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

 

[Blue]

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.

Pardon my generalization, but this is a very D&D-type calculation. Where the most common odds are win or die. Other shades of loss are not as commonly seen. (And when survival and win are the same, we often get players conflating their character winning with them winning, which is a closely related but completely separate problem.)

First, player don't understand the odds of dying. In many way this is a good thing. That's because the DM can establish stakes of fear of death, which is actually a good distance away from actual death. So lack of knowledge of the odds leads you to think that you've made a much bigger bet, and you can enjoy the adrenaline of that bet.

If you feel like you are betting 100 hours of play, you feel like you have it all on the line. Really, that's not the bet you are currently facing - there is a good buffer between down and dead. So really you are waging 15 minutes of non-activity - about one turn before someone stands you back up.

Even if you die, at 10th level you're now betting about getting hit with a revivfy, which is a noticeable but not exorbitant resource cost. Clerics, bards with magical secrets, divine sorcerers/warlock - lots of ways to have it. Safe bet is the party has it.

It's only after that where what you're wagering gets big - either significant amount of time sitting out until your character can be raised (after next long rest or after travel to an NPC), or (finally!) the 100 hours of play.

 

[Blue]

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.

As a side note, that amount of advantage is more than the official Samurai fighter subclass, which only gets 3 rounds per long rest, and it takes their bonus action to activate for each of those rounds. Combining with Action Surge most consider that enough.

 

[Shiroiken]

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.

I warn every new player I introduce (new to 5E or new to D&D). This is a new edition of the game, with new styles and rules. I usually place "Not everything can be defeated or overcome" right after "not everything requires a die roll," but just before explaining "what is a short rest vs a long rest." It's possible that some players get overwhelmed, but with 3E and 4E players, I've found more often than not they bring baggage from prior editions into the game (which we have all pretty much done unless we started with 5E; I STILL forget some of the things I remember from the playtests that were removed). When it happens the first time, I can understand, but I've had players continue this mentality even after a TPK, which leads to the following:

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.

I can accept that it's a playstyle, and that there's nothing wrong with it (even if I disagree with it). However, these players made the very odd assumption that they'd have to fight the dragon eventually, with absolutely no clues about it what-so-ever other than "it destroyed a small town and turned it into its lair." There were no adventure clues that led them in that direction, in fact they had lots of clues that led them elsewhere. They just thought they could take a dragon at level 3, because it's in the adventure. That's not a playstyle, that's meta-gaming the adventure.

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".

Not every monster is solvable, nor should it be. I'll admit that an adventure that fails to warn of ridiculous danger is wrong (such as the "open a door, rocks fall, everyone dies" trope). The only time an challenge (monster or otherwise) must be solvable, is if the adventure requires it to be overcome for success, not simply because it exists. If the players knew a dragon is in its lair, the only "solvable" solution is to avoid the place, which I have a hard time accepting as a solution, merely common sense (you don't get xp for avoiding monsters, for example). Warning the party of ridiculous danger, only to then have the party deliberately seek it (especially if it has nothing to do with the current agenda) is not a failure of adventure design, its a failure of the players.

 

[Hussar]

As a side note, that amount of advantage is more than the official Samurai fighter subclass, which only gets 3 rounds per long rest, and it takes their bonus action to activate for each of those rounds. Combining with Action Surge most consider that enough.

True, but, a Samurai also gets bonus HP, bonus proficiencies and, at 10th level, an automatic recharge of advantage every time you roll initiative. It's a bit more than the 2 rounds of advantage and nothing else that the homebrew class gave me.

And, @CapnZapp I strongly disagree. We SHOULD hold DM's up to the same standard as game designers if those DM's are choosing to be game designers. If they are offering options that are wonky mathematically, then players absolutely should stand up and tell them. Abandoning a character because the DM screwed you over because the DM doesn't grasp math is a very bad road to go down.

I mean, imagine the scene for a moment. "Yeah, I've been playing this homebrew class you've been working on for a while now. Just not feeling it, so, I want to drop this character for something out of the PHB" is going to go over like a lead balloon. It's pretty obvious what the player is doing. And, instead of working with the DM to try to fix the issue, the player is taking the passive aggressive path and sideways telling the DM that his or her idea is crap, but, not only is it crap, it's not even worth my time to try to fix.

I'd much, much rather players were far more open and honest with me than that.

So, yeah, a DM is absolutely "bound to offer only mathematically sound options. " A DM who forgets that is just screwing over his players.

 

[prosfilaes]

They just thought they could take a dragon at level 3, because it's in the adventure. That's not a playstyle, that's meta-gaming the adventure.

D&D Beyond has more than a page of dragons of CR 3 or less. I think you've overestimating how much the players know about anything; in D&D 3 and derived versions, any CR 1/2 humanoid could have 20 levels of a class. The only reason they think they can take anything is because it's in the adventure, or because the PCs are overconfident and practically suicidal--which is practically the definition of a PC.

If the players knew a dragon is in its lair, the only "solvable" solution is to avoid the place, which I have a hard time accepting as a solution, merely common sense (you don't get xp for avoiding monsters, for example).

Huh? Common sense says not to go in the dungeon; let someone else risk their life. But you don't get XP for avoiding monsters, and if that's too meta for you, you don't get GP or magic either.

Warning the party of ridiculous danger, only to then have the party deliberately seek it (especially if it has nothing to do with the current agenda) is not a failure of adventure design, its a failure of the players.

It certainly can be confusing what's ridiculous danger and what's reasonable danger. And the "current agenda" certainly makes it feel like the PCs can stay safe if they stay on the rails.

 

[Shiroiken]

The only reason they think they can take anything is because it's in the adventure, or because the PCs are overconfident and practically suicidal--which is practically the definition of a PC.

You have a strange definition of a PC, but whatever floats your boat.

Huh? Common sense says not to go in the dungeon; let someone else risk their life. But you don't get XP for avoiding monsters, and if that's too meta for you, you don't get GP or magic either.

I meant that as a "solvable" monster, simply avoiding it isn't solving it, which is why you don't get xp (or treasure or magic) from avoiding said monster. Thus the monster isn't "solvable," which was your original assertion. Some things simply cannot be solved.

 

[prosfilaes]

To make clear my position: a D&D world would realistically kill virtually all adventuring parties, as sooner or later they'd run into something they couldn't defeat and they couldn't retreat from. For a group of PCs to survive to high levels requires a lot of stacking of the deck towards them. That's why PCs have to be overconfident and nigh-suicidal.

I would say that there are times when a party should retreat and certainly times when they should parley. But the DM can't just tell the players that and expect not to have problems. You can railroad them, and punish them when they go outside the area you want. But providing reasonable options while not surprise killing the PCs is hard, and it's easy to blame the players for stuff that would have been hard for them to avoid.

I meant that as a "solvable" monster, simply avoiding it isn't solving it, which is why you don't get xp (or treasure or magic) from avoiding said monster. Thus the monster isn't "solvable," which was your original assertion. Some things simply cannot be solved.

So my assertion is false if you don't use my definitions. Okay?

 

[Hussar]

I'll give another example of risk/reward calculations.

In Star Trek Adventures, you are typically rolling 2d20 for most checks. Sometimes 3 (or possibly more) and sometimes 1d20, but, typically, you roll 2d20. Now, in the rules, if you roll a 20 on a check, you get a complication. But, and here's the kicker, the "complication" is largely left up to the DM to define.

So, think about it for a second. On 2d20, you have a 9.75% chance (just a smidge less than 1 in 10) of rolling a 20. If you have a group of 5 players, it's pretty much guaranteed that SOMEONE is going to roll a 20 every round. So, how much of a complication should this complication be? So far, in the game, it's been pretty brutal. The DM defines complication as a pretty serious failure, which means being out of position, easier to be shot, breaking equipment, etc. Since this is happening virtually every round, it has made the game extremely lethal.

I totally get what people mean about not understanding the math. If something is so common that it occurs all the time, then it cannot actually be much of an effect. Or, rather, it shouldn't be much of an effect. But, because of the vaguaries of the dice, it's actually a disadvantage to roll more dice, even though your chances of success increase, you are also increasing your chances of complications, which negate the successes.

It's rather frustrating to be honest.

 

[Fenris-77]

Hmm. I'd probably use the other die that isn't a 20 to rate the seriousness of the complication. 20 and a 3? Just a minor snafu. 20 and 19? Take cover Arizona. I like that answer because it uses the numbers already on the table in an intuitive way. Something of that sort should have been included in the game. Maybe not tables of specific fumbles, but a solid set of guidelines, or something. The system as is puts too much cognitive load on the GM IMO, absent a decent set of guidelines.

Edit - if more dice is meant to be a positive indicator of skill, I'd take the lowest non-20 result from the batch.

 

[aramis erak]

@Hussar STA playtest had much more concrete advice than the release. It was actually quite nice to have the explicit costs in threat.

The release does have some advice - either a trait, an unpleasant fact, or a change in threat rating... and traits are the really vague part:

1. +1 to some type of action
2. -1 to some type of action
3. Prohibit some kind of action
4. Enable some kind of action
5. use with momentum to establish a fact
6. (rarely) Allows purchase of a talent

This is where things start to fall apart: 3&4 are much stronger than 1, 2, and 5. 6 is just there for racial traits. But they have the same cost: 2 threat, or 1 complication.