Here's a basic summary of what you'll find in the rulebook.
When comparing numbers there are four possibilities:
1. Hero defeating Evil Character (EC)
2. EC defeating Hero
3. Both defeating each other
4. Neither defeating each other
Let's say our Hero is 6/6 and our EC is 5/5.
We take the first number of the Hero (6--which we call strength) and compare that to the second number of the EC (5--which we call toughness). Because the strength is greater, the Hero is defeating the EC. Now we take the first number of the EC (5) and compare to the second number of the Hero (6). The 5 is not greater, therefore the EC is not defeating the Hero. The result is #1 from above.
If we flip the numbers and say the Hero is 5/5 and the EC is 6/6, we do the same thing and get result #2--EC defeating the Hero.
Now let's say the Hero is 7/3 and the EC is 10/3.
If we use the same comparison, we see that 7 beats 3 and 10 beats 3 so both characters are defeating the other--result #3.
Let's flip the numbers again and say the Hero is 3/7 and the EC is 3/10. We see that 3 is not defeating 10 and 3 is not defeating 7. Therefore neither character is defeating the other--result #4.
For determining initiative, if one character is defeating the other (and not being defeated), the player with the losing character gets initiative.
If both characters are defeating each other (which is called a mutual destruction), the player who did not play the last card gets initiative.
Likewise, if neither character is defeating the other (which is called a stalemate), again the player that did not play the card gets initiative.
After each time a card is played, you should do an "initiative check" to determine which character(s) are being defeated. If one or both sides has multiple characters and/or multiple enhancements, add up all the numbers and do the comparison.
