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 think the math matters if the table decides it does. This is because D&D can be played in many, not necessarily disjoint ways, such as (wargame, story, TotM, ...).

If a game's math works, it can be ignored if you don't need it.

If it doesn't work, you can't just magically make it work if you do.

In other words, there's zero justification for broken game math. That doesn't mean you must play that way, only it needs to be there for those who want to use it.

 

[prabe]

If a game's math works, it can be ignored if you don't need it.

If it doesn't work, you can't just magically make it work if you do.

In other words, there's zero justification for broken game math. That doesn't mean you must play that way, only it needs to be there for those who want to use it.

Related: If the game's math is broken, and you're not a math person, you won't know why the game isn't working the way you expect and you won't have a prayer of fixing it.

 

[CodeFlayer]

What I find magical is how you got from what I said to where you went.

 

[Hussar]

What I find magical is how you got from what I said to where you went.

Not speaking for anyone else, but, I went the exact same way when I read your post. Could you perhaps rephrase it because, apparently, I'm not the only one who missed what you meant.

 

[CodeFlayer]

Sure - I'm in a thread discussing the appropriateness of teaching and/or requiring a working knowledge of probability to play reasonably well, as a wargame. What I am suggesting is that it is the body of players at the table together that decide what the ground rules are for the RPG. Most games I have seen give the GM wide latitude. It is the shared experience, and the quality of it, that is paramount. That means that, with the table's consent, I can take control of the mathematics of the simulation. The game designers don't reach that deep or that far, as I see it.

It is not my intend to sow discord - so please explain how you took my words some other way. I am new here.

 

[Hussar]

Ok. That clears it up. Your initial post made it sound more like math doesn't really matter because the group will just "work around" bad math.

Yes, we need to give the DM pretty wide latitude, fair enough. But, there does come a time when it should be appropriate, or, at least not seen as antagonistic, to question the DM's math. I find that in situations where the rules aren't terribly explicit, DM's often err far too much on the side of caution which turns a difficult task into one that's virtually impossible, or, where the rewards aren't worth the risk.

Take the old saw about swinging by the chandelier across the room to attack someone. There is a school of thought which says that you have to break that down into several individual actions in order to succeed. Jump to the chandelier, cut the rope holding it in place, make an attack. And, if any of those checks fail, the entire attack fails and the action is lost.

So, what sort of benefit should we give the PC for attempting something like this? Say it's a 50:50 chance for each step. That's a 1 in 8 chance of success. IOW, even though each step doesn't look that hard, (most DM's wouldn't consider a 50% chance of success as hard), by requiring so many checks, it becomes extremely unlikely to succeed. So, if you have a 1 in 8 chance of success, the reward has to be at least 4 times greater than if you just shot him with a ranged weapon.

How many DM's would allow you to deal 4X damage for this maneuver?

This is what I keep coming back to. Because the risk:reward calculation is so bad, no one tries doing anything outside the box because, most of the time, anything outside the box is either going to fail, or will never actually reward you as much as it should.

-----

Edited to fix math. Dammit.

 

[CodeFlayer]

There is more nuance here than perhaps I had first thought - I will reconsider. Thank you.

 

[clearstream]

Ok. That clears it up. Your initial post made it sound more like math doesn't really matter because the group will just "work around" bad math.

Yes, we need to give the DM pretty wide latitude, fair enough. But, there does come a time when it should be appropriate, or, at least not seen as antagonistic, to question the DM's math. I find that in situations where the rules aren't terribly explicit, DM's often err far too much on the side of caution which turns a difficult task into one that's virtually impossible, or, where the rewards aren't worth the risk.

Take the old saw about swinging by the chandelier across the room to attack someone. There is a school of thought which says that you have to break that down into several individual actions in order to succeed. Jump to the chandelier, cut the rope holding it in place, make an attack. And, if any of those checks fail, the entire attack fails and the action is lost.

So, what sort of benefit should we give the PC for attempting something like this? Say it's a 50:50 chance for each step. That's a 1 in 8 chance of success. IOW, even though each step doesn't look that hard, (most DM's wouldn't consider a 50% chance of success as hard), by requiring so many checks, it becomes extremely unlikely to succeed. So, if you have a 1 in 8 chance of success, the reward has to be at least 7 times greater than if you just shot him with a ranged weapon.

How many DM's would allow you to deal 8X damage for this maneuver?

This is what I keep coming back to. Because the risk:reward calculation is so bad, no one tries doing anything outside the box because, most of the time, anything outside the box is either going to fail, or will never actually reward you as much as it should.

It's tricky, though. The multiple of damage need not be the same as the change in chance to hit: the two are related, but not perfectly commensurable. Consider the power attacks (-5 for +10 damage).

And then there is also the nuance that I was going to hit in one of two possible worlds, now one of eight, so I would need four (not eight) attempts to be back to where I was. Suggesting a 4x multiple. I'm not knocking your example, only trying to say that the implications are far from straightforward even where one knows the odds. In a d20 system it might be about right to give +1 to +2 damage for each -1 to hit. I went from 11+ to about 18+ so anything from +7 to +14 damage could be right.

I honestly believe the conversation is somewhat empty without factoring in stakes. And one way to think about the odds is as offers to players (so that a DM offers a reward at some cost at some odds). It's usually up to the player if they choose to accept that offer (or should be). In our swinging chandelier incident, the offer might rightly be something equating to a power attack.

I wonder what the role of the player ought to be? Is the DMs responsibility to never offer unfair odds? When might it be okay to do so? Is the DM always required to know the odds, or do players bear some responsibility for that?

 

[Hussar]

Heh. Wasn't quick enough with my edit. Yeah, that should be 4x damage, not 8x. I hate math.

If the DM is offering unfair odds, in a game, then, IMO, that should be something very rare. And, frankly, if the odds are unfair, then the player probably shouldn't do it.

But, yes, you are totally right that it's not a straight line relationship. It's far, far more complex than my example. Totally agree.

 

[CapnZapp]

Related: If the game's math is broken, and you're not a math person, you won't know why the game isn't working the way you expect and you won't have a prayer of fixing it.

Sure.

As long as you aren't saying this to argue games don't have to have sound math, okay. Edit: which does not have to be true, either for you or the other poster.