Tag: probability

RPG-ology #23: Nonrandom Thought

This is RPG-ology #23:  Nonrandom Thought, for October 2019.


A long time back in Faith and Gaming:  Mechanics we talked about Fortune, one of three methods of resolving outcomes in our games:  the use of dice, cards, and other randomizers to create unpredictable random outcomes.  We discussed then the question of how Christian faith relates to randomness.

Of course, the randomizers we use in our games are not entirely random.  That’s what we’re talking about now.

17th Security Forces Squadron Police Officer, John Hernandez, practices approaching the scene of an active shooter during the tactical driving course at the shoot house on Goodfellow Air Force Base, Texas, Feb. 27, 2019. Individuals practiced engaging targets while operating a vehicle and navigating through multiple advanced driving courses. (U.S. Air Force photo by Senior Airman Seraiah Hines/Released)

As I was musing on probabilities, I read a headline that stated that there was a drive-by shooting in a nearby town.  I’m sure that the town would like to think of itself as a city—it happens to have the largest geographical area of any municipality in the state, and I am told that police in our county seat jokingly refer to their law enforcement division as “the real police,” but it is largely rural space save for a long developed commercial district along three or four crossing roads.  The headline surprised me, and got me wondering about the probabilities of being killed in a drive-by shooting.  It appears that there are hundreds every year in the United States, so the probability of someone being killed in such a shooting on any given day is near one hundred percent—but the probability that it would be any specific individual is negligible, something that could not reasonably be anticipated.

Still, I doubt anyone would argue if I suggested that the probability of being killed in a drive-by shooting is significantly higher in sections of Chicago than it is in the rural counties of New Jersey.  Such shootings may seem in one sense completely random, but they aren’t completely random.

That is our objective when we design fortune mechanics for our games:  attempt to reflect the probabilities of any particular outcome.  It is not particularly likely that a character would be killed in a drive-by shooting, but if we have that in our games we want it to be something that might happen in our cities and probably won’t happen in our towns.  On our “wandering monster” tables, dragons are very rare and orcs rather common, because we envision our fantasy worlds as overrun by orcs but containing relatively few reclusive dragons.  In some situations we achieve that by “curves”—the roll of three six-sided dice to generate character abilities in most versions of Dungeons & Dragons is a solid example.  One character in two hundred sixteen will roll a natural 18 strength; a like number will roll a 3.  One out of seventy-two will roll a 17, and a similar number a 4.  Most characters will roll more or less ordinary strength, between 8 and 13, just as most people have average strength.  The “randomness” is structured.

So, too, in combat, in most games there is a value that hits and a value that misses, and a range of values between the two for which how good the two combatants are, one at offense and the other at defense, determines which ones hit and which ones miss.  There is randomness—you can always roll a miss no matter who you are—but it is controlled.

So how do you do that?  This column can barely begin to scratch the surface of such discussions.  The primer in Appendix 3:  Basic Dicing Curves in Multiverser:  Referee’s Rules is eleven pages long.  There are a lot of ways to use dice to create different kinds of outcomes, and some of them are considerably more difficult to calculate than others.  However, the calculation process is part of the game design process:  you need to work out how your probabilities are falling.  This will at least get you asking the right questions, and in today’s world once you’ve asked the question you can find the answer somewhere.

Probably.


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Next article:  An Amusing Dungeon.

RPG-ology #17: With the Odds

This is RPG-ology #17:  With the Odds, for April 2019.


A few years ago I launched the mark Joseph “young” web log with post #1:  Probabilities and Solitaire, which talked about how to improve your success at that and other card games by considering the odds of any particular lay of the cards.  I do use those rules when I play the game, and this evening (by now probably a year ago) as I played I was in a situation in which the two black queens (with other cards descending from them) were atop the two right-hand piles, one atop five cards and the other atop four.  A red king appeared to the left, and I had to choose which queen to move.

Recalling the rule, I moved the queen from atop five cards, and continued play as the cards which were freed were one after another moved into other positions.  The fifth, the bottom card, was the other red king, and I immediately shifted the other black queen to open the other pile.  As I did so the phrase against the odds came to mind, which was in a sense true, as it was improbable that the red king would have been on the bottom of that pile given all the places it might have been—but my mind immediately corrected me that this was with the odds:  I had recognized that the red king was more likely to be in the pile with more concealed cards than the pile with fewer, and it in fact was.

Of course, it might not have been, but Damon Runyon said, “The race is not always to the swift nor the battle to the strong, but that’s the way to bet.”  If you know the odds, and you want to win, you act in accordance with your best chance of success.  Bridge players learn the odds of cards being one way or another, and play to the best chance to win.  Knowing the odds of success, and knowing how to make them better, is the best tool for winning in most games.

It’s different with sports and casino betting.  The house sets the odds according to the probability of success, such that although you will probably lose betting on a longshot, if you win you get a better return on the bet.  That helps lure gamblers into “sucker bets” so they will lose a lot of money in small wagers on long odds, and the big payouts are a small portion of the total take and an incentive to others to take the chance.  It also helps cover the winners who bet on the favorite, as if it’s obvious who is going to win and he does win, there will be a lot of winning bets to cover.

Having recognized this many years ago, I devised ADR’s and Surv’s—calculations of the average damage per round an Advanced Dungeons & Dragons™ character could deliver and the number of attacks he could survive as comparative numbers.  It enabled my characters and the others in my party to identify which were their best attack forms in various situations, and let us build strategies on who could deliver the most damage and who could survive the longest in a fight.  I still use a spreadsheet version of the program today when I play or run that game, and while the calculation itself doesn’t port well even to other editions of the game, the factors may well help you recognize the strengths of your own characters in other games.

Even if you don’t care to stretch your math skills to calculating odds, you should try to get a genuine feel for them, to know when things are likely to fall in your favor, and when they are likely to fall against you.  If the odds favor a particular course of action, that’s the way to play; if the odds are against you, it’s time to retreat.

That seems obvious.  What is not quite so obvious is that in life we have to guess quite a bit about odds involving factors outside our knowledge.  In a game, we can quantify enough of the information to do the math, quite literally, and know the probable outcome.  Of course, probable outcomes are not guaranteed, but they are always more likely than improbable ones.


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Faith and Gaming: Mechanics

The following article was originally published in June 2001 on the Christian Gamers Guild’s website. The entire series remains available at its original URL.

When I was working my way back toward the fundamentals of our game experience last month, just before I reached the point of discussing social interaction I mentioned mechanics. Mechanics are the stuff that makes games work, that makes games games. In a sense, it is game mechanics that separate games from all other forms of social interaction. That is, a game has rules. It has objectives which are to be sought, methods which are legitimate approaches, and penalties for breach. Like a story, it has conflict and resolution; unlike a story, the conflict is defined and resolved by specific limited tools, the rules of the game, the mechanics.

And if our faith is to infiltrate our lives completely, we may need to ask ourselves how it affects our regard for the mechanics within games.

dice03

In discussing the mechanics specifically of role playing games, three broad concepts of resolution systems have been identified. These have been labeled drama, fortune, and karma. And if we understand these concepts aright, we realize that they are present in all games in one form or another. We also begin to see that each of these concepts has aspects which fit our faith well, but each has aspects which are problematic for our faith. We’ll look at them individually. Read more