Ask the Slot Expert: Four-card royals happen frequently on video poker

One of the differences I've noticed between casual video poker players and more experienced players is that casual players are very interested in seeing what they almost got at the end of a hand. More experienced players just deal another hand after a losing hand, but casual players will say that they almost got four aces or a straight flush. And they always groan when they end up with four cards to a royal flush. "So close," they inevitably exclaim.

So close? Really? They are four-fifths of the way to a royal, but we draw to four-card royals quite frequently.

I never realized how frequently I ended up with a four-card royal until I was playing next to Henry Tamburin and heard him remark that he got another four-card royal. I started noting when I ended up with a four-card royal. In a few hours of play, I ended up with three or four four-card royals.

Jean Scott told me about a short-lived promotion from a number of years ago. This casino decided to pay something when players drew to a four-card royal. Apparently they hadn't done the math to calculate how frequently that happens. Jean said that players drove in from California to play in the promotion and the casino ended it not long after it started when they realized their mistake.

Let's calculate how many four-card royal hands there are in the deck. We'll include every hand, even if it is also a straight, straight flush or high pair.

There are five cards in a royal flush and we want to select four of them. In math terms, that's a combination of five things taken four at a time, C(5,4). The formula for combination is C(n,k) = n! / k!(n-k)!. Substituting in our values, we get 5!/4!(5-4)! or 5.

You probably already guessed that. We're choosing which one of the five cards in a royal flush we're not going to get, so the number of ways to do it must be five.

We have four cards in our hand. Now we have to choose the fifth card. There are 47 cards left in the deck that won't complete our royal flush. So, we have 5 times 47 or 235.

But wait, there's more. There are four suits in the deck, so we have to multiply by four to get 940 hands that are four-card royals. There are 2,598,960 five-card hands, so about 1 hand in 2765 is a four-card royal.

That's a lower number than I expected. Hmm. That number doesn't tell us how frequently we have a four-card royal at the end of a hand when the machine displays Game Over. It tells us how frequently we're dealt a four-card royal. We'll have many more four-card royals after we've drawn. If you doubt how valuable the ability to replace cards is, just look at the difference in payouts between a stud video poker paytable and a draw paytable. On a Three-Way Poker machine, a royal flush pays 4000 coins per coin bet on a dealt royal flush. On the five-card hand after the draw, the royal falls back to the usual 800 coins per coin bet.

Or consider this difference. We get a royal flush about once every 40,000 hands for most draw paytables. If we were not able to draw, we would get a royal once in 649,740 hands.

Calculating how frequently we have a four-card royal after the draw is much more difficult than on the deal and it depends on the strategy we're using. Maybe we can get a rough estimate with some observations.

I played 2,400 hands of 9/6 Jacks today. I had four four-card royals, one of which was dealt to me. Based on this small sample, it looks like we end with a four-card royal about once every 600 hands.

For comparison, we get four-of-a-kind about once every 423 hands on 9/6 Jacks. It's not surprising that whatever the casino paid for a four-card royal, it was paying it much more ferquently than it expected.

I'll continue refining this estimate as I play more.

Question: Why do I have to re-insert my players card for Boyd's Play 20 Get 10 promotion?

Answer: As part of its Young at Heart promotion for players 50 and over, Boyd gives a free gift after you earn a minimal number of points. One of those gifts is the Play 20 Get 10. You play $20 and then $10 in slot dollars (non-cashable credits) are added to your account.

You have to take out your card and re-insert it for this promotion and players are confused about why this is necessary.

Filed under Everything I Need to Know in Life I Learned from Star Trek: Do you remember in Star Trek II: The Wrath of Khan when Captain Kirk is reprogramming a command console on the Enterprise to use the prefix code for the Reliant, Khan's stolen starship, and he tells Lieutenant Saavik, "You have to learn why things work on a starship"?

To understand why there is the need to re-insert your card for this promotion, you need to learn why things work in a slot club.

To calculate how much you played and won or lost on a machine, the slot club system sends a message with the values of certain meters (like coin-in and coin-out) when you insert your players card. This is the Physical Card In message.

Your play isn't official until you pull your card out. This sends the Physical Card Out message, which includes the current values of those meters. The slot club software uses the differences in the values of the meters between the Card In and Card Out messages to calculate how much action you gave and how much you won or lost.

To claim the Play 20 Get 10 gift, you have to play the required number of points, then go to a kiosk to print a ticket, and then take the ticket to the club booth. A rep there loads the promotion onto your account.

First card pull: You have to pull out your card after you've earned the points so the slot club software on the central server will add the points to your daily total. This enables the Free Gift Choice menu option at the kiosk.

When you put your card in a machine after the promotion is on your account, a cryptic message about Play $20 Get $10 briefly appears on the card reader and a big button that says Slot Dollars appears next to the button you use to redeem points for credits.

You play more than the $20 required, but when you press the Slot Dollars button, nothing happens.

Remember, your play hasn't been officially recorded yet because you have not pulled out your card. The cryptic message merely indicates that the system will now track your play to award you the slot dollars once you have officially played $20.

Second card pull: You have to pull out your card to send a Physical Card out message so the central server can calculate that you have officially played at least $20. It then loads 10 slot dollars onto your account.

When you put your card in again, another cryptic message appears on the reader, but this message indicates that the slot dollars are available. When you press the Slot Dollars button now, the reader asks for your PIN and lets you download the slot dollars to your machine.

I frequently play with a group and we watch each other's machines while we go claim this offer. I always have a spare card on me, so I leave a card in the machine to indicate it is taken while I claim the offer. So, when I come back to the machine, I have to pull my card and re-insert it to get the system to start tracking my play for the promotion.

So, this is the way it goes for me and most of the people in my group. We earn a bunch of points, then pull out the card to have the play recorded and the Free Gift available at the kiosk. Insert the card because we're coming back to the machine and using a spare card at the kiosk and booth. After claiming gift, pull card and re-insert to get tracking play for promotion activated on our accounts. After playing at least $20, pull card and re-insert to get play recorded and slot dollars added to account.

Normal players probably just have one instance of pull and re-insert. They took their card out after earning enough points for the gift and used that card at the kiosk and booth. Then they inserted that card in the reader on the machine on which they're going to play to earn the slot dollars. For them, the confusing part is why they have to pull and re-insert their cards after they've played the $20.

To repeat, the reason your card has to be pulled after playing the $20 is to have the central slot club server record that you have played the $20 needed for the promotion and award the 10 slot dollars to your account. You can then put your card back in and the slot dollars will be available to be downloaded to your machine.