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

 

[Fenris-77]

@billd91 - I'm not fretting initiative at all actually. Just identifying a couple of ideas about it that don't really get a lot of thought. One, the impact it has on action adjudication, which is often to introduce an additional chance of failure to many potential actions (not just furniture parkour). Two, the way it can take the agency out of the players' hands to move the action forward in a positive way. Initiative and combat aren't bad things at all, I'm just counselling a moment of reflection about exactly when to call for that initiative roll.

I completely agree that you don't always want people swinging from chandeliers. That reminds me of watching my kids play Minecraft. They jump everywhere because it's marginally faster than running (or at least that's what they said) but if looks goofy as all get out. My point wasn't to privilege chandelier antics, that was just the example. The idea of running away in the face of discovery is a more mundane example of the moment I'm talking about. You round the corner and see a pair of the chancellor's guards. One of them spots you, what do you do? I can handle that with the surprise rules and a initiative roll, and sometimes I might, but I can also wait a beat and let the player decide how to answer the question I posed. If he draws his blade we go to initiative and combat, but if his goal is to run away, why would I immediately complicate that by calling for initiative? I can, obviously, but at that point the call for initiative is a consequence, I'm making his goal more difficult, and if I'm going to do that I want to be doing it for a reason, not just because it seemed like the thing to do.

 

[Hussar]

I guess I've never had the problem of someone stunting (chandelier swinging or whatnot) too often. IME, the problem is the other way, where the players refuse to move outside of the clearly defined box and try anything creative. So, on the occasions when players do try something funky, I now try to reward that as much as possible.

So, to use the swinging from the chandelier example one more time, I wouldn't really have a problem with simply saying, "DC 15 (or 10 maybe), you get advantage if you succeed" and no penalty at all for failure. I WANT the players to always be looking for something more interesting than "I swing my lumpy metal thing", so, I feel that it's better to use the carrot a lot more than the stick.

 

[clearstream]

So, to use the swinging from the chandelier example one more time, I wouldn't really have a problem with simply saying, "DC 15 (or 10 maybe), you get advantage if you succeed" and no penalty at all for failure. I WANT the players to always be looking for something more interesting than "I swing my lumpy metal thing", so, I feel that it's better to use the carrot a lot more than the stick.

If a costless benefit is offered, then what the DM seems to be saying is she's going to reward players who put in the effort to choose entertaining actions. That can be a good thing, and can inadvertently penalise quieter players or those who might see such freebies as cheesy.

I think some DMs can carry off a style that would not work for other DMs. My style is harsh, but my players tell me that they enjoy it. For whatever reason, it works for me. A friend who DMs is an absolute master of the unexpected catch. As others have said in this thread, the right balance of risk and reward will vary from house to house. Maybe variety is what is most needed. Some offers are gimmes, others would only be grasped in desperation (or error).

 

[Fenris-77]

If a costless benefit is offered, then what the DM seems to be saying is she's going to reward players who put in the effort to choose entertaining actions. That can be a good thing, and can inadvertently penalise quieter players or those who might see such freebies as cheesy.

I think there's a balance that needs to be struck. You can reward inventive players without penalizing quieter players if the rewards for inventive play don't outweigh the more standard options in terms of effect. That sounds weird, but I'm coming at this from the position that inventive actions and play are often actually penalized, sometimes unwittingly, by DMs because of the string of rolls or DCs they put on those actions.

 

[prabe]

I think there's a balance that needs to be struck. You can reward inventive players without penalizing quieter players if the rewards for inventive play don't outweigh the more standard options in terms of effect. That sounds weird, but I'm coming at this from the position that inventive actions and play are often actually penalized, sometimes unwittingly, by DMs because of the string of rolls or DCs they put on those actions.

I think (and I don't think you're exactly saying otherwise here) that there's a difference between penalizing creative play by gating it behind super-high DCs or strings of rolls--effectively guaranteeing that it won't work--and penalizing failure. Sure, you can try to talk your way past the ogres munching their meal of winter-starved deer, but the failure mode there is your one character against four ogres with backup a couple-three rounds away; that's not the same thing as making you roll for CHA(Persuasion) for every round you spend talking to the ogres. It's not radically different from the idea of letting someone try to swing from the chandelier and having the failure mode be one of falling damage, clinging to the chandelier as it sways over the enemy, or missing the chandelier and being prone (IMO).

 

[Fenris-77]

I think (and I don't think you're exactly saying otherwise here) that there's a difference between penalizing creative play by gating it behind super-high DCs or strings of rolls--effectively guaranteeing that it won't work--and penalizing failure. Sure, you can try to talk your way past the ogres munching their meal of winter-starved deer, but the failure mode there is your one character against four ogres with backup a couple-three rounds away; that's not the same thing as making you roll for CHA(Persuasion) for every round you spend talking to the ogres. It's not radically different from the idea of letting someone try to swing from the chandelier and having the failure mode be one of falling damage, clinging to the chandelier as it sways over the enemy, or missing the chandelier and being prone (IMO).

Yeah, for sure. The consequences of failure should be appropriate to the action. Swinging from a chandelier has a bunch of more interesting and potentially more dangerous failure states than swinging your sword. I definitively fall on the consequence side of things and not the gating side. I think players can get behind appropriate consequences more readily that strings of high DC rolls too, and that under those conditions will be more ready and willing to buckle a few swashes rather than coloring inside the lines all the time.

 

[billd91]

Yeah, for sure. The consequences of failure should be appropriate to the action. Swinging from a chandelier has a bunch of more interesting and potentially more dangerous failure states than swinging your sword. I definitively fall on the consequence side of things and not the gating side. I think players can get behind appropriate consequences more readily that strings of high DC rolls too, and that under those conditions will be more ready and willing to buckle a few swashes rather than coloring inside the lines all the time.

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.

 

[Fenris-77]

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.

I think the failures are as cool as the successes. I can make a lot of hay out of a failed chandelier swing, and the results could raise the encounter from solid to legendary.

 

[prabe]

I think the failures are a cool as the successes. I can make a lot of hay out of a failed chandelier swing, and the results could raise the encounter from solid to legendary.

Yup. Failure doesn't mean "you lose the fight." It means "you'll have to win the fight some other way, but first ..."

 

[Fenris-77]

Yup. Failure doesn't mean "you lose the fight." It means "you'll have to win the fight some other way, but first ..."

When I think of truly memorable encounters, and the equivalent scenes from movies, failure plays at least as important a role in those scenes as success does, if not a greater role. Complications make things interesting and memorable. Even John Wick gets shot and occasionally gets the crap beat out of him, or runs out of ammo. He's compelling because he keeps on ticking and finds a way to make things happen, not just because he's a giant sized badass.