So you wanna start a conversation. Let's examine this.
Conversations in Black Desert Online (BDO) function as one of the pinnacle interactions in the games knowledge database. Having successful conversations means you can unlock quest and rewards, etc from NPCs in the game. Each NPC actually has his or her own story and lore behind them.
So where do we start. When you approach an NPC with this possibility you will see something like this.
That middle button is the conversation button. It shows you the amount of energy needed to start the conversation over the amount of energy you currently have (not the maximum amount you can get).
The box to the left of the screen is the NPCs interest, e.g. what they want to talk about. This is your “deck” for that NPC for the conversation / knowledge game. If you have a series of “????????” here the NPC is not going to want to talk to you until you discover more about their interest.
At a certain point depending on how many items are in this list, the conversation button will become active. However, I strongly recommend trying to complete the interest list as much as possible in order to have the maximum chance at good conversations.
So how do you complete the list? It depends on what the interest is. Oddly if it's other NPCs like in this case merchants in this particular area, just find the merchants and talk to them, e.g. discover them. But the interest can be anything and that box on the left will tell you. It encourages exploration.
When you open your map you may even see '?' symbols. These symbols indicate a place where you can get knowledge. If you can't “discover” an NPC try learning more about the area around them and then coming back and see if they are interested in introducing themselves to you then.
Anyway, onward with the game. So let's say you have a full interest list here like mine, 17/17 in this example, and you have some stored up energy, it's time to “conversate”! Press the conversation button and you will get a screen like this.
Now on this screen is where the conversation game for any NPC is played. Keep in mind that each NPC has there own Zodiac sign like you. Apparently, according to Sam's research, if you share the same sign as an NPC they give you easier goals to achieve and gaining Amity with them is easier.
So what do you do here? Well on this “board game” you want to achieve the goals laid out before you at the top. “Talk freely” is one of the greatest ones because it essentially means you can do whatever the hell you want. Other times it can be things like “gain maximum favor of X” or “spark the interest 3 consecutive times”, etc.
Here, our goal is to gain some favor so let's try that. What you do is pretty straight forward once you understand that point. At the bottom of the screen are “cards” that represent the interest of this NPC, e.g. the box on the left earlier. Right clicking places these “cards” into nodes. Right clicking them on the nodes removes them.
Since our goal here is to get favor, we want to place the cards that give the higher amount of favor as described in their description on mouse-over. However, there is also an interest level on the cards, the lower the percentage the higher the chance for that card to fail. Try placing high interest cards first then low interest card later down the line, if not last, for best results. If you are trying to fail a conversation, turn the ship around and try the other way.
Once you successfully complete the goal of the conversation you will get this change on the scren and a break down of how much Amity you won in the round. But don't stop there if you don't need to. You can continue the conversation up to two times at the cost of no energy and if you successfully complete all three rounds, you not only get more Amity but returned a portion of your energy plus you're saving energy.
You want to do this most likely to unlock the rewards from the NPC which are again viewable here on the “board game” in this window. For a quick guide on these, “?” in boxes mean quests, “blue stuff” means lore or knowledge, and “red stuff” means buffs in exchange for energy, e.g. “Hi X I just made this new potion want to try it?”