Mathematics Demands Easy Encounters!

[PriestZero]

Hello, I would like to make some mathematical observations about role-playing games that I have periodically mentioned before on the Internet in other newsgroups with enthusiastic feedback. I assert that mathematics itself demands that encounters in traditional role-playing games be easy. My argument for this is very simple. Suppose I were to create a typical 'dungeon' adventure for a game like D&D in which the adventurers are exterminating a stronghold occupied mostly by goblins and kobolds, and the whole complex, on three levels, has about thirty rooms with plans for twenty fighting encounters. This is a fairly large dungeon plan for a first level party, but please bear with me for the sake of arguement. Suppose I make every encounter difficult enough so that the adventurers have a 50-50 chance of winning without running away. Thus, there is standard difficulty. The problem comes in when people try to live through successive encounters. Mathematically speaking, if you can win the first battle with 50% confidence, and the second battle with 50% confidence, then you can survive the first two battles in succession with 25% confidence of not losing a player character. Another battle with 50% odds drops the confidence rate to 12.5% and another battle after that drops the rate to 6.25%. By the time you fight your fifth battle, only one quarter of the way through the maze, you only have a 3% chance of not losing any player characters! As you can see, the problem is that each battle has even odds, producing a sticky 50% difficulty. This difficulty accumulates in a multiplicative way: the more battles you fight, the lower your survival odds get. You essentially exponentiate one-half to the power of how many battles you want to survive to get your survivial odds. Thus, by going halfway through my suggested maze, you have a one in one thousand chance of survival and by going all the way through twenty encounters you have a one in a million chance of survival. I began this discussion pesuming we were talking about first level characters, but really, the discussion pertains to any series of battles in which you have fifty percent odds of victory. To survive such a dungeon, you have to rely on evading encounters, and you have to be certain that you can indeed get away from the pursuing monsters. People don't like to evade encounters, either - they like to fight and win each and every battle. Without cheating, you have a one in a million shot at winning twenty battles in a row when every battle has a 50-50 percent chance of victory.:laugh:
Hence, I claim that mathematics itself necessitates that encounters in typical role-playing games be easy. If you have played the computer game Diablo 2, then you can imagine what I am thinking of as an ideal game. You can defeat monsters in that game by the dozens, but gradually, they wear down your endurance and ordinary monsters begin to get your health points down to about a middle range. When your health is bad in Diablo, you have to avoid large encounters with many monsters, but if you have high health, you can defeat twenty monsters at a time. I think that instead of pen and paper games that check percentages, we should measure a fixed or random amount of points against a diminishing point total. So for example, we might say that a fighter has 50 stamina points for his sword swinging skill, and each time he fights and kills an Orc, he loses some stamina. When he is fully rested, he can cleave a dozen Orcs without a problem, but when he is tired, he risks becoming so fatigued that the monsters can kill him. I think this would be a more effective model for conventional role-playing games than giving you a set percentage chance to hit and avoid striking becase the law of averages from statistics means that the more probablity dice you roll the more they tend towards average results - and the more often you have to face even matched opponents, the more your survival odds tends to diminsih exponentially. Please let me know what you think, and good luck!

[GawainBS]

So, you win as long as you have enough stamina remaining? Sounds pretty boring and without any sense of accomplishment.
How would you handle individual combats? How would you measure the effectivenis of swings?
I think that HP, no matter how abstract they may be, do the job in the best possible way already.
While you are right iin your analysis, you seem to forget that in PC-gaming, we can manipulate chance, by saving & loading.

[Celos]

I'm not sure I see a problem here. I can't recall having ANY trouble with the difficulty of encounters in any decent RPG I've played (the one exception that comes to mind is Gothic III, but that was just due to poor coding .. I'm also not sure if it qualifies as 'decent').

The whole point of this thread seems to be moot, seeing as most RPGs already contain easy encounters. (As a side note, the whole 50-50 chance to win a fight would make for some boring gameplay. Imagine if every rat you encounter from the beginning of the game had an equal chance of killing you...) Most of the time you work your way up to the big baddies through hordes of monsters below your level, who have a sort of a decaying effect on your HP, much like the stamina you described.

Your take on the percentages seems to be correct IF you exclude a whole bunch of factors usually implemented in RPGs, or in any game for that matter, to combat the issue. To implement the multiplication of the confidences, one would have to guess that the encounters come in rapid succession of one another and therefore leave the player no time to use any of the potions, healing abilities or even resting (at some locations) at his disposal. This, however, is rarely the case.