Straight or Straight Flush?

12 March 2022

By Jerry Stickman

Today we have a question from a reader:

Hi Stickman,

Hope you're doing well.

Today I have two good questions for you.

1. 7s,10s, Js, Kh, Ad: Win Poker 6 says to hold the 7s,10s, Js.

2. 9c,10c, Kc, Qh, Ad: Win Poker 6 says to hold the 10c, Kc, Qh, Ad.

I don't understand why the answers are not consistent. I mean if I go for the straight flush in each sample, I'd have two gaps with only one high card. If I go for the inside straight in each sample, I'd have one gap with three high cards.

With that being the case, why aren't the answers consistent? I mean in one it says to go for the straight flush and in the other it says to go for the inside straight. This doesn't make sense to me. Am I missing something?

How would you play these hands, Jerry?

It'd be nice to get some feedback because I'm caught in a dilemma here. Thanks for taking the time to answer my questions. I'm looking forward to hearing from you.

I hope you're having a nice day and good luck in the casinos $$$!!!

Jody

Hi Jody,

Thanks for the good wishes. I am doing well, thank you.

On to your questions – which are very good, indeed. Your observations are accurate. Let’s see why there is a difference.

You didn’t tell me the pay table you were using, so I tried a few different options. After running your first hand through the jacks or better 9/6, 8/5, 8/6, and 9/5 pay tables, it appears the pay table you are using is either the 9/6 or the 8/6 since they both show holding the straight flush as the best hold.

Here are the top two holds from the four different pay tables for hand number one:

7s Ts Js Kh Ad

9/6 and 8/6:
7s Ts Js – Returns 2.6873 credits for five credits played, on average.
Ts Js Kh Ad – Returns 2.6596 credits for five credits played, on average.

9/5 and 8/5:
Ts Js Kh Ad – Returns 2.6596 credits.
7s Ts Js – Returns 2.4838 credits.

Here are is the same information for hand number two:
9c Tc Kc Qh Ad

9/6 and 8/6:
Tc Kc Qh Ad – 2.6596 credits.
9c Tc Kc – 2.6133 credits.

9/5 and 8/5:
Tc Kc Qh Ad – 2.6596 credits.
9c Tc Kc – 2.4098 credits.

Look at the returns for the games where a flush pays 6-for-1 versus those where a flush pays 5-for-1. You should see a pattern.

• Holding four cards of an inside straight with three high cards always returns the same average amount – regardless of the pay table.

• Holding three cards of a straight flush with two gaps and one high card returns a different average amount for each of the lines above.

• The returns for both hand number one and hand number two are very close on a x/6 pay table. However, the returns for the straight flush are significantly lower than for the inside straight on the x/5 pay tables.

Why is that?

The answer can be found by looking at which possible winning hands for each initial hand combine to produce the overall return.

Four cards of an open straight with three high cards can produce only 47 different hands. This is because there are 47 cards left in the deck and only one slot to use each one. They can only become one the following hands:

• 34 non-winners
• 9 jacks or better hands paying 1-for-1
• 4 straights paying 4-for-1

The pay table never changes for these specific winning hands; therefore, the average return is always the same regardless of the pay tables.

Three cards of a straight flush can produce 1,081 possible hands. Some of these 1,081 possible hands and pays are:

• 126 hands of jacks or better at 1-for-1
• 27 hands with two pairs at 2-for-1
• 9 hands with three of a kind at 3-for-1
• 44 hands with a flush at 6-for-1 or 5-for-1 depending on the pay table.
• 1 straight flush at 50-for-1

The lower pay for flushes explains why four cards of a straight is always the best hold on the x/5 pay tables.

Additionally, there is one winning hand for three cards of a straight flush hold the is different for the two hands – straights. Hand number one has 15 possible straights and hand number two has only 11.

How can that be? Both holds are three cards of a straight flush with two gaps and one high card, aren’t they?

Of course, they are. The difference is that in hand number one, you are not discarding any cards that could complete a straight (8 or 9), where in hand number two you are discarding a queen that could be used as one of the two cards needed to complete the straight (jack, queen).

That is the difference, Jody.

The combination of close returns for the two holds on x/6 pay tables and elimination of one of the possible cards to complete a straight in hand number two explains the seemingly weird best holds.

Hand number one has just enough extra return for a hold of three cards of a straight flush with two gaps and one high card to overcome a hold of four cards of an inside straight with three high cards when using a pay table that pays 6-for-1 for a flush.

Hope that makes sense to you.

And to answer your final question, Jody, I would play these hands exactly as the strategy shows.

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