Reader Disagreement with Video Poker Strategy Quiz: Two-card Royal Flush

30 September 2023

By Jerry Stickman

Note: The article in question “Quiz: Two Card Royal Flush” was posted 19 August, 2023

From Darren:

I have to disagree big time on this one.

Yes, dumping the 10 gives you a tiny bit higher outcome overall, but that's because now you're drawing four cards as opposed to three, so there are more chances of getting two Kings.

Two Kings is simply a break-even. It's meaningless if you're playing hundreds of hands over hours of time. No one in the world stops playing if they simply get Jacks or Better.

(Sure, there's a rare chance you'll get four Kings, but you could also potentially still do that holding the 10.)

But giving up the matching suit 10 means you now have no chance of a straight flush or a royal flush -- the hands worth playing for. These are hands that might make you a real winner.

Anyway, keep on keeping on!

Darren

Hi Darren,

This is not the first time that readers have disagreed with the answers to strategy quizzes. Your arguments seem to make sense. It is true that discarding the 10 of hearts, eliminates any chance of getting a straight flush or royal flush.

Remember, that the goal of using the strategy is to maximize the return of every hand that is dealt – not just try for hands that “make you a real winner.” Serious video poker players may decide to stop after a big hand, but more frequently, they use other criteria. They know that if they have an edge, they want to play all they can.

In order to calculate the best hold, strategy generation software calculates the number of possible hands that can be occur with the number of open slots (the number of discards). From there, the software determines the number of each winning hand that is possible and factors in the pays for those winning hands. The highest total amount is the best hold.

With that in mind, let’s look a little closer at the two holds in question – the king and 10 of hearts versus the lone king of hearts.

First, the king and 10 of hearts.

There are three open slots from the three discards. A total of 16,215 different three-card combinations can occur with the king and 10 being the fourth and fifth cards. These 16,215 possible hands produce the following:

Non-winners: 12,018 – a little over 74 percent of the total hands
Jacks or Better: 2,955
Two Pairs: 711
Three of a Kind: 281
Straight: 110
Flush: 118
Full House: 18
Four of a Kind: 2
Straight Flush: 1
Royal Flush: 1

Holding the lone king of hearts leaves four open slots. A total of 178.365 different four-card combinations can occur with the king being the fifth card. These 178,365 possible hands produce the following:

Non-winners: 119,047 – about 66.75 percent of the total hands
Jacks or Better: 45,456
Two Pairs: 8,874
Three of a Kind: 4,102
Straight: 336
Flush: 210
Full House: 288
Four of a Kind: 52
Straight Flush: 0
Royal Flush: 0

Now let us compare the two. When holding the lone king, it is true there are no straight flushes or royal flushes. But, there are seven percent more winning hands when holding the lone king.

When comparing the percentage of different winning hands for the two holds, the lone king outperforms the king / 10 on the following winning hands:

Jacks or better: 1.27 percent versus 0.91 percent.
Two pairs: 0.50 percent versus 0.44 percent.
Three of a kind: 0.34 percent versus 0.26 percent.
Full house: 0.073 percent versus 0.050 percent.
Four of a kind: 0.036 percent versus 0.015 percent.

When adding all of the average returns for each winning hand, holding the lone king returns 2.298825 credits for five credits played compared to the king / 10 average return of 2.291088 credit for five credits played.

The difference may seem insignificant at .007737 credits. It amounts to nearly one cent per hand on a quarter game ($1.25 per hand) and almost four cents per hand on a dollar game ($5 per hand). This is not “meaningless if you’re playing hundreds of hands over hours of time.

The strategy is not designed to trigger stopping points in play. It is designed to get the player the most from their play. When the player stops is up to the player. So is making the most from their play.

Getting the maximum return from every hand is the only way to do the best you can overall while playing video poker. Going for hands that “make you a real winner” may feel good at the time, but over time, your bankroll will suffer.

As always, may all your wins be swift and large, and your losses be slow and small.

Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack and video poker and advantage slot-machine play. He is a regular contributor to top gaming magazines. He authored the video poker section of "Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo, and Pai Gow Poker!" You can contact Jerry “Stickman” at stickmanjerryg@gmail.com