Tips for catching the 4-card flush

Feb 22, 2005 7:48 AM

A couple of weeks ago, I discussed how to handle the many variations of a 4-card straight. This week, I’ll tackle the 4-card flush. Unlike straights, flushes are easier to deal with. You don’t have to worry 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 them. It’s just that it doesn’t change its place on our strategy table.

Four-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 much more money than you arrived with. The expected value for a 4-card flush is about 1.22. 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 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, unless it is 10-Q-K-A or the like and would also be played as a 4-card royal. From this, we learn that if you have a 4-card flush that contains a 3-card royal, go for the royal.

A 4-card flush with two high cards has an expected value of 1.28. If it has one high card it will be 1.21, and with no high cards, it is 1.15. Because of this gap, there is no need to separate the 4-card flush by the number of high cards for jacks or better.

From looking at the strategy table, we can figure out how to play the 4-card flush when it overlaps with other hands. 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.

Another important strategy point is that we 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 four units, flushes pay six and full houses pay nine, 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.