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. Sep 11, 2012 John noticed a $1 denomination ($5 for max play) video poker machine where the display read that the jackpot was $104,000 for a royal flush. If you don’t play video poker, just know that a normal payout for a royal on a $1 machine is $4,000. The progressives are reset at $4,000 and move up as the game is played. But I will grant you that saying that a royal flush occurs every 40,000 hands is leaving out an important phrase. Royal flushes do occur about once every 40,000 hands on the average or in the long run. Any set of 40,000 hands may contain 0, 1, 2 or any number of royal flushes. Rather have them over for a beer, pizza, and fun with your very own Royal Flush Skill Stop Slot Machine.Other features on this slot-play machine include a security key, reset switch, and optional ability level differentials. The easy to read working manual discusses each attribute and performance on your Slot Machines Game, and in case you.

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 Hand	Chance 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.)

Slot Machines Royal Flush

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%.

Hand	Contribution to Return
Royal Flush	1.9807%
Straight Flush	0.5465%
Four of a Kind	5.9064%
Full House	10.3610%
Flush	6.6087%
Straight	4.4917%
Three of a Kind	22.3346%
Two Pair	25.8558%
High Pair	21.4585%
Total	99.5439%

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

Tamburin’s Tip o

Slot Machine Royal Flush