Quiz: Two-Card Royal or ??

15 April 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.

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

Today’s quiz might be an easy one. Let’s see.

Here is today’s dealt hand: 4h, Ad, Th, Jh, 7s
• 4 of hearts – (4h)
• Ace of diamonds – (Ad)
• 10 of hearts – (Th)
• Jack of hearts – (Jh)
• 7 of spades – (7s)

Let us look at the options for a hold. Only two holds seem worthy:
1. Th, Jh – (Two-card royal flush – only one high card)
2. Ad, Jh – (Two unsuited high cards)

Choice 1 (Th, Jh) – this two-card royal flush can produce every paying hand.

Choice 2 (Ad, Jh) – this hold of two unsuited high cards can produce all of the paying hands except a royal flush, straight flush or flush.

Let us look at the returns from each of these holds along with an explanation of which winning hands play a part in the respective return.

1. Th, Jh:
Long-term return – 2.4206 for five credits bet.
• 16,215 possible final hands.
• 2,847 high pairs paying 1-for-1.
• 711 hands with two pairs paying 2-for-1.
• 281 three-of-a-kinds paying 3-for-1.
• 220 straights paying 4-for-1.
• 116 flushes paying 6-for-1.
• 18 full houses paying 9-for-1.
• 2 four-of-a-kinds paying 25-for-1.
• 3 straight flushes paying 50-for-1
• 1 royal flush paying 800-for-1.

2. Ad, Jh:
Long term return – 2.3716 for five credits bet.
• 16,215 possible final hands.
• 5,022 high pairs paying 1-for-1.
• 711 hands with two pairs paying 2-for-1.
• 281 three-of-a-kinds paying 3-for-1.
• 48 straights paying 4-for-1.
• 18 full houses paying 9-for-1.
• 2 four-of-a-kinds paying 25-for-1.

Explanations:

Hold 1 (Th, Jh) – this hold can produce all the winning hands including three straight flushes.

Hold 2 (Ad, Jh) – this hold can produce all of the winning hands except royal flush, straight flush and flush. This limits the return from the hold. Also, because the ace is one of the two high cards, there are many fewer straights possible.

This hold does produce about twice the number of high pairs as hold 1, however. That is not enough to compensate for the lack of royals, straight flushes and flushes, as well as the reduced number of straights.

The winner?

Hold 1 (Th, Jh) is the proper hold – by a small margin.

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