The human ability for random-sequence generation (RSG) is limited but improves in a competitive game environment with feedback. However, it remains unclear how random people can be during games and whether RSG during games can improve when explicitly informing people that they must be as random as possible to win the game. Nor is it known whether any such improvement in RSG transfers outside the game environment. To investigate this, we designed a pre/post intervention paradigm around a Rock-Paper-Scissors game followed by a questionnaire. During the game, we manipulated participants’ level of awareness of the computer’s strategy; they were either (a) not informed of the computer’s algorithm or (b) explicitly informed that the computer used patterns in their choice history against them, so they must be maximally random to win. Using a compressibility metric of randomness, our results demonstrate that human RSG can reach levels statistically indistinguishable from computer pseudo- random generators in a competitive-game setting. However, our results also suggest that human RSG cannot be further improved by explicitly informing participants that they need to be random to win. In addition, the higher RSG in the game setting does not transfer outside the game environment. Furthermore, we found that the underrepresentation of long repetitions of the same entry in the series explains up to 29% of the variability in human RSG, and we discuss what might make up the variance left unexplained.