Im not sure if randomness is really absence of pattern. Randomness as in chaotic system can have pattern like fractals, but a small change in starting condition will have unpredictible effect on the outcome. In this view randomness is a product of complexity, as number of input factors and relationship between them. Which is why thermodynamics doesnt work in open systems because entropy dominate.

But even for gambling if the game is fair there should be a know distribution of events, its less and less random on longer period, the problem is having limited supply and not being able to play long enough to win the jackpot before you go bankrupt depending on the odds you take on a limited sequence.