Take The Money And Run?

Editorial Staff | Posted on October 8, 2011 |

Some video poker players say that after hitting a royal flush, you should switch machines. But what’s the smart play?

By Henry Tamburin

The RNG (Random Number Generator) doesn’t track the number of royals it gives to players. It randomly selects the cards on each hand, regardless of what cards it selected on previous hands. The RNG has no “memory.”

Here’s an email I received from a reader…

“Please settle a dispute I’m having with my husband. I hit a royal flush, and after I received my hand pay, I continued to play on the same machine. My husband, however, insisted that I should switch machines because the likelihood of hitting another royal on the same machine is very low. I disagreed and stayed put. Who was right?”

Squabbles like this often occur when one (and sometimes both) parties don’t understand how video poker machines actually work. Before I answer the question, let me briefly review how a video poker machine deals cards.

Imagine if I handed you a deck of cards and said, “Let’s play some video poker. You deal.” You’d probably shuffle the deck and then randomly deal me five cards. You’d wait until I decided which cards I wanted to hold and which ones I wanted to discard.  Then you would place the discards to the side, and deal me the replacement cards from the 47 unplayed cards.

If I had a winning hand, you’d pay me off. If I lost, you’d collect my losing bet. After the hand was finished, you’d collect all 52 cards, shuffle them, and deal the next hand the same way.

Computer chips in video poker machines work the same way. They randomly deal cards on every hand from a 52-card deck (a 53-card deck is used in Joker Wild games), except they use virtual cards, and the random selection of each card for the initial five-card hand and for the replacement cards is done by a software program known as the random number generator (or RNG). It’s not necessary to understand how the RGN works; what is important to understand is that the RNG randomly selects the cards, meaning what you were dealt on previous hands has no bearing on what you will be dealt in future hands.

Based on this, we can state the following facts about video poker machines:

1. Every hand that you are dealt is from a shuffled 52-card deck, and each card in the deck has the same chance of being selected by the RGN.
2. The replacement cards are picked randomly from the 47 unplayed cards. This means it’s impossible to discard, say, a 6 of clubs, and have it pop up again as a replacement card. (Many players swear that a card they just discarded came back on the screen on the draw, but in reality this is impossible.)
3. Since every card in the 52-card deck has the same chance of being selected, the odds of ending up with any winning hand can be calculated with great accuracy. By way of an example, the table below shows the odds of getting each winning hand for 9/6 Jacks or Better, expressed in frequency of occurrence (this comes from www.vpgenius.com).
4. The frequency of getting a royal flush is roughly 1 in every 40,000 hands. This doesn’t mean that you should expect to get exactly one royal flush after playing exactly 40,000 hands. What it means is that after many cycles of 40,000 hands, you will average one royal per cycle.
5. As long as the cards are dealt randomly from a 52-card deck, the casino can’t alter the frequency (or odds) of hitting a royal flush (or any other winning hand) in a video poker machine. What the casinos can do is to change the amount you will be paid for a winning hand. This is why checking the pay schedule on video poker machines is so important.

9/6 Jacks or Better

Now, with these facts in hand, let’s go back and answer the question posed by the reader. Was her chance of hitting a royal on the same machine any worse after she just hit a royal flush? The answer is no. She had a 1 in 40,000 chance of hitting the first royal, and the same 1 in 40,000 chance of hitting the second royal on the same machine.

The RNG doesn’t track the number of royals it gives to players. It can’t adjust its random selection process. It randomly selects the cards on each hand, regardless of what cards it selected on previous hands. In other words, the RNG has no “memory.”

I’m going to share with you another real world video poker experience that happened to my wife Linda, because it ties in with the question posed by the reader. Linda recently encountered a “royal flush drought,” meaning she suffered through quite a long period without hitting a royal. In fact, the last royal she’d hit was way back on July 31, 2010 in a casino in Las Vegas. Now let’s fast forward, exactly one year, to July 31, 2011. Coincidentally, we were sitting side-by-side playing video poker in the same casino where she’d hit the royal flush a year earlier.

All of a sudden, Linda nudged me after she was dealt four cards to the royal flush. I wished her good luck, she hit the draw button, and up popped the card she needed for that long-awaited royal flush.

I keep a gambling log of all our playing sessions, and Linda had played roughly 122,000 hands since her last royal flush—meaning she’d played three royal flush cycles without hitting a royal flush during that year-long drought. (The probability of this happening is around 5%, which makes it unlikely, but not all that shocking.)

Anyway, after the slot attendants paid her for the royal, she continuing playing on the same machine. About an hour later, she was dealt another four-card royal flush, nudged me again, and bingo—she hit another royal flush. So for those players who believe you can’t hit a royal flush twice on the same machine in the same session, it can happen. Remember, what happened on previous hands has no bearing on what is going to happen with future hands.

Note: The facts in this article assume a random selection of cards from a 52-card deck on a Class III video poker machine. (Most machines in established casino destinations, such as Las Vegas and Atlantic City, have Class III machines rather than Class II.) However, in casinos on most Indian reservations and in some states (such as New York), the video poker machines are Class II, meaning the hand you are dealt is predetermined based on the results of a bingo or lottery game. I’ll discuss this distinction, and what it means to video poker players, in a future article.

Tamburin’s Tip Of the Month

You’re playing Double Double Bonus, where four aces and a kicker (i.e., 2, 3, or 4) pays 2,000 coins with maximum coins bet. You are dealt the following hand. How would you play it?

Most players would keep the three aces and the deuce kicker, hoping to draw another ace for the 2,000-coin payoff. However, this is a mistake. The play with the higher average expected value is to keep the three aces and draw two cards.

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