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# Feeling Flushed?

9 February 2005

Unlike Straights, Flushes are much easier to contend with. You don't have to worry about whether it's inside or outside. You don't have to bother counting High Cards. That's not to say that a Flush with High Cards isn't worth more than a Flush without High Cards. It's just that it doesn't change its spot on our strategy table.

Unlike 4-Card Straights, 4-Card Flushes have an expected value (EV) GREATER than 1.0. This means that if you were to get one 4-Card Flush after another, you'd probably go home with more money than you arrived. The expected value for a 4-Card Flush is about 1.22. The irony is that there is actually no single 4-Card Flush that has this exact EV. Because this is the average of all 4-Card Flushes, the specific EV depends on the number of High Cards. A 4-Card Flush with four High Cards is actually a 4-Card Royal and its expected value is around 18.66. A 4-Card Flush with three High Cards would be played as a 3-Card Royal with an expected value of 1.41. So from this, we already learn that if you have a 4-Card Flush that contains a 3-Card Royal, go for the Royal Flush. The 4-Card Flush with 3 High Cards has an expected value of only 1.34, so this explains our decision.

A 4-Card Flush with 2 High Cards has an expected value of 1.28. If it has 1 High Card it will be 1.21, and with 0 High Cards, it is 1.15. If we look at the strategy table for full pay jacks or better, we'll find that there is nothing between 1.41 (the 3-Card Royal) and 0.87 (the 4-Card Straight with 3 High Cards), other than our 4-Card Flush. Because of this gap, there is no need for us to separate the 4-Card Flush by the number of High Cards for jacks or better.

So, what are some other key strategy points to know about the 4-Card Flush? First of all, we do not discard High Pairs to go for the Flush. The High Pair has an expected value of 1.54, so this error would be rather costly. We DO, however, discard ALL Low Pairs in favor of the 4-Card Flush. The Low Pair with an expected value of only 0.82 is an expected loser as compared to the 4-Card Flush, an expected winner.

The next key strategy point is that we NEVER, NEVER hold 3-Card Flushes in jacks or better. There are a handful of less common games (such as Power House Poker and Nevada Bonus Poker) where 3-Card Flushes are playable, but just barely ranking above a Razgu. We also NEVER play for a 3-Card Straight Flush when one is found within a 4-Card Flush. While many 3-Card Flushes ARE playable and frequently missed by beginner players, the expected values of these hands are about half of our 4-Card Flush.

Because Straights pay 4, Flushes pay 6 and Full Houses pay 9, you'd think that the frequency of these hands would be such that Straights occur much more frequently than Flushes and Full Houses, and that Flushes would occur much more frequently than the Full House. In reality, however, this simply isn't so. While the original inventors of video poker may have assumed this would be the case based on the pre-draw frequencies of hands, the computer analysis shows that these hands occur with roughly the same frequency. In fact, Full Houses will actually occur MORE often than the other two in jacks or better, by a small margin. When playing Expert Strategy, we can expect a Full House every 87 hands, while a Flush will occur every 91 hands and a Straight every 89 hands. These are, of course, long term averages. These numbers will flip-flop around a bit depending on the version of video poker you are playing, but in most games, they stay very close to one another.

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Elliot Frome

Elliot Frome is a 2nd generation gaming author and analyst. His father, Lenny Frome was considered one of the premier authors of Video Poker books. Titles include, Expert Video Poker for Las Vegas and Winning Strategies for Video Poker, which includes the strategy tables for 61 of the country’s most popular versions of Video Poker. Check out Compu-Flyers website at www.vpheaven.com, or drop Elliot an e-mail at compuflyers@prodigy.net.

www.vpheaven.com

#### Books by Elliot Frome:

Elliot Frome
Elliot Frome is a 2nd generation gaming author and analyst. His father, Lenny Frome was considered one of the premier authors of Video Poker books. Titles include, Expert Video Poker for Las Vegas and Winning Strategies for Video Poker, which includes the strategy tables for 61 of the country’s most popular versions of Video Poker. Check out Compu-Flyers website at www.vpheaven.com, or drop Elliot an e-mail at compuflyers@prodigy.net.

www.vpheaven.com