Poker 4 Aces Royal Flush

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The chance of getting winning hands

By Henry Tamburin

One of the nice features of the Video Poker for Winners software program is that it will compute the probability of every winning hand for any video poker game. For example, the Table 1 shows the probability (or occurrence) for 9/6Jacks or Better.

If you glance at the table, you’ll see some interesting facts about 9/6 Jacks or Better.

  • You’ll hit a royal, on average, once in every 40,390 hands.
  • You are more likely to hit a full house than either a flush or straight.
  • Your chance of hitting a straight is nearly the same as a flush.
  • The reason you rarely hit a straight flush is because the odds are pretty steep. (Once in every 9,148 hands).
  • Getting a high pair (Jacks-Aces) is a fairly frequently event. It will occur roughly once in every five hands.

Suppose you are planning to play four hours of 9/6 Jacks or Better. How many four-of-a-kinds would you expect? Care to guess? Actually, you don’t have to guess. If you assume a leisurely pace of 600 hands per hour and use the occurrence data in the above table, you would arrive at six expected four-of-a-kinds on average. (If you end up losing money after your four hour session, one reason could be that you had less than six four-of-a-kinds.) I’ve calculated in Table 2 how many of each winning hand on average you can expect in every four-hour session, assuming 600 hands per hour, and I rounded up or down).

Usually, a video poker player will end up wining money in a four-hour session when he or she gets either a royal flush, straight flush, or more than six four-of-a-kinds. Losing sessions usually occur when you get more than 1,311“no win” hands. Here are some more interesting facts to ponder based on the above data:

Poker 4 aces royal flush gameAces

1.You lose more hands than you win when you play video poker. (In the above ex-ample of a typical four-hour session, you can expect to lose 1311 times for every 1091 times you win something).

2.Because you can expect more losing sessions than winning sessions when you play video poker, you can expect your bankroll to head south.

3.You will recoup your losses over time when you hit a royal flush.

4.Since a royal flush only occurs once in every 40,000 or so hands on average, you need patience and enough bankroll to sustain your play between one royal flush and the next one.

5.Playing 600 hands per hour, you can expect to get a royal flush once in every 60hours of play. That’s an average. Sometimes you’ll hit more than one royal in 60 hours of play and other times you will experience a “royal flush drought.” (That’s when it takes longer than 60 hours to hit a royal flush, which is why having enough bankroll is so important.)

4 Aces Poker Chips

Here’s another bit of information to ponder. It’s based on what video poker players frequently tell me; namely, that “they never seem to win playing a specific video poker game at Casino X but they win more times playing the same game at Casino Y. Based on this “recollection,” they incorrectly conclude that Casino Y must offer better odds at video poker than Casino X.” The facts are this: Casinos do not alter the odds in the above table for getting each winning poker hand (if they did and got caught, they could lose their gaming license).The only thing they can and often do is change the payoff odds for some of the winning hands (which is why you should always check the pay schedule on a video poker machine to be sure the game is paying the maximum amount for each winning hand, known as a full pay game). As I often tell students in my video poker classes, it doesn’t matter where you play a specific video poker game because the odds of get-ting any winning hand are the same regardless if the casino happens to be in Las Vegas, Atlantic City, the Midwest or even Timbuktu.

Bottom line: Unlike slot machines, casinos do not change the odds of getting winning hands in video poker machines (that randomly select the cards for every hand).

HOW WOULD YOU PLAY IT?

You are playing Jacks or Better and are dealt the following hand. How would you play it?

Normally you would keep a suited J-10 over an unsuited J-K but this hand also contains a 3 of hearts, which is a flush penalty card. This means if you discard the 3♥ (along with the 5 and King), your chances of getting a flush by holding the J-10 suited have been slightly reduced (because you’ve removed from play one of the flush cards when you discarded the 3). Therefore, the presence of the flush penalty card makes the Expected Value slightly greater for holding the unsuited J-K over the suited J-10. Remember: Hold suited J-10 over unsuited J-K except if there is a flush penalty card, in which case, hold the unsuited J-K.

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?

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.

RF Cards in Initial Five-Card HandChance of Hitting the Royal Flush

0

1 in 383,484

1

1 in 178,365

2

1 in 16,215

3

1 in 1,081

4

1 in 47

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?

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%.

HandContribution to Return
Royal Flush1.9807%
Straight Flush0.5465%
Four of a Kind5.9064%
Full House10.3610%
Flush6.6087%
Straight4.4917%
Three of a Kind22.3346%
Two Pair25.8558%
High Pair21.4585%
Total99.5439%

Poker 4 Aces Royal Flush Kit

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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Poker 4 Aces Royal Flush 2

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.