I purchased this more for the GM Emulator features than the Roleplaying system. The main purpose of this system is to allow you to apply the tools in this book to play any RPG adventure without requiring a game master. This allows solitaire and cooperative play. The foundation is actually pretty simple system with two key parts: Yes/No table and two-word keyword system.
The Yes/No table can be used to present Yes/No questions to the system, with the chart providing a mechanism to determine the % chance of yes, no or exceptional yes/no. You roll percentile dice (1-100) to get the result. You ask questions of the system as you might ask a game master when you need more details of a setting or what's happening, such as "Is the market crowded?", "Do I find the gem on the dead goblin?", or "Is the weapons officer a traitor?" To provide a weight to favor the more likely answer, you determine how probable it should be for the answer to be Yes. For example, "Do I find the gem on the dead goblin?" might be unlikely if you have more powerful enemies that haven't been defeated and the gem is key to the story, or it could be very likely if you slayed the goblin in a dungeon where the type of gem is pretty common for the treasure the dungeon contains. You cross-reference this probability of being likely with a Chaos Factor, which begins at 5 on a scale of 1-9. The higher the Chaos Factor, the more likely are Yes and Exceptional Yes responses. This factor goes up or down between each "scene" of your adventure based on how chaotic you think the previous scene was.
The Yes/No table can also be used to determine % of a challenge succeeding based on the cross-reference of the skill of the character attempting the challenge with the difficulty of the obstacle or competing character. For example, if you want to determine if a Ninja succeeds in hitting a target with a shooting star, you would consider the Ninja's skill (likely Exceptional) with the difficulty of hitting the target (average for a target character with average dexterity). You then get a % chance of getting a Yes, No, Exceptional Yes, Exceptional No and roll percentile dice (1-100) to get the result. This is using the exact same table as above.
Finally, there is a two-word keyword system designed to provide you with a random two word combination to help stimulate (or "seed") your imagination to apply it to the current situation. You have a supporting table that can also determine the subject of the keywords, if applicable. For example, this can be used to generate a random event in a scenario when doubles are rolled on the percentile dice. The first roll would determine the subject, such as Player Character Favorable, and the next two rolls determining the two words from two different keyword tables that are used in combination. Each table has 100 different keywords. For example, you might produce a result of "Passion" and "Attention" from the two tables. So if you're a spy sneaking into a secret base and get a random event with "Player Character Favorable -> Passion Attention", it's up to you to apply it to the situation. In this case, I might say that nearby guards are chatting with a beautiful officer in the hallway that would allow me to sneak past them undetected.
The book contains more information about how you can apply this to your adventures, and it even uses this system to let you play a full RPG game without requiring any other RPG rules. Where the book really shines is in the way it demonstrates the use of the system in a variety of settings (Sci-Fi, dungeon, mystery, etc.). But if you already have a rule set that you like, such as Pathfinder, you can use the tools mentioned above to allow you to play your campaign without a dedicated game master (though one player or the group will have to provide interpretations on the results produced by the system, as well as when and how to apply the charts.
Why does this work so well? If you're just setting up the adventure without any guidance, you tend to direct the adventure along a particular path. Once you've set this process in motion, your mind will tend to propel forward in a particular direction. When you use the Mythic system, you interrupt your story at various points to determine whether the story proceeds as you initially design. When you get a No, Exceptional, or keyword response, you're forced to stop and reevaluate your story and might be forced to redirect the narrative path. That's where the surprise comes in.
The only problem I've had with this is that I haven't felt like the Chaos Factor has worked for me as intended. I've had several times when the Chaos Factor keeps dropping to the point where I can't get anything to happen. But I need to play around with this more, as I might need to be more proactive in making something happen, even if it's in a different direction.