One method for randomly assigning 60 participants to three groups, ensuring each group has 20 participants, is to use a random number generator. Assign each participant a number from 1 to 60, then divide the numbers into three equal ranges (1-20, 21-40, 41-60). Finally, randomly assign each range to one of the three games, ensuring an equal distribution of participants per game. This ensures that each participant has an equal chance of being assigned to any of the three games.