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HOME > HI-ROLLER > Gaming Tips > Three Card Flushes

Three Card Flushes

6 May 2012

By Donald Catlin

When playing 9/6 Jacks or better Video Poker it is tempting to hold a three-card Flush. After all there are still ten suited cards in the deck so this seems like a reasonable play. Unless there is a possible Straight Flush draw, however, it is the wrong play. Even some hands that are possible Straight Flushes are not always worth holding; these have to be analyzed separately using proper 9/6 Jacks strategy. So let me show you by example that you should not hold three card Flushes in this game.

Consider the hand KC, JC, 7C, 8D, 4H. The following chart shows that holding the KJ is better than holding the KJ7.

Hand

Pay

KJ

Prod

KJ7

Prod

Zip

0

9,935

0

766

0

J or B

1

5,022

5,022

240

240

2 Pair

2

711

1,422

27

54

3K

3

281

843

9

27

Str.

4

126

504

0

0

Flsh.

6

118

708

45

270

Full

9

18

162

0

0

4 Kind

25

2

50

0

0

SF

50

1

50

0

0

Roy

*800

1

800

0

0

Totals

---

16,215

9,561

1,081

541

*Assumes 5 coins played

The third and fifth columns show the hand frequencies and the fourth and sixth columns show the number of coins returned to the player. The amount returned to the player per coin played is 9561/16215, or 0.5896, for the KJ and 541/1081, or 0.5467 for the KJ7.

Now one might reason that if there were no high cards in the flush then holding the three flush is better than getting a whole new hand. The following table shows that this isn't so. Consider the hand TC, 7C, 4C, 6D, 9H.

Hand

Pay

None

Prod

T74

Prod

Zip

0

1,178,068

0

976

0

J or B

1

241,680

241.680

24

24

2 Pair

2

71,802

143,604

27

54

3K

3

31,502

94,506

9

27

Str.

4

5,296

21,184

0

0

Flsh.

6

3,103

18,618

45

270

Full

9

2,124

19,116

0

0

4 Kind

25

344

8,600

0

0

SF

50

17

850

0

0

Roy

800

3

2,400

0

0

Totals

---

1,533,939

550,558

1,081

335

Getting a whole new hand has an expected return per coin played of 550558/1533939 or 0.3584. Holding the three flush yields a return per coin played of 335/1081 or 0.3469. One can infer from this example that when dealt a three flush with one high that one should hold the high card.

So when playing Video Poker, should you always discard a three Flush? Yes, if the game is 9/6 Jacks. However if you were playing 10/7 double Bonus Video Poker you should hold some three Flushes; a strategy table for the game will tell you when. The lesson here is that you should learn to play one game well and not infer strategy decisions from it for other games. Common sense I guess. See you next month.


Don Catlin can be reached at 711cat@comcast.net


This article is provided by the Frank Scoblete Network. Melissa A. Kaplan is the network's managing editor. If you would like to use this article on your website, please contact Casino City Press, the exclusive web syndication outlet for the Frank Scoblete Network. To contact Frank, please e-mail him at fscobe@optonline.net.

 
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

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Lottery Book: The Truth Behind the Numbers
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