The skinny on straight flushes
By Henry Tamburin
When was the last time you hit a straight flush? If you are like me, it’s probably been awhile. (Although shortly I’ll tell you a true story of an unbelievable adventure my wife had with straight flushes.)
So why is it that we never seem to hit a straight flush? The reason has to do with the frequency (or number of times) that we can expect to get it.
The following table summarizes the frequency for each hand in video poker. (Data from a table of Jackpot Frequencies on www.videopoker.com; frequencies vary based on the game played.) For example, you can expect to receive a straight flush as a final hand once in every 9,148 hands, on average. Most players play about 500 hands of video poker per hour (considered a leisurely pace); therefore, this means about once in every 18 hours of play you should expect to get a straight flush. (Note: This is an average over many 18 hours of play; sometimes you’ll get more than one straight flush, other times none.)
If you play about four hours of video poker on each of your casino visits, then on average, you should get a straight flush about once every five trips. In other words, a straight flush is a rather rare hand which is why it pays the second most of all winning hands on games that don’t pay a bonus for four-of-a-kind hands (e.g., for Jacks or Better, you’ll get paid 250 coins for five-coin wager; only the less frequent royal flush pays more).
Sometimes you will receive a four-card straight flush on the draw and you need one card to hit the straight flush. Other times you will be dealt perhaps three or two cards to the straight flush. The following table shows the odds of hitting that straight flush on the draw, depending on how many cards to the straight flush you are holding when you draw. (Note: Numbers rounded.)
*If you hold a four-card consecutive straight flush, you have a 1 in 24 chance of getting the fifth card you need for straight flush. If instead, you are holding a four-card straight flush with a gap, the odds are 1 in 47 to draw the one card you need for the straight flush.
Therefore, if you are lucky enough to be dealt 4♥ -5♥ -8♥ -7♥ -10♦ the odds of getting the straight flush are 1 in 47.
How would you play these hands that contain parts of a straight flush? (Assume a 9/6 Jacks or Better game.)
On the first hand, most players are tempted to hold the four-card consecutive straight flush (with its potential juicy 250-coin payout) rather than the holding the paying straight and the guaranteed 20- coin payout. The Expected Return (ER) for holding the four-card consecutive straight flush is 17.23. This means if you are a dollar player, you stand to lose $2.77 on average every time you hold the fourcard straight flush. The rule is: hold all paying straights over any (i.e., with or without gaps) four-card straight flush.
The second is an interesting hand because it contains a four-card straight flush (8-10-J-Q), a fourcard royal flush (10-J-Q-A), and a paying flush. The ER’s for each hold are below; the correct way to play this hand is to hold the four-card royal flush over a paying flush or four-card straight flush.
The last hand contains a four-card straight flush (with a gap) along with a high pair (Q’s). Again, you should always hold any (with or without a gap) four-card straight flush over a high pair.
Here’s another interesting fact about straight flushes. Of the 10 hands in, say, a Jacks or Better game that returns at least even money, the contribution of the straight flush toward the overall 99.54% return (9/6 Jacks or Better) is the lowest at only 0.55%. Therefore, in the short term if you are not lucky enough to get a straight flush, your overall return will drop by only 0.55%. (Meaning your bankroll doesn’t suffer as much as, say, not hitting a four-of-a-kind, which contributes 5.91%, nearly ten-times more, toward the overall return of the game.)
Finally, care to guess what the odds are for hitting a straight flush on the initial deal of the five cards? Is it:
- 1 in 32,000
- 1 in 55,000
- 1 in 72,000
The odds are actually 1 in 72,193; quite long but, hey, it can happen. (Skeptical? Then keep reading.)
My Spouse’s Story
The day after I wrote this column, my wife played a four-hour session of video poker with me. I got zero straight flushes; she managed to hit not one, not two, but three straight flushes, and two of them occurred on the deal. (That’s three straight flushes in roughly 2000 hands, two of them on the deal, which is way below what you would expect.) Bottom line: Sometimes you can get lucky and beat the odds in video poker.
Henry Tamburin, Ph.D. is a blackjack and video poker expert. He is the author of the Ultimate Guide to Blackjack (http://www.888casino.com/blog/casino-guides /blackjack/), editor of the Blackjack Insider e-Newsletter (www.bjinsider.com), lead instructor for the Golden Touch Blackjack course, and host of smartgaming.com. For a free three-month subscription to his blackjack newsletter, go to www.bjinsider.com/freetrial. To receive his free Casino Gambling Catalog, call 1-888-353-3234 or visit www.smartgaming.com.