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.

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.

diceluck.jpg

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
 

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Lewis Pulsipher

Lewis Pulsipher

Dragon, White Dwarf, Fiend Folio

Fenris-77

Small God of the Dozens
Supporter
Nice article. I feel the lack of a bell curve diagram though. People always feel like they know where they're at with a bell curve. It gives them a comfortable sense that the abyss of probability isn't actually staring back at them, but just inviting them over for a nice cup of tea.
 
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Ovinomancer

No flips for you!
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.
Pedantic quibble and pet peeve: No, probabilitues are NEVER a cause of anything. Teams lose for specific reasons, not probabilities. Probabilities are models that can help inform decision making, but do not have any impact on actual outcomes. Else the sports betting industry would be terribly boring.
 

GMMichael

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

To summarize: For designers, fudging the dice (or the quality of the opposition) is inevitable. For players, it helps to understand probabilities in games
Is there an implied "traditional" in "RPG combat?" Because some games don't treat combat as sport. Some games treat it as a gruesome, dirty, blood-spitting disaster (thanks, Zweihaender).

I wouldn't say that dice-(or opposition)-fudging is inevitable. I'm reading that to mean that fudging must sometimes be used to allow PCs to win a contest, so designers shouldn't stress too much about making a fair game. But what if the game's rules aren't set up to determine win/loss? Or what if the game allows the GM to write "victory" into the script, before the battle has begun? Or it has a built-in fudging rule (like fate points) that players can use? It's not "fudging" if there's a rule for it!

A follow-up article to this might discuss why GMs should understand the odds behind specific dice-contests, because as the ones with the primary responsibility for modifying those contests, GMs should know the fire with which they're playing. E.g. how adding a bonus point to a roll in D&D is not equal to adding a bonus point to a Fantasy AGE roll.

PS - Totally agree that PCs shouldn't expect to win every battle. My characters usually like to avoid combat, in a sort of "I like living" way!
 
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clearstream

(He, Him)
Pedantic quibble and pet peeve: No, probabilitues are NEVER a cause of anything. Teams lose for specific reasons, not probabilities. Probabilities are models that can help inform decision making, but do not have any impact on actual outcomes. Else the sports betting industry would be terribly boring.
I had a similar quibble, but decided the analogy was only there to illustrate compound odds, not to claim any virtue as a simulation.

Still, I think explaining compound odds isn't all that helpful. Most people struggle to really grasp what it means to have a non-zero chance of failure in the first place. I find myself asking people to first of all think about a coin-flip. And then think about what kinds of things they might be willing to risk on a coin-flip. And then think about possible worlds, where each side of the coin lands us in a different possible world. I then talk about near-certainties, and what that might feel like. And so on.

Working along those lines seems to gradually bring people to understand odds.
 

clearstream

(He, Him)
Is there an implied "traditional" in "RPG combat?" Because some games don't treat combat as sport. Some games treat it as a gruesome, dirty, blood-spitting disaster (thanks, Zweihaender).

I wouldn't say that dice-(or opposition)-fudging is inevitable. I'm reading that to mean that fudging must sometimes be used to allow PCs to win a contest, so designers shouldn't stress too much about making a fair game. But what if the game's rules aren't set up to determine win/loss? Or what if the game allows the GM to write "victory" into the script, before the battle has begun? Or it has a built-in fudging rule (like fate points) that players can use? It's not "fudging" if there's a rule for it!

A follow-up article to this might discuss why GMs should understand the odds behind specific dice-contests, because as the ones with the primary responsibility for modifying those contests, GMs should know the fire with which they're playing. E.g. how adding a bonus point to a roll in D&D is not equal to adding a bonus point to a Fantasy AGE roll.
I wrote an article a while back about stakes. Odds mean nothing without stakes. And the stakes in games follow some interesting patterns.
 

atanakar

Hero
I never fudge the dice as a DM. Everything is rolled in front of the screen. What's the point of having odds if the GM cheats all the time. PCs should fail or succeed on their own merit or lack of.

As a DM I feel it's my responsabilty to explain odds of success before a Player wants his PC to do something very unlikely to succeed. I call that a Wisdom 3 moment. If the player persists he will live with the consequences.
 

univoxs

That's my dog, Walter
Supporter
A trope I dislike in traditional TTRPG is that every foe is meant to be fought or else would not be placed before the characters. It is gerenally assumed by the party that every monster is somewhat appropriate for their current power level. Anyone with experiance in WoD games sees this a different way. I encourage my players to talk first stab later, no matter the game.
 

Blue

Ravenous Bugblatter Beast of Traal
I'm with Lewis on this one - most people don't actually understand probabilities. I will often see common sense - and completely wrong - assumptions. From easy things like not understanding bell curves and thinking d20 is just like 3d6 but with two extra/less at either end, to not understanding the actual odds of X successes before Y failures, to more in depth ones.

A challenge of design is to make these clear. "d20+modifiers >= DC" isn't hard to grasp, fudges 4dF even easier while a die pool with a required number of successes may mask probability from the casual gamer. Especially when balancing tryign to let the dice tell the whole story - an 11 doesn't say if you succeed or fail, but some systems have penalty dice built in so that the roll determines success or failure without any additional manipulation - but often at the price of obfuscating the odds even more.
 

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