Quiz: Two Card Royal Flush

19 August 2023

By Jerry Stickman

This article contains a video poker strategy quiz. The game is full-pay (9/6 – 9-for-1 full house, 6-for-1 flush) jacks or better.

The quiz assumes the maximum five credits is played. The maximum bet produces the highest long-term return because the royal flush pays 800-for-1 (4,000-for-5) rather than 250-for-1 when less than the maximum is bet.

Look at the dealt hand below and decide which card or cards you would hold. Then read on to see if you are right.

Note: The statistics shown are from “Video Poker for Winners.”

These quizzes will be posted periodically and will feature hands that have holds that produce very close results.

Here is today’s dealt hand: Kh, Th, 9d, 4h, 3c.
• King of hearts – (Kh)
• 10 of hearts – (Th)
• 9 of diamonds – (9d)
• 4 of hearts – (4h)
• 3 of clubs – (3c)

Three likely holds are:
1. Kh, Th, 4h – (Three-card flush)
2. Kh, Th, 9d – (Three-card straight)
3. Kh, Th – (Two-card royal flush)


Choice 1 (Kh, Th, 4h) – out of 1,081 possible results, a three-card flush can produce 45 flushes, nine three-of-a-kinds, 711 hands with two pairs, and 132 high pairs.

Choice 2 (Kh, Th, 9d) – out of 1,081 possible results, a three-card straight can produce 16 straights, nine three-of-a-kinds, 27 hands with two pairs, and 132 high pairs.

Choice 3 (Kh, Th) – out of 16,215 possible results, a two-card royal flush can produce one royal flush, one straight flush, two 4-of-a-kinds, 18 full houses, 118 flushes, 110 straights, 281 3-of-a-kinds, 711 hands with two pairs, and 2,955 high pairs.

Returns

Hold 1 (Kh, Th, 4h) – returns 2,2340 credits on average for 5 credits bet.

Hold 2 (Kh, Th, 9d) – returns 1.2812 credits on average for 5 credits bet.

Hold 3 (Kh, Th) – returns 2.2911 credits on average for 5 credits bet.

The winner?

The three-card straight is not even in the running. The two-card royal flush only returns 2.2911 credits. Did we overlook something?

We certainly did! Holding the lone king of hearts returns 2.2988 – slightly more than the two cards of a royal flush. This is a common problem for many players. It is very easy to grab two cards of a royal flush with one of them being a 10. Many times, it is preferable to hold the lone high card,

Did you play this hand correctly?

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