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.

Picture courtesy of Pixabay.​

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

 

[CapnZapp]

I see noone has mentioned the obligatory "dwarves in Runequest charging the enemy" remark.

 

[prosfilaes]

As for everything should be fought... that's a mentality I've tried to break from a lot of 3E and 4E players.

Is that fun for them? I think it would be much more fun to have someone discuss new expectations for this game, then kill my character for not playing by rules I had no reason to know.

They just heard about the dragon and assumed they were supposed to kill it.

That's a playstyle question. A lot of DMs would rather that then worry about spending all session trying to get the PCs to follow a plot hook and them discussing whether they should kill the dragon or maybe it's just plot color.

This is a failure of adventure design. If you're going to have a party run across something that's way beyond their power level, there should either be hints beforehand (warning them to plan appropriately to avoid or flee) or it should be set up in such a way as to allow the PCs to see the enemy before they can be seen. No one wants a TPK just because of a bad roll on a random encounter table or because they had no idea the cult had managed to summon a demon.

If you're complaining that

It is gerenally assumed by the party that every monster is somewhat appropriate for their current power level.

then every monster still is somewhat appropriate for their current power level. You're just demanding the players use a wider set of tactics. You can say that that is a failure of adventure design, but I think it's one encouraged when people are too free with "not every monster should be defeatable" and forget, or forget to mention, that "every monster must be solvable".

 

[Hussar]

I would take a more modest position:

most people don't actually understand how hard people find probabilities.

Fair enough. It's two sides of the same coin really. At the end of the day, a very large number of people don't understand probabilities and gut feelings are extremely poor judges as well. You see it all the time on the forums when people talk about why their players don't try actions that aren't specfically covered by the mechanics. "My players never think outside the box" goes the cry.

The trick is, they do think outside the box, but, they quickly realize that anything outside of the box is a suckers better and they are far, far better off staying inside the box.

 

[CapnZapp]

My point is:

The best designers do not merely have a good grasp of probabilities, they also have a good grasp of how bad human intuition is at probabilities. Then they steer their design away from leading people into "probability traps".

Obviously too many designers don't even clear the first step, but not stopping there with my analysis was my point.

 

[clearstream]

As far as I understand it, @lewpuls ,the opaque odds of dice pool games (e.g. Vampire) was intended to be a feature not a bug. That is, people play that game because they don't want to know the (exact) odds.

As someone with a fair grasp of maths and statistics, I have never understood that sentiment. I have always preferred the percentile die as the best resolution system (e.g. Basic Role-Playing) precisely because it makes it very easy to see the odds. (Assuming you understand percentages, of course)

But I guess (and this is not intended to be a personal insult to anyone) if you don't do math, playing a game with opaque probabilities (figuring out the odds in dice pool games is fiendishly difficult) evens out the odds compared to a friend that do math...

I feel like it is not so much knowing what the odds are, but knowing what that implies, that is at issue. I mean that as you say - percentiles can display the odds plainly - but knowing how to take that is another matter. Say I succeed 75% of the time: what should I stake for what pay-out at those odds, and how should I understand the set of possible future worlds that I might land in?

In very simple terms, I want stake / 75% to be < pay-out. So were we dealing strictly in gp with all values known, then I should not put up 10gp for anything less than say 14gp. The trouble is, and this I guess is part of the OPs general point, that values may be obfuscated. Compounding odds is one way they might be obfuscated, but I think that is fairly easy to notice. Consider the difficulty of knowing going in what sort of creature is worth fighting for how much divers loot and XP? The stakes and pay-outs aren't necessarily commensurable!

One important stake is real time invested in a character, which increases as they go. When I roll up a character, I might have invested say an hour or less. A year in, I might have invested 100 hours or more! That means that odds that might have seemed reasonable (if I knew them) at level 1, might be very unreasonable at level 10. So this is where I find the initial analysis in this thread needing to be expanded on. Yes, compounding odds are often misunderstood, but for me that barely scratches the surface of this complex and interesting aspect of RPG.

 

[Hussar]

My point is:

The best designers do not merely have a good grasp of probabilities, they also have a good grasp of how bad human intuition is at probabilities. Then they steer their design away from leading people into "probability traps".

Obviously too many designers don't even clear the first step, but not stopping there with my analysis was my point.

Yup. Agree with that.

And, compounded at the table is ego issues as well. Being able to tell someone that not only is their math wrong, but, why, when their "gut" is telling them that the math is right is such a huge uphill battle. I remember one DM I had, in a 5e game, who homebrewed a fighter subclass that got, more or less, 2 rounds of advantage on attacks 1/short rest and then 2/short rest later on down the line. I played the character for quite a while and then complained that my fighter was really, really not dealing much damage and I was really performing under par for a fighter of my level.

No amount of math that I could produce would budge the DM who was absolutely convinced that there was no problem. I actually had to track the group's damage, round by round, for about 20 rounds and then show him the empirical evidence (my fighter was bottom of the damage pool, and not by a little bit. By a whole lot) before I could convince him that this wasn't cutting the mustard.

 

[CapnZapp]

I feel like it is not so much knowing what the odds are, but knowing what that implies, that is at issue. I mean that as you say - percentiles can display the odds plainly - but knowing how to take that is another matter. Say I succeed 75% of the time: what should I stake for what pay-out at those odds, and how should I understand the set of possible future worlds that I might land in?

In very simple terms, I want stake / 75% to be < pay-out. So were we dealing strictly in gp with all values known, then I should not put up 10gp for anything less than say 14gp. The trouble is, and this I guess is part of the OPs general point, that values may be obfuscated. Compounding odds is one way they might be obfuscated, but I think that is fairly easy to notice. Consider the difficulty of knowing going in what sort of creature is worth fighting for how much divers loot and XP? The stakes and pay-outs aren't necessarily commensurable!

One important stake is real time invested in a character, which increases as they go. When I roll up a character, I might have invested say an hour or less. A year in, I might have invested 100 hours or more! That means that odds that might have seemed reasonable (if I knew them) at level 1, might be very unreasonable at level 10. So this is where I find the initial analysis in this thread needing to be expanded on. Yes, compounding odds are often misunderstood, but for me that barely scratches the surface of this complex and interesting aspect of RPG.

Not sure we're talking about the same thing.

If I can spend a "build point" (or whatever) on getting +5% to my Diplomacy skill of 45%, or to "Murder With Axe", or whatever, I know what I'm getting. What I'm getting is a Diplomacy skill of 50%. Or, given everything equal, I hit with 10 out of 20 axe-swings instead of 9 out of 20 swings.

If I instead get an extra die to my pool of four dice, what do I get?

To me, the number crunching needed to arrive at "a fifth die increases my odds from 47% to 51.9%", ergo I get 4.9% for my money, is entirely and wholly unwelcome. Why would anyone want to go through this step (in practice you need an online probability calculator)?

Zapp

PS. I mean, apparently the answer is "some don't care", so hey, this man's garbage is your treasure, and so on...

 

[CapnZapp]

No amount of math that I could produce would budge the DM who was absolutely convinced that there was no problem. I actually had to track the group's damage, round by round, for about 20 rounds and then show him the empirical evidence (my fighter was bottom of the damage pool, and not by a little bit. By a whole lot) before I could convince him that this wasn't cutting the mustard.

Honestly, I would have tried a different approach. Instead of bludgeoning him with math, I would simply choose to play a different character. I would say "your subclass is probably fine, I just want to try out this druid here or that sorcerer there".

That is, a GM should not be bound to offer only mathematically sound options. We can and should hold professional game developers to this standard, but I wouldn't impose this on homebrew content.

 

[Nutation]

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.

I didn't see much discussion of this. It's not that the GM might need to fudge the die rolls, it's that the designer has already fudged things so that a "moderate" encounter is heavily weighted in the players' favor, and a even a "deadly" encounter is as well.

 

[aramis erak]

Again, reduction to the absurd. Mr. Pulsipher, you really need to think through your editorial comments better, because if they are in fact reflective of your thought processes, then you're not seeing the obvious in front of you. And if they aren't reflective, well, then dumbing them down is not a service.

Fairness in RPG combat is artifice, but it's not illusory. There are several kinds...
There is the "Fair Encounters reduce X resources" mode of almost all editions of D&D.
There is the "Even odds" mode of some other games, where PCs and NPCs of similar rating are of similar threat, as in Dragon Warriors. If the party meets a party of same rank-equivalent, it's abut 50-50 odds.
There's the "should be able to complete in X turns" approach of Sentinel Comics... it's "balanced" encounters are suitably set for genre emulation. Actual defeat of the major foes is under 50%... they have minions and lieutenants to prevent their being killed or captured. Stopping their current plan, however... well, let's just say, of the hard scenes, less than 50% were successes in stopping the plan, either.
There is the "no difference in rules" approach of Traveller, Runequest, and many others. It's an entirely different level of fair. And I've had many a campaign cut short because players assumed that the odds were tilted towards them... in greivous error.

Excepting that first type, no one wants a fair fight.

That's also different from a "Balanced Encounter" as laid out in D&D 3E, 4E, and 5E... which is a specific subset of the resources spend. A 5E encounter of hard isn't so much "players will have a hard time winning" as "players will have a hard time winning without notable costs."

Fairness in RPG combat is many different things.

Now, the odds in combat are one element - and the "balance" is most keenly desireable there.

Your example of tournament play of team sports is, however, unsubtle and almost misleading. RPG combats are not "Win or Lose." And this is this week's element handled poorly, apparently not thought through in your editorial.

RPG combats have, at the very least, three axises of result:

1. Achieve the goal of combat or not, or even partially
2. Expend all, most, some, a few, or no resources. (damage, ammo, exhaustion, minions)
3. Player satisfaction with the way it plays out. (noting that Satisfaction may not be enjoyment in the immediate scene, but can result from eventual overcoming of the issues the character faced in scene.)

I've seen cases where player satisfaction was lowered because of success without costs... anticlimactic combat isn't fun for everyone, especially not me.

I've also had sessions which players labeled "Not fun, but really, a great story came out of it"...

Knowing the odds going in also can reduce player satisfaction... which is why the 3E, 4E, and 5E D&D DMG's various methods of "balanced" encounters don't encourage telling players what difficulty level the encounter was set at.