How often should I complete certain hands?

7 May 2016

By Jerry Stickman

Those who have played any reasonable amount of video poker have noticed instances where they do not complete any four-of-a-kind hands when three of the quad are dealt, or complete any flushes when four are dealt, or any straights when four are dealt. At times it seems the machines may be rigged because time after time no flush is completed even though the player is dealt four to a flush over and over.

The observation and feeling is so prevalent that there are writers and pundits that claim a dearth of flushes signals a crooked machine.

Let’s take a look at the odds of completing a flush when four are dealt. Five cards of a 52-card deck have been dealt with four of them being one suit. There are 13 cards in each suit. That leaves nine cards of the same suit in the remaining 47 cards. So the odds of completing the flush are nine in 47 or just slightly worse than 1 in 5. On average you should complete the flush about once every five times you are dealt four of a flush.

How many times have you been dealt four of a straight flush? Probably not many, but you tend to remember each of them that didn’t fill.

What are the odds of completing a straight flush when dealt four? It depends on whether the four cards are “open” or “inside”. An open straight flush can be completed by adding a card on either end of the four. It does not have any gaps in the four cards. For example 2, 3, 4, and 5 of the same suit is open, where 2, 3, 5, and 6 of the same suit is inside. An ace, 2, 3, and 4 of the same suit would be inside since only the 5 will complete the straight flush.

There are two cards out of the remaining 47 that will complete the open straight flush, making the odds of completing it 2 in 47 or 1 in 23.5. So on average it will be completed once every 23.5 hands. That is a lot of disappointment before hitting a payday.

If the straight flush is of the inside variety (and, incidentally, all four of a royal flush hands are inside since there is only one card that will complete it), the odds of completing it are cut in half – only once every 47 hands on average will four of an inside straight flush be completed. No wonder there aren’t many straight flushes. It is rare to complete this hand even when you already have four – and you don’t get dealt four very often at all.

What about completing four-of-a-kind when you are dealt three-of-a-kind? This is somewhat similar to completing four of an open straight flush, but it plays out a little differently. Rather than having two cards to fill one slot, there is only one card that could fill two available slots. The odds are same; 2 out of 47 or once every 23.5 hands. Not a long shot, but not very common either.

Completing a straight when four of a straight are dealt works similar to completing a straight flush when four are dealt. If the four dealt cards form an open straight there are a total of eight cards the will complete the straight – four cards for the low side and four cards for the high side. The odds of completing an open straight are 8 in 47 or just slightly worse than one hand in six. In Jacks or Better, an inside straight is never held unless there are three high cards. In this case there are four cards out of 47 the will complete the hand which works out to 4 in 47 or just better than one hand in 12.

There is one more hand that occurs fairly frequently that I would like to cover – completing a full house when saving two pair. In this case there are four cards (two of each of the saved pairs) out of 47 that will complete a full house. So, the odds of completing a full house when saving two pair are four out of 47 or just a tad better than once in 12 hands. Even this fairly frequent completion can seem to take forever to complete. Twelve hands are a lot of two pair hands!

So, even though you are dealt four of a particular hand, it is still a relative long shot to complete it. Just because you remember incomplete hand after incomplete hand, doesn’t mean the machine is rigged or the video poker gods are out to get you. The math will prevail but it can take a while.

May all your wins be swift and large and all your losses slow and small.

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 stickmanjerry@aol.com