There's two things odd about Mat's luck. He is very lucky at games of luck which are not necessarily connected to his role in the Pattern as taveren and he can hear the dice in his head when important events that ARE connected to his taveren role happen.

Regarding the second, we saw that all three taveren can get things to work their way (or the Pattern's way). But unlike Rand and Perrin whenever taveren effects are working through Mat he feels them like dice shaking in his head, a very unpleasant feeling. It should remind us of a faulty mechanism. For example a good car drives smoothly and quietly when you use it, a bad car on the other hand cough, and shakes whenever you want to drive with it. Similarly unlike Rand and Perrin's tavereness which operates smoothly and without a hitch with them hardly noticing that it's working, Mat's tavereness deafen him and shakes him to the bones whenever it's turned on.

As to the first, it looks like a perversion of his tavereness. Instead of working for the good of the Pattern it helps him in a more selfish way. Of course it still helps the pattern indirectly due to Mat's character but the way it works is a bit shady. It is unique to Mat and doesn't have any parallel in the lives of Rand and Perrin or even any of the historical taveren we hear about.


How do we explain these things, the faulty mechanism and the perversion of Mat's taverenness?

The unnatural luck at games of chance starts according to Mat after he was tainted by the Shadar Logoth dagger. We are supposed to link it with the saying about the Dark One's own luck. The Shadar Logoth taint is different than the DO's but the Shadar Logoth mantra was to use the same means that the Shadow uses to fight it because those are the most effective. Presumably they managed to duplicate this unnatural luck. It fits because both show a tendency for selfishness. Presumably then the Dagger's taint managed to pervert the workings of Mat's taveren powers (making them more selfish) and suppress his positive taveren powers (he only shows unusual luck that helps others after he is completely healed of the taint). When he was healed these skewering of his taveren nature remained since the Aes sedai didn't really heal him, only burned out the taint itself from him.

The second effect, that of hearing dice in his head is the result of the healing he received in Tar Valon. When he was healed the parts of him that were tainted were burned out of him. Instead of a whole man he became a tattered one. The alternate memory patches he got from the Finns didn't really help, they weren't parts of him and the people he received them from weren't taveren either. Thus his taveren nature had to work through his compromised life thread and so though still managing to work couldn't manage to do it flawlessly and without notice.