casinos aren't in the business of giving out more money than they take in. Even with a mix of high and low-paying games, casino operators know the machines that return over 100% will still make money because not everyone who plays them is an expert. Just like in blackjack, only a small fraction of all players is skilled enough to play with a positive expectation of winning. Once you have mastered the basic strategy for a type of video poker, and find a high-paying machine, then you can expect to make money in the long run. What does this mean? It means that after about 50,000 hands, the odds dictate that you will have hit every possible hand combination, including the coveted royal flush. Surely, that sounds like a lot of hands, but this game can go very quickly, especially for experienced players. It is not uncommon for a skilled video poker player to turn in 750 hands an hour - and even more if that person is playing two machines at once. If the player keeps this blazing pace up for eight hours a day, it will take just over eight days for the player to reach an expected win of around 1,750 credits. You can see why some people are very serious about this game - because you really can win at it. The only drawbacks are the time commitment required, and the potential swings in bankroll. Also, just because the odds say you should get a royal flush every 40,390 hands doesn't mean it's guaranteed. You could go five times that many hands and never hit one, or get five in the first hundred hands. Both scenarios are improbable, yet quite possible. Such is the allure of chance. Such is the allure of video poker.

Video Poker Odds Of Royal Flush

Odds Of Hands (Jacks or Better)

The chart above represents the pay schedule of a 9/6 Jacks or Better game playing the maximum five unit bet. The reason you should always play the maximum five units because this bet is required to win the 4,000 credit (or max) jackpot. If you got a royal flush playing only one or two credits, the payout would not be proportionally equal, so there is a strong incentive to always play take the five unit bet. If five credits per hand is too steep for your bankroll, there should be plenty of .25 credit machines for you to play. Online casinos always offer bets in multiple denominations, generally having a range that includes .25, .50, 1, 2, 5, and sometimes even higher credit betting units.

From studying the Jacks or Better payout odds table, you may notice an inequality between the true odds and payouts of certain hands. Despite the fact that a full house is more likely to happen (1 in 86) than a flush or a straight, it has a larger payout. This goes against the grain in that the rest of the schedule is set up to reward hands that are less likely with higher payouts. Why is this? Again, game makers have slightly adjusted the payouts, but in this case it actually favors the player. In terms of payout percentages, there is a variety among video poker machines just like there is with slots. Remember, the lower-paying 8/5 video pokers are likely to be more common. Many land based casinos don't even feature the 9/6 variety. And, you definitely won't see any at convenience gambling locations such as bars, strip clubs, or airports. So be choosy. It's what will give you the positive expectation to win and what will make playing more fun.

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The ins and outs of that most elusive of hands

By Henry Tamburin

I get many questions about a royal flush in video poker. That’s not too surprising since the royal flush is the premier hand that all video poker players dream (and hope) of getting. Here’s a sample of questions and my responses.

Q: I’ve been playing video poker several times a week for over a year. You keep saying that a royal flush occurs once in every 40,000 hands yet I still haven’t gotten a royal. What gives?

Firstly, I never wrote that you could expect one royal flush after playing 40,000 hands (or one cycle). What I wrote was, “On average, you will hit a royal flush once in every 40,000 hands.” The word “average” means a whole bunch of sets of 40,000 hands. In other words, in any given set of 40,000 hands, you could hit more than one royal flush or, heaven forbid, possibly no royals. In fact, you have a 36.8% chance that you won’t get a royal in one cycle (40,000 hands), and a 13.5% chance after two cycles (80,000 hands). Ouch! Therefore, the fact that you went over a year without a royal is statistically possible.

Q: How come every time I need one card for a royal flush, it never shows up, but that exact card that I needed always seems to show up on the very next hand?

That’s because you have “selective memory.” The computer program in the video poker machine that randomly selects the cards for each hand doesn’t use the information from previous hands to determine which cards it will deal. Every hand is a random deal regardless of what cards appeared (or didn’t appear) on the previous hand.

Q: Over three years, I hit seven royal flushes in the same casino and none in two other casinos that I play regularly. I’m beginning to believe those casinos somehow tighten their video poker machines so players can’t get a royal.

You will average one royal flush per roughly every 40,000 hands at any casino. Casinos can’t change the odds of hitting a royal flush. (What they can do is change the payout … some casinos will pay less than 4,000 coins for a royal flush; therefore, always check to be sure that the payout for a five-coin royal flush is 4000 coins.) The bottom line is as long as the pay schedule is the same for a particular video poker game, the odds of getting a royal flush will be the same no matter where the machine is located (assuming a random deal).

Q: I’ve been dealt many three- and four-card royal flushes lately. What are the odds of this happening?

Playing Jacks or Better, you’ll experience the thrill of being dealt a four-card royal flush once in every 2,777 hands (roughly once every four hours on average). Once in every 92 hands, on average, you’ll be dealt a three-card royal flush (about 7-8 per hour). This is what makes video poker exciting; namely, that you’ll have several opportunities to draw for a royal flush even if the odds are somewhat long (see next question).

Q: When you hold three cards to the royal flush, what is the chance of getting the two cards that you need on the draw for a royal flush?

Video Poker Royal Flush Odds Explained

You have a one in 1,081 chance of getting the two cards you need for the royal flush. The following table shows the chance of hitting the royal flush on the draw when you hold x cards to the royal flush.

Q: If I’m dealt a three-card royal flush and a high pair in the same hand, why does the strategy say to hold the high pair when the royal flush pays so much more?

Video Poker Royal Flush Odds

You need to analyze all the possible winning hands that you could get when you hold a three-card royal flush vs. when you hold a high pair in the same hand. These calculations have already been done for you. For example, suppose your initial hand contains 10-J-Q of diamonds along with a queen of clubs. The expected return (ER) for holding the pair of queens is 7.6827 vs. 7.4098 for holding the three-card royal flush (this is for 9/6 Jacks or Better). In dollars and cents, you’d earn 27 cents more on average for a max coin wager on a dollar denomination machine by holding the high pair vs. the three-card royal flush in this example.

Q: My wife plays Jacks or Better. The other day she was a dealt a hand that contained a four-card straight flush with a gap and a three-card royal flush. She held the three-card royal flush. Was that the correct play?

I’m sorry to say it wasn’t. The correct play was to hold the four-card straight flush—even with a gap—over the three-card royal flush. (Tip: If your wife had a strategy card with her, she would have made the right play.)

Q: What are the odds of being dealt a royal flush in the initial hand?

The odds are one in 649,740 hands. You might think that’s close to impossible but it could happen. (This happened to me once while I was showing my father-in-law how to play a Triple Line video poker game in a Las Vegas casino, resulting in a royal flush on each line. How’s that for luck?)

Q: How much does the royal flush contribute to the 99.54% return for 9/6 Jacks or Better?

The royal flush contributes 1.9807% toward the overall 99.64% return. The following table summarizes the contribution of each winning hand toward the overall 99.54% return (for 9/6 Jacks or Better). When you don’t hit the royal or straight flush, the best return you can expect, even playing perfectly, is about 97%.

Got a video poker question? Send it to HTamburin@aol.com.

Tamburin’s Tip of the Month

You are playing NSU Deuces Wild. How would you play these hands that don’t contain a deuce?

In the top hand, your best play is to hold the consecutive three-card straight flush 6-7-8 (2.77 ER) over the four card straight 5-6-7-8 (2.55 ER). In the bottom hand, because the three-card straight flush has a gap (2.47 ER) your best play is to hold the consecutive four-card straight 4-5-6-7. When you play NSU Deuces Wild and your initial hand doesn’t contain a deuce, you should hold a consecutive three-card straight flush (5-6-7 through 9-10-J) over a consecutive four-card straight (from 4-5-6-7 to 10-J-Q-K), but the latter over a three-card straight flush with one or two gaps.

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Henry Tamburin is a blackjack and video poker expert. He is the host of the smartgaming.com website and the editor of the Blackjack Insider newsletter (for a free three-month subscription, visit www.bjinsider.com/freetrial). For a free copy of his Casino Gambling Catalog, which contains books, strategy cards, and software for video poker players, call toll free 1-888-353-3234, or visit the web store at smartgaming.com.