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Dungeons and probability

  The dungeon master made a hat appear out of nowhere, flipped it with his fingers and gently let it rest on his head. Satisfied with the new fashion addition, he announced to the assembled group of adventurers, “It’s time I tell you the rules of this dungeon. They are simple enough that even an orc can manage”.

  The dungeon master gestured to the three doors in front of us and continued, "You must choose one of the three doors before you and step through. Once you have cleared the room, you will be brought back here, to this very room, and to a new set of doors. On and on, as many times as it takes—until you are either through to the final room…or you are dead”. He spontaneously broke into a tap dance routine at the end of that. I sighed, watching his theatrics that embraced every cliche for a villain imaginable.

  Dust interrupted the dancing figure. “So, we clear a room, come back here and a fresh set of doors will appear? We pick a new door and repeat this game endlessly, until the dungeon wears us down and takes our lives, or we stumble on to the final door by chance?”

  The dungeon master clapped his hands together and replied enthusiastically, “Yes, exactly. Couldn’t have explained it better myself. The objective is to find the door to the final room, the farthest room from where we stand, the journey's end”.

  He continued, “This dungeon is adversarial by nature. The challengers—that’s you—take the first step, trespassing into the dungeon grounds. The adversary—the master of the dungeon—sets the rules. The challenger then picks the room and the adversary populates it with denizens of the dungeon. The adversary and the challengers take turns to play this game. The adversary reacts to your actions, and you do the same in return. A dynamic game of choices and chance”.

  I raised my hand. “The three doors that are presented to us at each turn—how are they decided? If you decide where the doors take us, that makes it two moves in a turn for the ‘adversary’?”

  He squinted his eyes, studying me closely. “The doors are randomly decided”. That was the only explanation he offered.

  I poked him further for hints. “Do all the doors have equal probability to show up then? Surely, we wouldn’t stumble on to the final door in the very first try by pure chance? A lower probability for a door further down the path? Is that how it’s designed?”

  The dungeon master stayed silent. Though he had the appearance of a villain about to go on a long monologue, he managed to keep his lips sealed. The design was ours to figure out.

  Elric groaned. “Lady, I don’t know what on earth you two are talking about. Enough with all that talk, let’s pick a door and be done with it”. Of course, in a world rife with illiteracy, the concept of probability was too much for their thick skulls.

  The dungeon master cleared his throat to speak. “Patience. I am not done with the rules”. Once he was certain he had everyone’s attention, he continued, “You may split up into smaller groups if you can’t agree on a door. Once a door is picked, that door is no longer available for the other groups to pick during that round. Since you have three doors in front of you, that means no more than three groups are allowed. Once you split into smaller groups, you can never go back to a bigger group. You may split up further if needed”. He wanted us to split into smaller and smaller groups, didn't he? That would make it easier to kill us.

  The endless lecture on rules continued. “Needless to say, once you decide on a door and walk through it, you can not return here unless the room is cleared. All the doors in this dungeon only open in one direction. You can not take the same door to trace your steps back to this room. Your way back will be revealed only once you are through with a room”.

  “Too many rules for a dungeon. It’s hurting my head”, the half-orc complained.

  “To help you with your choice, I offer you the guide”, the dungeon master said, pointing to the black crystal ball on the pedestal. “The guide will recommend you a door, from all the doors in this room. Of course, it is up to you whether you wish to take that path”. A round of applause followed that declaration.

  “The guide isn’t free. It comes with a cost”, the dungeon master added. The applause quickly stopped. “To seek the services of the guide, you must give up something every time—a level or one of your skills. This is expected from everyone in a group that requests the guide’s help”, our adversary explained. The room erupted into protests.

  The dungeon master was clever. Not everyone would feel the same way about giving up their hard-earned levels or skills. Not everyone was in a position to do that. The disagreement would force us into smaller groups. The loss of levels would weaken those who agreed to the trade for a chance at getting closer to the destination. How much of a chance? The specifics were omitted. Did the dungeon master cheat? Were there hidden pitfalls that came with the rules? Was there really a clear path to the destination as he claimed, or were we just destined to go around in circles forever?

  The dungeon master was very careful with his choice of words, making sure there was no room for a different interpretation, or perhaps leaving room for one.

  “Of course, if you choose to give up a skill, the system points that were used to purchase them will be refunded once you exit the dungeon, but the skill will forever be lost to you. It will never come up for purchase again. If you choose to sacrifice a level, the system points and the attributes that came with it will be taken away from you and returned upon exiting the dungeon”. A small consolation, even an opportunity? I couldn’t use the dark-primer spells in the presence of humans. A chance to get a refund. I didn’t want to give up the intermediate tier spell, but my second spell tied to the dark primer—Shadow mist—was made redundant by the newly acquired spell Blinding radiance. They both served the same purpose.

  More importantly, if the dungeon master could seize our levels and claim our skills, the dungeon master had access to our systems. I looked at the man and his strange sense of fashion that stood out like a sore thumb. The music that played in the background was almost like a mash-up of a dozen songs from Earth. My system had access to Earth and its culture. All the pieces suddenly came together in my mind. The dungeon master was just another instance of the System, a child thread forked from the same parent thread that spawned my System, and everyone else’s. The adversary was an instance created in the image of the System, tasked to run a dungeon instead. It was a startling revelation.

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  “I have heard enough of these rules. I came here to slay the monsters, not to read a rule book”. Roth began to restlessly pace the length of the room.

  “Best to get this over with, before the dungeon tires us out. We will take the services of the guide”, the leader informed.

  “No, wait”, I said. “We still don’t know enough. Let’s not weaken ourselves further by surrendering our levels”.

  “Of course, you are opposed to the idea. You don’t have enough levels to begin with”, Elrick said.

  “No hard feelings, lass. A dungeon instance like this does not come very often. The adversary has truly outdone himself. Surely, there is some good loot at the end of something so elaborate”, Holt added. I could read between the lines—I wasn’t going to be part of their group, because I couldn’t afford to pay the guide.

  “The rewards at the end of the dungeon will also consider the levels and the skills that you gave up. A greater sacrifice opens up the path to greater rewards. Not to mention, all the rewards in this dungeon are tailored to your needs”, the dungeon master sweetened the deal further.

  The leader’s eyes went wide. He spoke, as his mind went through a thousand possibilities, “Can we give up more than a single level at once?”

  The dungeon master smiled. He had them just where he wanted. “Of course”, he replied. The dungeon master had dangled enough fortune and riches in front of them to make them lose any semblance of commonsense.

  “What are you thinking? Why would you willingly give up more levels than you have to”, Dust tried to bring them back to their senses.

  They were all driven mad by greed at this point. Holt’s face contorted with anger as he spat venom at the bespectacled young man, “Shut up. For all we know, the next door we open could be the final room and we have wasted our chance at a greater reward. Besides, the levels aren’t truly lost. We will get it back once we exit the dungeons”.

  “If you exit”, I mumbled.

  Elric put an arm around Dust and spoke, “I know why you are hesitant. You are almost in the same boat as her—not enough to pay the guide. You Joined the guild just as you met the level requirement for a class, didn’t you? Level ten, then? Maybe eleven. You are worried the System will take back your class if your level drops below ten”.

  Dust looked to the dungeon master questioningly to confirm if that was how things worked here, but got no response in return. Splitting the group down the middle was better for the dungeon master’s schemes, than having all four of them together. The dungeon master knew exactly how to drive a wedge between them.

  “Looks like you are stuck with the unclassed magic user. If I were you, I would ditch her and just go solo”. Elric snickered and stepped away, leaving Dust to his thoughts.

  The dungeon master’s booming voice echoed, “So, here you stand at the origin—three forks in the path. What will you choose?”

  “You haven’t made it clear exactly how the guide works”, I pointed out the obvious fact that nobody seemed to care about.

  The dungeon master glared at me. “I’m getting to that part”, he declared. Were you really?

  He explained, “The guide makes its recommendation based on two principles: one of its directives is to maximize the distance between the last room you triumphed over and the new doors presented to you—always opting for the farthest door. The second consideration is to pick out a door that progresses you in your path to your destination. Two voices bound together—one urging on to take the big leap of faith, while the other pleading to stay the course”.

  That was preposterous. “And if the two requirements are at odds with each other, which one does the guide prioritize then? Will it always pick a room that takes us closer to our goal, or could it send us to a distant room in the opposite direction?”

  “In such an event, when the two principles don’t align, the guide will make a random choice out of the two options”.

  That design wasn’t a mistake. It was deliberate. If the guide was truly meant to be helpful, then the magic crystal would first narrow it down to only those doors that take us closer towards the goal and then pick the farthest one out of it. No, the guide was a crystal ball with a split personality, constantly torn between choosing the big leap or the precise step, as it ate our levels and spat out a recommendation based on a coin toss.

  I was furious and I didn’t bother to hide it. “In short, the guide can lead us astray, just as easy as it can show us the way?”

  It was Holt who responded, coming to the dungeon master’s aid. “It is worth the risk. The rewards alone make it so. The alternative is to stumble in the dark”, he said. It was all about the rewards, wasn’t it?

  “Aye”, Elric shouted in agreement.

  “There is another way”, I said, pointing to the symbols engraved on the doors. “They have markings on them—a piece of the larger puzzle. We survive enough rounds, until the patterns start to make sense. We keep our levels and skills, even if that means we have to settle for a lesser reward. We prioritize our survival”.

  “And who will put the pieces of this puzzle together? Certainly not Roth”, he looked at the half-orc and chuckled, and then back at me. “You? Well, I don’t know you well enough to trust you with our lives, but I trust my party to survive this dungeon, even with some levels lost”.

  The dungeon master smiled triumphantly. He added, “If you need more incentive—in the event that two groups ask for the same door, the ties are also broken based on—”

  I cut him off, “Fine. I get it. You have done enough to convince them”. Not me. “Save your speech”.

  As the trio from Dragon claw debated among themselves, the dungeon master turned to face me. “I have been entrusted with a divine message to pass on to you, hero Alysa”. He knew I was a summoned hero! The trio weren’t paying attention, but Dust’s eyes widened in shock.

  The dungeon master came to stand right next to me and whispered in my ears, “The gods hope that the dungeon is to your satisfaction and not lacking in…depth”, he made sure to emphasize the last word, as he gave the most sinister smile.

  It was no coincidence. A reference to my conversation with the System yesterday, which could easily be construed as blasphemy against the gods. They were paying attention.

  I was in deep water now.

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