Radom walks theory is a well studied topic in mathematics and gives rise to explaining the basis for gambling.

Random walks always start at the origin in any dimension, and have an equal probability of moving in any direction. They move one step at a time. The "big" results are that they are recurrent in dimensions 1 and 2, but transient in dimension 3 and higher. This means random walks in 1 and 2 dimensional space will touch every point infinitely often with probability 1. While in dimensions 3 and higher they will not touch the same point twice with positive probability.

Gambling at a casino is similar to a random walk in one dimensional space. A player win moves the walk to the right, while the house winning moves it to the left. The probability of winning is not 1/2 in a casino game ( there is a minor drift toward the casino's favor ). Regardless the walk will still be recurrent, so you will eventually win as much money as you could imagine ( same is true about the casino ). 

The problem with gambling is a finite amount of money. Both the player and house must stop when they run out of money. Gamblers generally have limited resources, hence once the walk goes to far negative the gambling stops ( and all monies are lost ). The same is true for casino's, however it is understood that they have nearly unlimited financial capacity ( when compared to an individual gamblers ). Therefore random walk theory with allow the casino's to keep playing, but gamblers are more likely to fail.

One solution for gamblers would be to pool their money together.....essentially creating a gambling bank. However human trust issues would likely cause this solution to fail.