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Worlds of Design: Always Tell Me the Odds

If GMs (and game designers, and gamers) understand “the odds” they will be able to make better choices and understand why some things happen in their games - and some don’t.

Never tell me the odds!
--Han Solo (Star Wars)​

Most people don't understand odds and randomness in the most simple dimensions, especially when you're talking about dynamic odds.
--Keith S. Whyte. Executive Director. National Council on Problem Gambling​

We often hear about “the percentages” and “the odds” in sports. For example, the odds for the home team winning (regular season: NBA 59.9%, NFL 57.1, NHL 55.1, MLB 54.0, MLS soccer (where there are draws) home win ratio of 49.4 percent over a 15 year period, compared to just 26.5 percent away wins). Though game design does not require higher math, game designers need to know simple arithmetic and probability. There are some odds we can talk about in RPGs, as well, and about how people react to those odds.

The notion that it can be a "fair fight" in an RPG? 50/50? Nope.

How much is a fight biased toward the adventurers? Let’s consider the NCAA Basketball tournament. Let’s say that a team is so good, it can win 90% of its games against the better teams, the ones in the tournament. This is unlikely: how many teams have a season record as good as 27-3 (90%) though they’re playing weak as well as strong teams? When you’re playing the stronger teams, 90% is quite unlikely. But let’s use that anyway.

So what are the chances of winning the tournament (six games in a row) even with that 90% (beyond-likelihood) capability?

90%​
win 1 in a row​
81.00%​
win 2 in a row​
72.90%​
win 3 in a row​
65.61%​
win 4 in a row​
59.05%​
win 5 in a row​
53.14%​
win 6 in a row​

Even that most unlikely team that can win 90% of games against tournament-quality opposition, only has a 53.14% chance of winning the tournament. Even a team with a 99% win likelihood wins the six-game tournament only 94.15% of the time (“fail on a roll of 1 on d20").

(How is this calculated? You multiply, you don't add. So to win three games in a row, it’s 90% times 90% times 90%.)

This is why the “best team” often fails to win the tournament. This is why some pro sports play seven-game playoff series, in the hope that luck “evens out” and the better team will win.

Translate This into RPGs

Extrapolate that into RPG sessions with perhaps one big battle per session, or maybe more! Practically speaking, either you need really astute players willing to run away from almost any encounter, in order to avoid taking chances, or you need to arrange a huge bias in favor of the players in a typical encounter. Or they're going to lose and possibly die pretty soon.

Go back to the tournament example. If the players are 90% likely to win, after six encounters there will be around a 47% chance that they will have lost one of those encounters.

The whole notion of RPG combat as "sport", as something that's "fair", is nonsense in light of these calculations.

Playing Styles

Some play for "the rush", for glory, and like Han Solo don't want to know the odds before they do something. If you accommodate them, then the bias in favor of the players must be even greater, or you'll have dead characters in no time. (This brings up the question of "fudging" dice rolls in favor of characters, which I may address another time. Some GMs do it routinely, others never.)

Is it fun to play to survive, to “win”, instead of for glory? Depends on the person. It is for me, when I expand it to include survival for the entire group, not just my character(s). In contrast, in the late 70s I played in a game that was supposed to act as the stimulus for someone to write a story. I tried to do something "heroic". My character got dead.

Many gamers don't understand probability, and so over- (or under-) estimate their chances of success. Some don't understand the scope of the chances. 1 in a thousand vs 1 in a million is a massive difference, but people often don't see it that way. It's yet another case of perception not matching reality.

That's where we get those who don't understand odds, who think that anything (no matter how outlandish) ought to be possible once in 20 (a 20 on a d20) or at worst once in a hundred (100 on percentage dice). No, the chance of most anything happening in a given situation are astronomically against. (And "astronomically" is practically the same as "impossible".)

Recently I talked with a gamer who is very skeptical of probabilities, but doesn't understand them. He thought it was terribly unlikely that a player could roll five dice in a row and get at least a 4 on every roll. The chances, 50% to the fifth power, amount to better than 3%. For some reason he thought that rolling the dice successively rather than altogether made a difference - nope, what's come before has no bearing on what comes after, in odds. And what about five 1's in a row? That's 16.66% (a 1 on a d6) to the fifth, .000129 or .0129%. One tenth of one percent (one chance in a thousand) is .01%. So slightly better than one chance in a thousand. Rolling seven 1's in a row is about 3.5 chances in a million. Or perhaps more easily, rolling a 1 on every one of six 10-sided dice is a one-in-a-million chance.

To summarize: For designers, fudging the dice (or the quality of the opposition) is inevitable. For players, it helps to understand probabilities in games

Reference: James Ernest (Cheapass Games) - Probability for Game Designers | League of Gamemakers
 
Last edited by a moderator:
Lewis Pulsipher

Comments

Ulfgeir

Explorer
Plus, swashbucklers don't always succeed even in the movies - and as long as the consequences are entertaining, it's still good. Just watch the early part of the 1973 film of The Three Musketeers for examples.
Love that old movie. ;)
 

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CodeFlayer

Explorer
It is in my thoughts that often seemingly independent events are often the opposite. I have noticed that in the world of dubious undertakings, if it is well begun the odds of success seem to go up substantially. The only example I can think of is someone attempting to jump a canyon on a motorcycle. The quality of the take off seems to highly influence the odds of a good landing, but is no guarantee. A simple mechanic might be added to reflect this - if the first action is very successful (high roll), then perhaps it confers advantage on the next one in the event chain. I am a proponent of such dubious undertakings in RPGs - it is comedy gold!

In the matter of the chandelier, I was barely involved. :)
 


Livemike

Villager
It gets really bad when mechanics become opaque and improperly explained. The original skill challenges in 4e were like this. Markov chain probabilities are not obvious to most folk. It was obvious when one did the math that the original designers hadn't. And that's before the inclusion of auto-fail options in the scenario like the example SC had. The odds of success without the DM doing something 'off-book' were terrible.
All TTRPGs should have what the numbers mean explained, including but not limited to skill ratings, character stats and difficulty ratings/modifiers. That explaination has to include the probabilities of a character accomplishing something. RPGs are languages and the maths is part of the definition of characters, situations and objects.

Take the system I'm working on "Exceptional", what would it mean for a difficulty number to be 24? Well the "Roll Base" table describes what numbers characters should have for particular ability levels. An average person with a minimally trained skill has a base of 11 while someone with a good relevant stat and professional training has a base of 20. The difficulty table gives an approximate probabilities for characters of various levels of ability. Looking it up you see that DF 25 translates to about a 28% chance for Joe Average and 90% for the professional. So you actually know what DF 25 means. You know what having a skill total of 11 or 20 means. Because I put it all the tables so people understand what's going on.

If you just say "4 is a high skill" but don't explain what that means in terms of success chance you're not really translating the world into a language people understand. Players shouldn't have to do the math, firstly because most don't want to and secondly because the designer ought to have done it himself. If he hasn't then even he doesn't know what the world he's describing is like. If plate mail gives a +3 to damage resistance does that mean it's really good or marginal? If he hasn't had the math worked out he doesn't know. If he has then he should write down so we don't have to repeat the work.
 

Livemike

Villager
Sorry, that's unconstructive and antagonistic to me.

You might find that changing your uncompromising stand makes more DMs willing to have you as a player.
It's entirely constructive to say "Your homebrew class doesn't work mathematically.". DMs don't have the right to be sheilded from facts. It's not antagonistic to say that the DM made a mistake in changing the rules in some way. It would be different if it were a subjective thing, like how that particular fictional society works, there is no "mistake" there, just subjective difference. But giving players a less powerful class is screwing them over. If you created that class then it's your job to make it worthwhile. You didn't have to homebrew and a player shouldn't have to choose between keeping a character and being significantly weaker than the other PCs.
 

Livemike

Villager
I want to understand the motives for a thing in order to critique that thing. Thinking about dice pools, I can appreciate their tactile qualities - it's really pleasant to pick up a bunch of dice and roll them - and the way they push me toward an intuitive and approximate rather than analytical and exact idea of the odds. A long time ago, and ultimately unsuccessfully, I designed an RPG in which the dice represented spirits that players can use and exhaust; each having faces with unique numberings and additional game effects. There have of course been many other forays into this design space.

It seems like the purpose of dice pools might be exactly contrary to the assumptions of the OP, whose analysis appears built upon a notion that players should, and need to, know their odds. The question it makes me ask is, why? Why does it really matter that players know their odds? I could come back with a notion that they should not know their odds, but only when their chances are improved or worsened, and when they are stronger or weaker. I could even think that knowing the odds in any exact sense is a chimera.

Not that I am not defending any specific position here. I'm digging into when and why one might not want to know the odds. The OP offers a one-dimensional analysis of the subject, notwithstanding that I appreciate the thought and effort in writing, and that it has prompted an interesting discussion.
Yes they should know the odds, at least approximately and unless there's a factor the PCs are unaware of. If you don't know how likely a character is to be able to do something you don't really know that character. Imagine if you were given a level 1 ranger to play and there's an opportunity to track something or try something else. What is the chance you'll be able to successfully track? If you don't know you don't know if your character is at one with the forest or a noob who can barely follow a trail. The PC would know this. They know if they're capable of doing something. There might be circumstances where things are harder or easier than they appear but unless your character took "Dunning-Kreuger" as a disadvantage they should generally know how good they are. Otherwise every choice you make is a pure guess at what would be realistic in the circumstances, which isn't realistic. Mages know if they can cast a spell. Warriors know if they can do a headshot at 100 paces. Theives know if they can climb a wall. A player should be able to know it to, or he's not playing his character.
 

clearstream

Be just and fear not...
Yes they should know the odds, at least approximately and unless there's a factor the PCs are unaware of. If you don't know how likely a character is to be able to do something you don't really know that character.
I don't know how likely I am to do something, and yet I think I know myself at least as well as I know a character I am playing. On the other hand, our RPG world is kind of flattened - it is a simplified or precised version of reality - the numbers work as a kind of shorthand for the lived knowledge we of course have: I imagine that might be in the direction of your thought here? I feel like a DM can have divers ends, and those ends might not always call for precision.

Imagine if you were given a level 1 ranger to play and there's an opportunity to track something or try something else. What is the chance you'll be able to successfully track? If you don't know you don't know if your character is at one with the forest or a noob who can barely follow a trail. The PC would know this. They know if they're capable of doing something.
The ranger can know those things without knowing the exact numbers. They can know they are at one with the forest. They know they are capable of following the trail and - compared with others - very likely to do so. Dice pools can be good at suggesting skill level... simply, I roll more dice thus I am better.

There might be circumstances where things are harder or easier than they appear but unless your character took "Dunning-Kreuger" as a disadvantage they should generally know how good they are. Otherwise every choice you make is a pure guess at what would be realistic in the circumstances, which isn't realistic. Mages know if they can cast a spell. Warriors know if they can do a headshot at 100 paces. Theives know if they can climb a wall. A player should be able to know it to, or he's not playing his character.
Under circumstances, maybe you might be thinking of cases like contests or DCs where the target should be unknown, so things are harder or easier than they appear. A point I am making is that knowing you are good, and knowing the precise probability, really are separate concerns. In DragonQuest there was a spell - Whitefire - that even a great caster would have only a few percent chance of casting. On the other hand, a 90% chance of walking successfully is not really that good. These things are relative: knowing the numbers won't necessarily narrate that to you... or at least, is not the only means of doing so.
 

CapnZapp

Legend
It's entirely constructive to say "Your homebrew class doesn't work mathematically.". DMs don't have the right to be sheilded from facts. It's not antagonistic to say that the DM made a mistake in changing the rules in some way. It would be different if it were a subjective thing, like how that particular fictional society works, there is no "mistake" there, just subjective difference. But giving players a less powerful class is screwing them over. If you created that class then it's your job to make it worthwhile. You didn't have to homebrew and a player shouldn't have to choose between keeping a character and being significantly weaker than the other PCs.
I see no reason to rehash this issue.

Some GMs aren't as mathematically gifted as you might be, and besides, if I had a nickle for every time someone said "it doesn't work mathematically" when they meant "I can't get the powerups I want" I would probably be able to buy a coffee.
 

Hussar

Legend
I see no reason to rehash this issue.

Some GMs aren't as mathematically gifted as you might be, and besides, if I had a nickle for every time someone said "it doesn't work mathematically" when they meant "I can't get the powerups I want" I would probably be able to buy a coffee.
I would say that it's rather equally antagonistic to presume that the player is simply power gaming instead of honestly evaluating the math. Doubly so if the GM isn't as mathematically gifted.

Note, this little sidebar started with me telling an anecdote where I actually tracked the math for dozens of rounds of combat before the DM would accept that the math was off. As a player, it's a good idea to have a LOT of evidence on your side before talking to your DM, because, well, as @CapnZapp here nicely demonstrates, DM ego tends to be a much larger issue in these conversations than anyone's actual math abilities.
 

Fenris-77

Small God of the Dozens
Supporter
I would say that it's rather equally antagonistic to presume that the player is simply power gaming instead of honestly evaluating the math. Doubly so if the GM isn't as mathematically gifted.

Note, this little sidebar started with me telling an anecdote where I actually tracked the math for dozens of rounds of combat before the DM would accept that the math was off. As a player, it's a good idea to have a LOT of evidence on your side before talking to your DM, because, well, as @CapnZapp here nicely demonstrates, DM ego tends to be a much larger issue in these conversations than anyone's actual math abilities.
Is it not also pretty antagonistic to assume that DM ego is going to be a regular barrier to service? I'm not sure that's any more likely or common than the powergaming comment you're responding to, and that example is actually really common. Generally speaking, someone who is going to analyze the math underlying a class is doing so to see how 'powerful' it is. That's my experience anyway. Some of those people aren't making choices based on that power level (like you), but lots are.

I'll say this though. Anyone who writes a class and puts it into play without playtesting is definitely asking for trouble, one way or another.
 

Hussar

Legend
Is it not also pretty antagonistic to assume that DM ego is going to be a regular barrier to service? I'm not sure that's any more likely or common than the powergaming comment you're responding to, and that example is actually really common. Generally speaking, someone who is going to analyze the math underlying a class is doing so to see how 'powerful' it is. That's my experience anyway. Some of those people aren't making choices based on that power level (like you), but lots are.

I'll say this though. Anyone who writes a class and puts it into play without playtesting is definitely asking for trouble, one way or another.
That's pretty much the point I was trying to make. Ego on either side of the screen is a problem. If someone isn't very good at math, then, well, maybe homebrewing a class is a bad idea. But, if someone isn't very good at math AND they refuse to accept other people doing the math for them, well, that's just a recipe for disaster.

The whole point of analyzing the math is to determine if something is balanced or not.
 

Fenris-77

Small God of the Dozens
Supporter
That's pretty much the point I was trying to make. Ego on either side of the screen is a problem. If someone isn't very good at math, then, well, maybe homebrewing a class is a bad idea. But, if someone isn't very good at math AND they refuse to accept other people doing the math for them, well, that's just a recipe for disaster.

The whole point of analyzing the math is to determine if something is balanced or not.
That's fair, I wasn't quite sure from your post if that was the goal. My point about a certain kind of 'math-y' player stands though, some of those guys are all about optimization, and their critique of a homebrew class is going to be colored by their preoccupation with white room stats crunching and what the 'best' option is. We all know a guy or two like that.
 

Hussar

Legend
That's fair, I wasn't quite sure from your post if that was the goal. My point about a certain kind of 'math-y' player stands though, some of those guys are all about optimization, and their critique of a homebrew class is going to be colored by their preoccupation with white room stats crunching and what the 'best' option is. We all know a guy or two like that.
Oh, for sure. Honestly, the best solution I've found is, if you have to talk to your DM about the math of the game, spend some time actually gathering data from the game. If you think this character is over or under powered, either way, track it for a couple of sessions. That way you can show, rather than tell, which, as you say, tends to run into white room theory crafting territory.
 

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