Three Card Straight Flush versus Four Card Straight

19 November 2022

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.

Here is today’s dealt hand: 8d, 5c, 9s, Ts, 7s
• 8 of diamonds – (8d)
• 5 of clubs – (5c)
• 9 of spades – (9s)
• 10 of spades – (Ts)
• 7 of spades – (7s)

There are really only two apparent best choices of cards to hold:
1. 9s, Ts, 7s – (Three-card inside straight flush, one gap – no high cards)
2. 8d, 9s, Ts, 7s – (Four-card open straight – no high cards)

Choice 1 (9s, Ts, 7s) three cards of an inside straight flush can produce a straight flush, flush, straight, and more.

Choice 2 (8d, 9s, Ts, 7s) four cards of an open straight with no high cards can produce a straight and not much else.

Let’s 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. 9s, Ts, 7s: Long-term return – 2.5486 for five credits bet.
• 1,081 possible final hands.
• 24 high pairs paying 1-for-1.
• 27 two-pair hands paying 2-for-1.
• Nine three-of-a-kind hands paying 3-for-1.
• 22 straights paying 4-for-1.
• 43 flushes paying 6-for-1.
• Two straight flushes 250-for-1.

2. 8d, 9s, Ts, 7s Long term return – 3.4043 for five credits bet.
• 47 possible final hands.
• Eight straights paying 4-for-1.

Explanations

Hold 1 (9s, Ts, 7s) can produce all the paying hands on the pay schedule except a full house, a four-of-a-kind, or a royal flush.

Hold 2 (8d, 9s, Ts, 7s) can produce nothing other than a straight – yet the return is .85 of a credit higher than hold 1. How can this be?

Hold 1 has 1,081 possible outcomes. There are only 127 possible winners (11 percent) – 45 of them pay more than a straight, 22 pay the same, and 60 pay less.

Hold 2 has only 47 possible results with 8 of them winners (17 percent) – all of them pay 4-for-1.

The higher percentage of winning hands at four-for-1 is enough to outperform lower percentage of hands paying a range of amounts.

Hold 2 (8d, 9s, Ts, 7s) is the proper hold – by a decent amount.

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, 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