Sid Meier (Civilization) gave a great GDC keynote in 2010 where he describes his multi-decade struggle to convey to users ideas like "Stuff that only has a 10% chance of happening still happens sometimes."
Multiply that by a million daily active users and it really works out to "Stuff that has a 1-in-a-million chance of happening will happen to somebody every day". Leading to player reviews like "The game rolled me a 1-out-of-10 SIX TIMES IN A ROW!!! The game is explicitly cheating me!!!" every day. Thus games tend to use random shuffles rather than independent random numbers so as to better align with common misunderstandings about statistics...
I'm not sure if probability modifiers are applied appropriately when modeling combat in games. If you are an advanced fighter, you get a +30% chance of winning, right, so you get one biased roll to see who wins. But when I play a better player in tennis say, they win the match almost every time. Of course I win games, but over the match they will take the lead every time.
I think fighting in real life is like this, not a single roll but a set of rolls that magnifies the advantage.
tl;dr I think Civ players are right to expect to win when they have a better unit.
Civ 1 had two statistics: attack and defense, which were rolled in a simple way. This lead to lucky Roman legions defeating tanks occasionally. Civ 2 added two more statistics (health and "firepower") which more clearly divided units into eras.
For example, Musketeers will almost always lose to Riflemen even though their stats are very similar apart from the Riflemen unit having 100% more health.
There are some things I disliked about the game, for examples city walls turns any city into an almost impregnable fortress until the very end of the game, but the unit health system was satisfactory.
Actually, in Civ 2, Riflemen and Musketeers both have 2 hit points and 1 firepower.
A good replacement example would be Archers (3 attack, 2 defense, 1/1 hit points/firepower) vs Musketeers (3/3 attack/defense, 2/1 hit points/firepower).
Regarding city walls: If the units inside are musketeers or weaker, cannons may do well (depending on the units' respective veterancy). If they're riflemen or higher, I think veteran artillery will still generally win. And then, of course, there are bombers and howitzers in the later game.
Oops! I always thought riflemen had more hit point stats. Your example is much better. Sorry.
About city walls:
The computer loads cities up with a massive amount of units on deity (usually enough to defend against a one-turn attack, I find it difficult to park enough cannons or artillery next to their cities). The only reliable way I have found to take out cities is to spam their cities with diplomats and sabotage until I get their city walls, it is always the very last thing he will sabotage.
It's hard to get a technological advantage for a long time because computer players will always help each other with technologies so in that sense they can get 6x as much science output as the player, although usually less because the computer is not very clever about boosting their trade.
I think the balance would have been better if catapults, cannons, and artillery straight up ignored city walls like the howitzer does.
The pollution from nuclear missiles contributing to global warming make the endgame frustrating too because the computer loves to use nukes, and you are punished for their pollution squares as well as your own. Sigh, time for a new game. lol
> The pollution from nuclear missiles contributing to global warming make the endgame frustrating too because the computer loves to use nukes, and you are punished for their pollution squares as well as your own. Sigh, time for a new game. lol
For a more realistic and complex treatment of nuclear warfare, I strongly recommend DEFCON.
> Sid Meier (Civilization) gave a great GDC keynote in 2010 where he describes his multi-decade struggle to convey to users ideas like "Stuff that only has a 10% chance of happening still happens sometimes."
Slightly OT, but I found the argument most convincing that the "improbable=impossible" way of thinking sometimes produces logically inconsistent or plain impossible results.
The classic wheel of fortune is an example: You're playing wheel of fortune with three other persons. The wheel is evenly split into four quarters, with each of the quarters having the name of one person written on it. (So one of the four quarters is "your" quarter) The wheel is spun and the person whose quarter ends up on top gets the reward.
How gif is your chance to win? 1 / 4. How big is your chance not to win? 3 / 4. So it's unlikely that you will be the winner. However, the wheel is fair, the probability of winning is the same for each player. So it's unlikely for anyone to be the winner. At the same time, it's physically impossible for the wheel not to produce a winner.
If you think of unlikely events as "practically never occuring", this is a logical contradiction. Only if you accept that unlikely events do happen, the contradiction can be resolved.
In the code of XCOM2, modders have discovered that the game cheat in your favor by increasing your chance to hit if you've missed in your lasts shots. And lower the chance of the enemy hitting you if they've already hit you this turn.
So you can (and will) miss 90% shots, it should not happen twice in a row the same turn.
I was a developer on Dead Man's Hand published by Atari and developed by Human Head. I was assigned the development of a mini poker game that pops up before each level and potentially rewards the player with extra ammo, armor, etc. In real life, great poker hands don't come along often. In our game, we wanted the flip the odds so the player usually won something and only lost it all on occasion. I basically scripted the game based on what I wanted the odds to be and produced hands to match. This includes when the user trades in cards. The result ended up being very addictive and was called out specifically this review:
Was it obvious, or acknowledged publicly, that the odds had been manipulated? I can just imagine your users going on to try real poker and not understanding how they lose so much.
>Extensive play-testing revealed that a player who was told that he had a 33 percent chance of success in a battle but then failed to defeat their opponent three times in a row would become irate and incredulous...So Meier altered the game to more closely match human cognitive biases; if your odds of winning a battle were 1 in 3, the game guaranteed that you’d win on the third attempt...
Fire Emblem (another strategy game series) solves this problem by taking the average of two random numbers. If the average is lower than the "to miss" value, an action succeeds [0]. This skews the probabilities at the low and high ends so that an 80% chance becomes 92%, 90% becomes 98%, etc, to minimize the occurrence of "spearman defeats tank" scenarios where players assume a 1/10 chance of failure will never happen.
> So Meier altered the game to more closely match human cognitive biases; if your odds of winning a battle were 1 in 3, the game guaranteed that you’d win on the third attempt
I wonder how many people are going to learn probabilities all wrong because of this. Whatever they learn just won't feel right because hey all these games work the way it makes sense intuitively.
Imagine a coin that flips heads exactly every 2nd time because it's a 50% probability. Would make magnificent future casino patrons or startup employees or ... well a lot of things that rely on chance and probability.
Good point. I once heard "playing/games" defined as learning in safe setting. It would be ironic if we self-sabotage our (already bad) sense of probability.
An interesting side-effect of this style of RNG is that if you need to get a particular RNG roll to win a PVP conflict, you can 'farm' up the roll by waiting until you've gotten sufficiently unlucky during PVE, then go to PVP where you will have a much higher chance of getting one right away.
I'm not sure if Dota2 has mitigations against that, but I've certainly seen it in other games.
Go and hit a neutral unit so that you have 2+ hits in a row without your ability/item proc'ing and then save the next hit for an enemy player since your next hit is likely to have a higher chance of proc'ing.
In league of legends you could previously "auto-cancel", and critical hits have different recognisable animations. So if you were about to crit a minion you could cancel the auto-attack and "store" the crit to hit an enemy with it.
I think that's been patched now but it was there for a good while.
I hate this system with a fiery passion. On the low end it turns a doable-but-not-great chance of hitting, say 30%, into a you-might-as-well-not-try 9%. I wanted to punch someone when I read about the fake percentages on a forum and suddenly understood why I never seemed to hit anything below 50%.
edit: My example's not averaging, forget which game I was using where they multiplied them together somehow.
I'm a big XCOM fan so I can say for that game that the RNG is messed with on lower difficulties to protect you from a bad streak. So if you miss 3 70% shots in a row, the next one will actually give you an 80% chance, escalating as your bad luck streak continues. On non-easy difficulties the chance to hit is honest as far as I know, a 30% chance to hit is actually a 30% chance.
It is increasing your chance to hit if you've a missing streak and if you have lost soldiers. And lower the chance of the enemy hitting you if they've already hit you this turn and you have less than 5 soldiers.
So you can (and will) miss 90% shots, it should not happen twice in a row the same turn.
This actually makes me sad. A 1/10 chance should happen sometimes (as a 1 in a D20) and the randomness is part of the fun of the game. If a 80% chance is actually a 92%, I think should just show a 92% chance, it would be more fair.
I think this unfortunately contradicts player expectations most of the times. Even for non-gaming "random" things, people tend to see patterns where there aren't any, and "fairly close to true" random functions feel like they're being modified even when they aren't.
I'm briefly recalling some lectures during University that we're hardwired to find patterns, even when there aren't any, and we make some pretty wild conclusions about the patterns we find this way. I've seen otherwise fairly reasonable players during DnD tell me it's time to "switch to the late night dice" because the current D20 hits a bad luck streak after awhile, and they adamantly adhere to this.
With games it's the same way. League of Legends tweaked it's crit chance algorithm to be a little less random because it could be so wildly swingy and players didn't like it - crit reliant champions would either feel amazing as they melted, or they'd feel useless after a series of successive non-crit attacks. The Dodge mechanic was removed almost entirely since a few select champs could have amazing fights where they got lucky and got 3+ dodges in a row even at relatively low dodge percentages.
It sucks to be the type of person that does understand probability in a reasonable way, but the evidence in games shows that just isn't how the grand majority of players operate.
I see many echoes of the sentiment that players don't understand probability in this thread, but I think it's worth considering that maybe also a compromise between randomness and determinism in games is more fun than either alone.
Have you ever heard people hating on you in a forum for adding randomness to a multiplayer game. And its not even limited to one side- both sides will hate on you.
One side, because you "rigged" the game, the other because they can not be sure, whether there victory is down to being lucky.
They dont want randomness- they want that sweet Adrenalin shot, when things go wrong and you barely succeed with your head on your shoulders on third try.
And yet I bet they're more addicted or fueled in their rage. The most vile gaming communities are also huge. It may not be a causal link, but I wouldn't be surprised.
I'm fairly certain Battle for Wesnoth does this and it just made the game frustrating for me when very low probability events occurred. Probability doesn't scale mentally that way. I mean, I have a degree in Mathematics, and I know what this means. I still didn't like it happening.
Battle of Wesnoth probabilities are often frustating, yeah, but at least it teaches a lesson of independent random events and proper perception of probabilities.
"Some designers have sworn off pulling the levers of luck at all. For a long time Larry DeMar, a noted pinball-game designer who worked with Williams, avoided using the ball-saver in the company’s designs, believing it undermined the purity of the game. If you lose, you lose—tough luck for you."
Having worked with Mr. DeMar, I can also say that he engineered other things to make you feel lucky without being so obvious.
It was only recently discovered that in Robotron:2084 (a video title he designed with Eugene Jarvis), the game's difficulty would ratchet down dramatically if your game started out badly (i.e. you were getting killed over and over before making it out of the first wave).
There were also some clever things Larry put into stuff like pinball match routines. This is the "random" number that would come up at the end and if your last two score digits matched, you won a free game. Cleverly, if you were playing a multiple-player game, the odds of one person winning a free game would suddenly increase - thereby increasing the real-world chances that the rest of the players would insert more money for another round.
Wow, I've played Robotron a ton at a freeplay arcade and I noticed it seemed to feel a little different in difficulty some games compared to others. I didn't quite put my finger on why, but it was probably the games where I lost a couple of lives in the first wave. Thanks for sharing that.
I was a programmer on several baseball games on Playstation (1) & Windows. Among my duties was AI. That meant consuming, encoding, and deploying a lot of historic stats. They'd be sliced and grouped and accessible across interesting combinations of team, opposing team, player at bat, player pitching, players fielding, stadium, inning, absolute score, score difference, time of day, and really just a fascinating set of inputs. We'd license the historic stats.
Baseball is a game of obsessively recorded stats anyways, and we'd use that to our advantage to model pitches, plays, games, seasons, etc. into something that 1) reflected what truly (historically) would/could/should happen in a given scenario, and 2) was fun and kept the player coming back for more. (Or else we'd hear about it in reviews!)
Well, turns out #2 is really, really important. Playing to statistical misunderstandings had to be part of the consideration. "That pitch/play/decision/outcome would never happen as often as it does! Fix it!" a producer with more baseball knowledge than I would claim. "It's happening exactly as frequently as it does/has historically," I would counter. Doesn't matter. Games need to be enjoyable and that means playing to common (mis)perceptions even if they're statistically wrong. But not too wrong. (Or else we'd hear about it in reviews!) :-)
Is there in general a formula for fudging statistics in the direction of bias? I.e., 90% becomes 99% as 10% becomes 1%? Was there a general algorithm you used. I'd be interested in hearing the technical details.
What you describe (non-linear) would probably have been superior but in my youth and inexperience over 15 years ago (and pressed with time and code-size constraints) I am sure I did nothing more than a scalar, maybe clamped with a C macro MAX() or MIN(). Sorry to disappoint; sometimes game AI and sim work just needs to be "good enough" and ... most importantly, needs to ship on time (on shelves, yes shelves, X weeks before opening day of baseball season) with zero bugs (no online patches in those days). So there is a certain satisfaction in that. :-)
f(x) = (sin((pi * x) - (pi / 2)) + 1) / 2
where x is between 0 and 1
I'm a collector of randomness functions for games. Weighted, gaussian, linear, etc. This sinusoidal randomness will be handy! Thanks for the inspiration.
There's another more technical instance of engineered luck in video games: too-simple RNGs (as a result of system limitations) that they've been fully reverse-engineered. Tool-assisted speed runs of games have their own category for runs which utilize these shennanigans: http://tasvideos.org/LuckManipulation.html
Most of thoses require faster-than-human actions, though. But some RNGs are even simpler: in the GBA RPG Golden Sun, the RNG is seeded only when the system is turned on, so you can engineer any rare drop just by following an action script. (I wrote a blog post about this specific instance awhile ago: http://minimaxir.com/2013/05/guaranteed-to-be-random/ )
Too-simple RNGs can qualitatively change games. Example: In Final Fantasy 3 (SNES), a certain item was supposed to be obtainable, but it required RNG sequences that never occur.
Makes you wonder if something like Estamel's Modified Adaptive Invulnerability Field is rare because the loot tables are broken. (This is an Eve online item that is rarely seen. Only two ships have ever died with one equipped at least as of a year ago. Its rarity is such that it's worth 24B ISK -- or the equivalent of $2,000 in ingame currency.)
Ive never quite understood that stuff. Monster Hunter, Fire Emblem, etc, all have seeded RNGs. In some cases, with fixed tables to make it even worse so that grinding for something for months will never get you what you want without restarting in some cases.
Are those devices really unable of anything better?
If the hardware doesn't have a clock that keeps track of the current time, the game could still re-seed based on the timing of player actions, because there's a certain amount of unpredictability there (at least, more than "seed with 0, only iterate on easily-controlled player actions"). It could do something like iterate the RNG every frame that the player doesn't move.
This might be one of the reasons I've always tended to prefer games that trend toward or actually are simulators. It's very hard to notice a "luck" mechanism designed by a skilled and thoughtful developer but those are few and far between. The more experience one has with a game, the more apparent things like the holy "RNG Jesus" become apparent.
The greatest enjoyment I derive from games is that of accomplishment. To me, there is no greater feeling of accomplishment than placing well in an iRacing league race or having a great dogfight against a human opponent in a DCS server. I don't even need to win the race or shoot them down to derive a sense of satisfaction as the outcome is entirely determined by skill and one can always strive to improve their skills.
I've always subscribed to the line of thinking that luck is where preparation meets opportunity. Whatever "luck" one experiences in a simulation type game, whether or not it is in their favor, is still something that required skill if it was to be taken advantage of. If I skip a yellow flag pit stop and make a fuel mileage gamble, I still have to have a feel for how far I can stretch the tank and how skilled the other drivers are as if they race clean all the way to the finish I'm going to still be a lap short. Sure, my opponents might say I "got lucky" but my luck was a result of a calculated gamble rather than an artifact of a lucky roll in the game's algorithm.
I'm probably the outlier but I think there's something to be said for games that refuse to introduce artificial luck. They aren't for everyone but they deliver an experience that can't be matched any other way.
I think this is partly the reason games like Rocket League, League of Legends and Counter Strike are doing so well these days. They're just pure team-based competitive games where the only things that affect the outcome are the rules of the game, the game's physics, and the skill of the players.
There are very small elements of luck, just enough to stop the games from feeling sterile or unnatural, but nothing big enough to decide the outcome of a match without being completely overshadowed by the strategic decisions leading up to it.
This idea is covered really well in Richard Garfield's book Characteristics of Games.
The metaphor he draws here is what he refers to as the skill chain. Each link in the chain reflects the point at which the player on the lower link is unable to defeat the player on the higher link above some small percentage. The longer the chain the more skill is rewarded by the game.
However this has a downside for an online game that isn't as popular as the ones you mention, you will be unable to find interesting games without having to wait for a long time for the correct opponent to appear. And it makes matching up well against your friends less likely.
Randomness can be used as s tool by a skilled game designer to shorten the chain and allow for more player to compete with each other. It also gives the player an element outside their own weakness to blame when they lose and that can make the game more enjoyable.
So it's something pro players tend to dislike but is typically accepted as the price of having diversity of skill in the player pool. (Poker vs chess for example)
This is only somewhat true. Most shooters rely on the concept of a shot pattern - that where you place your crosshair is only statistically the center of where your shot will land.
This is actually exactly what real life shooting is like. There is RNG in the process.
What a developer CAN do is control just how tight the shot pattern is. One example is to have a wide shot pattern when the player is standing, tighter when crouched, and really tight when prone. Or use an "iron sights" mode for tighter aiming.
I've just started playing CS:GO, in that you can tighten your shot pattern with practice too -in a different way. Continuous bursts spread in a predictable trend (a different trend with different weapons), shot interval feeds in to spread as a multiplier.
I've not worked out yet whether higher rank/XP and health status (HP) are also factors on shot spread and the progression of spread under continuous fire?
The Dark Souls (Demon's Souls) series did this very well I think. You essentially learn the physics and limitations of the game to beat it. You are put in tough situations, and only through trial and error can you learn the best way to exploit the situation. That gives you skills moving forward to use on later situations. Not much of Dark Souls comes down to luck.
Most multiplayer games still have sizeable luck component, at least when considering the results of a single game, because game designers found that having an element of randomness makes the game massively addictive because it forces players to play the game for longer to get a reward, trudging through losses or mediocre results in order to finally win a victory or two and be able to go to bed happy. In League of Legends the other team might pick characters that just wreck your team's. In SC2 your opponent could blindly pick a strat that counters yours 90% of the time. And anyway in most ranked games you're matched up with people of equal skill (via ELO systems), so there's an emergent tendency to win/lose ~50% of the time. Even though the result is determined by skill, it's still basically a coin toss who wins :-)
The Sims had to dumb down the AI, because the autonomy algorithm for deciding what to do next in the absence of player input was based on dynamically scoring every possible interaction.
But if the characters always autonomously chose the best interaction, then almost anything the player told them to do would distract them from their perfect AI driven routine, and effectively make their lives less efficient and more miserable.
So instead of picking the top scoring action to do next, it fuzzed their behavior by picking randomly from the top several actions, making them less compulsive and more whimsical, and giving the player more opportunities to have a positive effect on their lives, instead of being a negative influence.
Then again, some people would prefer to play The Sims that way, by bringing them down like they're wearing a turtleneck and a backpack all day, messing up their otherwise perfectly balanced idealistic lives by acting as Satan instead of as God, more like Afterlife and Dungeon Keeper!
I have a high preference to games of skill over games of chance. Most of the fun I get out of video games is in understanding the patterns and behaviour of the game world, and then using that understand to master the environment. For this to work, the game needs to be fairly deterministic in nature.
It's interesting that when tried World of Warcraft, I lost interest quickly as I found it too much like a slot machine.
I don't know if it's a personality trait (I'm a programmer so I tend to analyze everything) or because I grew up in the era of 8/16-bit games, where games were a lot more skill based in nature.
In Surely You're Joking, Mr. Feynman Feynman tells of gambling at Vegas for the first time. He calculated his expected loss at craps at around a penny a game, so he tried it and lost 5 dollars right away -- and never gambled again. This lousy luck and good meta-luck has been engineered away, apparently.
In A Theory of Fun Raph Koster says fun is basically about learning. What video games teach you a feel for probabilities? There's poker -- anything else? There ought to be.
Which is why companies offer free starting money to gamble. That just clicked for me, it's the drug-pushers standard. Remove the downside long enough to get them hooked.
Bringing this up made me wonder if we couldn't have a game that's to poker what Go is to chess -- simpler rules, deeper play, keeping poker's nondeterminism and incomplete information.
Tetris gets into this too. The official modern Tetris rules (known as the Tetris Guideline) reportedly specify the use of a shuffle bag [1] to avoid having too-short or too-long periods between repeats of any given shape. Other versions have their own methods of making the distribution "fairer".
This is a very fine article, but I keep hoping to see an article that's more general and discusses the real-world consequences (such as having to hire spoiled employees) of the ways games systematically distort reality and rewards.
We know that the more TV kids watch, the more likely they are to end up in hospital from an accident - their view of physics and risk has been distorted. Are heavy game players more likely to get fired from their first few jobs?
I grant that games have to be fun, but I wonder if there isn't a way to both please the player, as is done now; and inform them about the downsides of reality too - by showing them the contrast with a reality-run-through (maybe as an option), or by showing them after the game where they got an assist, or something.
I started thinking about this topic heavily after playing Borderlands 2 a lot. Quite apart from the sociopathic role-playing bits, it became very clear to me that mere perseverance was being rewarded far more than skill, or increases in skill. Much less real learning. Just churning through a level badly a few times would you'd level up enough to be able to Steam through it. (Pardon the pun.) I don't know what the effects of this on developing minds are - will they persevere at hopeless real-world tasks futilely waiting for the pity-timer to kick in, but not really try to learn or improve in the meanwhile? Will they rarely persevere 'cause the rewards are too slow in coming? I dread to think (but could be wrong to be pessimistic.)
I do think I learned a lot about learning when playing solo computer games decades ago in a way that is all but impossible now, since online players or your buddies will tell you the most efficient way. There's nothing like realizing you've played the carriers in Starcraft the wrong way for years to make you reevaluate whether you're a good learner or have really tried to figure out how the world works; or really understand the world, your relationships or anything else.
I've always wondered how learnable an understanding of unlikely events is but never investigated further. I guess a population of online poker players with increasing number of hands played (10k, 100k, 1 million etc.) (preferably winning ones) and others could yield interesting results.
I had that urge last week, and found that it had disappeared from my Steam library. Granted, I purchased it with the "Valve Everything Pack" in 2008, but the rest of the games from that pack are available. I guess it's just another lesson in "you don't get to keep the stuff in your digital library".
https://www.youtube.com/watch?v=bY7aRJE-oOY
Multiply that by a million daily active users and it really works out to "Stuff that has a 1-in-a-million chance of happening will happen to somebody every day". Leading to player reviews like "The game rolled me a 1-out-of-10 SIX TIMES IN A ROW!!! The game is explicitly cheating me!!!" every day. Thus games tend to use random shuffles rather than independent random numbers so as to better align with common misunderstandings about statistics...