We've addressed this question many times, but it's a difficult concept to grasp and it keeps coming up in different forms. Note that different gambling jurisdictions have different requirements, so this answer applies to the machines you play in the major gambling areas, such as Nevada, Atlantic City, and Mississippi.
The answer is that video poker machines must be based on a random deal from a complete 52-card deck, 53 cards if there’s a joker. (See QoD 7/13/06 for a full discussion on the idea of "random").
This precludes a video poker machine from doing anything but dealing out random hands every round. Conceivably, VP machines could be programmed with "hot and cold cycles," but that would essentially constitute rigging the game: One player might come in at the beginning of a programmed down cycle and lose his shirt, while another player might come in at the beginning of an up cycle and win the moon.
Yes, this sometimes happens anyway, but since every hand is a function of a random deal, the cycles, too, are random functions of luck -- or what mathematicians refer to as "variance" or "fluctuation."
In the end, a machine gets to its specified rate with play volume, in accordance with its pay schedule.
Let’s take a 9/6 Jacks or Better schedule, the full-pay version of this game, with an expected return of 99.54%. (See QoD 5/14/06 for an explanation of 9/6.) The more hands you play, the closer the machine will get to returning $99.54 for every $100 you put through it. (Note that this assumes perfect play; imperfect play brings the expected return down to less than the quoted return percentage).
Now, compare that to the 8/5 version of Jacks or Better, with an expected return of 97.3%. The more hands you play, the closer the machine will get to returning $97.30 for every $100 put through assuming perfect play. Then there are the 7/5 version, with an expected return of 96.15%, and the 6/5 version, with an expected return of 95%.
This explains one of the attractions of video poker for the player: Simply by reading the pay schedule, which is posted on the face of every machine, you can determine what the return rates will be in the long term against perfect play. You can’t do that for slot machines.
So back to the original question, the machines in Nevada and similarly regulated jurisdictions are not programmed with streaks.
