The Attacking Dialog with Expert Options appears when one of your navs attacks a pirate. You need to choose how aggressively you want to fight. If you want the fight to end in a tie, choose to attack Cautious. This will improve your odds of ending in a tie. If you don't want the fight to end in a tie then choose to defend Aggressive. This will improve your odds of the attack not ending in a tie. You CAN avoid the fight if you want to by pressing the Cancel button.
Cautious: Make Pirate Tired Button
Choose this if you don't like the odds of winning and instead you want to tire the pirate out so that another nav can finish him off. In the above example you have an excellent (90%) chance of a tie if you choose to defend cautious. Energy cost is 20.
Aggressive: Try to Capture Pirate Button
Choose this if you want a greater probability of the swordfight ending in a win or loss and you like the odds of you winning. In the above example you have a 60% chance of a tie if you choose to defend aggressive. Energy cost is 25.
The number at the top (71%) is the probability of you winning the swordfights that do not end in a tie.
The Combat column at the bottom stands for Combat Strength. Here is how Combat Strength is determined