Is there a name for this?

Even if I am just sitting within earshot of a slot machine, and I hear two successive bonus reels hit but not a third, I tend to hear the expectation of the third whether it hits or not.

Because I don't know the name if any for this effect, I'm calling it gambling rhythms.

Even when I try to ignore it, I hear them. Especially in long game playing.

Other than the mind trying to make sense of something random, is there an actual name for this, other than a known cause for a gambler's fallacy?

It's called "priming." There's a reason why you hear the two tones, often in a rising sequence, as the first two reels hit. It's to induce in your brain a logical expectation of the third and final tone. When that fails to happen, you become agitated, and your brain wants to repeat what you just did in the hope that the outcome will be just a little better; that you get that third tone. (in this case, your brain says, "Hey, maybe if I play that machine, I'll get the third tone!" Your brain, you must realize, is kind of an idiot--it's an ape brain trying to run software it was never designed for.)

It's a powerful concept in advertising and marketing--which is pretty much what those auditory signals from the slot machine are. For instance, if you want to sell more French wine in your supermarket, you play French music over the P.A. I'm sure you can think of a thousand different ways this tactic is used in casinos.

It's important to note that the auditory cues are aimed at passersby, NOT the player who is actually playing the machine at the time. That player is already being primed by the visual signal of BONUS--BONUS--???? You, walking by, hear it and get interested. (Though when I'm walking by and hear that bird-screech from those Buffalo machines, what I want to do is grab a baseball bat and silence the screeching.)

The little tricks and stratagems that the casino uses to get you to gamble (and to keep gambling) are masterworks of applied psychology. They help to explain why so many people gamble longer and for more money than they thought they would.

Someone on this forum told me that his friend couldn't stop playing slots. He was an AP. He was winning. But committed suicide. Is it possible that these machines have multiple subliminal messages that put one in withdrawal and depression if you stop?

Yes...but only for passers-by :)