Four of a Flush or Three of a Royal?

30 August 2025

By Jerry Stickman

You are playing a full-pay 9/6 Jacks or Better game with the maximum of five credits bet.

You are dealt the following hand:
- Ace of diamonds (Ad)
- King of diamonds (Kd)
- 10 of diamonds (Td)
- 5 of diamonds (5d)
- King of spades (Ks)

This hand is interesting as it contains several possibilities – including a sure winner. They are:
- High pair (Kd, Ks)
- Three cards of a royal flush (Ad, Kd, Td)
- Four cards of a flush (Ad, Kd, Td, 5d)

How would you play this hand?

Many gamblers would hold the three cards of the royal flush, desperately hoping for the thrill of a huge win. They may also reason that there is still a shot at a flush, a high pair or even a three-of-a-kind.

Others may choose to hold the four cards of a flush. Their logic being, a flush pays decently. Also, the odds of hitting the flush are much better than snagging the royal flush. Nine of the remaining 47 cards in the deck will complete the flush – about a one-in-five shot for a decent six-for-one payoff.

Still other players might be happy holding the sure thing – the pair of kings. They reason that it is a sure winner, plus there is the possibility of three-of-a-kind, a full house or even a four-of-a-kind.

How about you. What would you hold?

Here are the top returns that are possible from this hand:
- Holding the high pair returns 7.6827 credits for the 5 credits bet.
- Holding the pair of kings and any one of the other cards returns 7.0814 credits.
- Holding the four cards of a flush returns 6.2766 credits.
- Holding the three cards of a royal flush returns 6.1980 credits.

Holding the high pair not only guarantees that you get your bet back, but out of 16,215 possible results, these hands will occur:
- Jacks or better paying 5 credits – 11,559 times
- Two Pairs paying 10 credits – 2,592 times
- Three-of-a-kind paying 15 credits – 1,854 times
- Full house paying 45 credits – 165 times
- Four-of-a-kind paying 125 credits – 45 times

There is no logical reason a player would hold the two kings plus on additional garbage card, so the results of that hold are not shown here.

Holding the four cards of a flush has 47 possible results as follows:
- No winner paying 0 credits – 33 times
- Jacks or better paying five credits – 5 times
- Flush paying 30 credits – 9 times

Finally, holding the three cards of a royal flush will produce 1,081 different results as follows:
- No winner paying 0 credits – 795 times
- Jacks or better paying five credits – 207 times
- Two pairs paying 10 credits – 21 times
- Three-of-a-kind paying 15 credits – 7 times
- Straight paying 20 credits – 15 times
- Flush paying 30 credits – 35 times
- Royal flush paying 4,000 credits – one time (but what a glorious time)

Holding the pair of kings is right hold – by a decent margin. Even though there is no shot at a royal flush, the cumulative results of the other possible winning hands make it so.

How did you do?

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

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 and 888casino.com. 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