Well if you look at trading, especially on the low timeframes like 1M or so, thats pretty much considered random. There are many people who are buying and selling at random times of the day that the charts on the small timeframes basically look completely random, if you move up to 5M or 1H charts then its different because those have levels or resistance or support.

In dice or other games, the bets are considered random because they are generated with a hashed seed and the result outside the house edge is considered completely random, each and every roll is independent of the last. So you can have someone who bets for 10 years and gets 40 wins in a row like the monkey but its basically out of luck why he won and everything was random.