Who wins is not all about attack and power....
If you read the rules, there is an amount of chance in every fight.
(copy from the rules page)
"In a round, it's the Attack (ATK) of the characters that represents the chances of winning. If your character has an Attack of 10 and your opponent has the Attack of 5, it means that you have 10 chances over 15 to win, versus only 5 over 15 for your opponent."
A card with 1 attack still has a 2% chance to win agianst a card with 50 attack.