Probability in Games (XCOM)

[That Guy Ya Know]

I think the randomness problem X-Com has is actually that the RNG is doing too much of the work.

I've been playing an SRPG recently which essentially has the same RNG mechanics (saved seed) for determining hit chance, but every attack is actually a small series of exchanges (by default the attacker and defender get two swings each, but if one unit is faster than the other they might get both of theirs in a row, an extra swing, or both), so an "Attack" is actually a series of four or five rolls which means that the effects of the RNG are averaged out, and you accept the occasional miss with better grace because it comes in a series of other attacks which hit.

That could also be a subtle difference between this new X-COM and its predecessors, purely from the unit cap. With a larger number of units you'll find each individual alien fight relies on multiple calls to the RNG rather than one all powerful dice roll. In the new game you'll often find you're in a situation where you have one and only one shot on a target, and if you miss you're all but guaranteed to lose a team member. The outcome of a single roll is more extreme. To coin a phrase, it's "roll two or more to not die".

This seems like bad strategy rather than bad game design. You shouldn't be gambling on a single shot most of the time. Keep your squad tight enough that they can cover each other. move forward slowly. Take 2 turns to move using over watch rather than 1 turn sprinting. And if you do find yourself in a situation where one soldier has to gamble everything on a single shot then retreat instead of firing. Move back and take the shot turn when everyone can help.

Sure you'll still run into some situations where there's not anything you can do but roll the dice and pray but that has always been part of the fun of xcom. But with good planning and strategy you shouldn't find yourself in those situations too often.

On the subject of randomness this video springs to mind:

Spoiler

<youtube=LElyagQ0n_g>

 

[GloatingSwine]

That could also be a subtle difference between this new X-COM and its predecessors, purely from the unit cap. With a larger number of units you'll find each individual alien fight relies on multiple calls to the RNG rather than one all powerful dice roll. In the new game you'll often find you're in a situation where you have one and only one shot on a target, and if you miss you're all but guaranteed to lose a team member. The outcome of a single roll is more extreme. To coin a phrase, it's "roll two or more to not die".

Yes, this is an instance where they've made one change whilst not considering knock-on effects. UFO had rookies be terrible shots but it didn't matter because you had twelve of them and you lined them up in a giant firing squad whilst the guy who farted in the skyranger went to find the aliens and if one whiffed all his shots then no matter, you moved on to the next one.

In the new game, at least in the unrewarding early sections where you're dealing with sub 50% hit chances at any kind of range you can't do that because you only have four guys. But that means it's harder to strategise effectively because doing what you're technically supposed to do to compensate for poor accuracy (move and flank) is bad because it opens more monster closets, so it's better to camp in places where you minimise the number of return shots the aliens can get and grind the maps out sectoid by sectoid until you get a few squadsight snipers.

The actual praying to the Random Number God on the higher difficulties is hoping that the nations that inevitably leave due to the gotcha abduction missions* are the shitty ones you didn't care about anyway.



* These are actually terrible, it's a transparent way to force the player to make a "difficult choice" about what they wanted to respond to, whereas in the original game any such choices were organic because there was a very high level of UFO activity and your skyranger was on cooldown for 24 hours. They could have put the same resource tension in this game simply by upping the level of UFO activity to what it was in the first game and counting on the fact that your squad get frequently wounded to attrit the player into thinking "do I really want to respond to this shitty scout, my best guys are in hospital and the backups don't really cut it".

 

[BloatedGuppy]

* These are actually terrible, it's a transparent way to force the player to make a "difficult choice" about what they wanted to respond to, whereas in the original game any such choices were organic because there was a very high level of UFO activity and your skyranger was on cooldown for 24 hours. They could have put the same resource tension in this game simply by upping the level of UFO activity to what it was in the first game and counting on the fact that your squad get frequently wounded to attrit the player into thinking "do I really want to respond to this shitty scout, my best guys are in hospital and the backups don't really cut it".

There's actually quite a few mods out that let you intercept and deal with all those abduction ships, with the result that you're inundated with crashed UFO missions. This has a couple of side effects, none of which are particularly desirable. One, they become a bit of a slog after a while. Two, you're absolutely swimming in UFO parts, alloys and elerium so any resource management part of the meta game is out the window, and three with all the abductions gone panic management is absurdly easy. It's absurdly easy post alien base anyway, but this makes it even easier to the point where it simply ceases to be a factor at all.

I don't mind the panic spiral, really, I think it puts a positive pressure on the player to not drag ass too much, but I think it does give a deceptive impression that you are LOSING THE GAME when in fact Classic is balanced in such a way that you're intended to lose a handful of countries before you hit the alien base. It makes your victory there and the subsequent global panic reduction that much sweeter.

 

[GloatingSwine]

There's actually quite a few mods out that let you intercept and deal with all those abduction ships, with the result that you're inundated with crashed UFO missions. This has a couple of side effects, none of which are particularly desirable. One, they become a bit of a slog after a while. Two, you're absolutely swimming in UFO parts, alloys and elerium so any resource management part of the meta game is out the window, and three with all the abductions gone panic management is absurdly easy. It's absurdly easy post alien base anyway, but this makes it even easier to the point where it simply ceases to be a factor at all.

Which makes it even more like the original UFO

I'm not sure as the panic management is a particularly positive gameplay element though, certainly not in the way it's actually implemented.

I don't mind the panic spiral, really, I think it puts a positive pressure on the player to not drag ass too much, but I think it does give a deceptive impression that you are LOSING THE GAME when in fact Classic is balanced in such a way that you're intended to lose a handful of countries before you hit the alien base. It makes your victory there and the subsequent global panic reduction that much sweeter.

It feels to me more like backwards ass design. Now, the challenge curve of UFO has always been backwards ass, it starts off hard because your gear and squad are rubbish and eventually ends up piss easy because you have flying jesus snipers who can never miss ever from all the way across the map and guys with super TU and reflex scores who never get out-rolled on reaction tests. (and this is still true in new X-Com, with various abilities)

But the strategic layer in original felt like it was escalating as the game went on. Because you started with only one teeny little radar at the start of the game you didn't see most of the UFO activity, and besides most of what you did see was little stuff and the council didn't really care about it, but as the game went on you started getting more and more serious activity going on, a wider range of alien missions would open up so you'd get bases, and countries leaving, and battleships out the ass and it felt like the situation was getting worse, whereas in the new game if you get through the first couple of months without too many or any important countries leaving it feels like the threat slackens off because you get more detection but the level of alien activity never increases past one or two UFOs a month and you can respond to everything except the bullshit "you must choose one and only one" abduction sites and generally keep them all happy from then on.

 

[Mycroft Holmes]

Oh, please keep "doing the math" on your fictional scenario

It's not fictional, I just didn't sit there and write down the move by move, I was more in awe that it was happening at all.

and bemoaning the unfairness off it all.

Where did I bemoan the unfairness of it? It's perfectly fair, in fact, because the seed generation for the game is equivalently produced for both aliens and humans and is there for perfectly fair. I also had a 4 round bout where nearly all my shots landed at 25% chances and the aliens missed every single shot they made. My point is that the random number generator is poorly set up, and instead constantly sticks to statistically unlikely trends.

We all stand to profit so much! Seriously!

You stand to profit as much as you are willing to. There's a lot to learn about coding systems and how they effect the games they form. A solid rotating seed could easily solve this problem with no important drawbacks. Which makes it funny that they chose a broken system. Usually in game theory its about gains and losses determining what you choose. But with this there's absolutely no solid reason to choose the system they did.

Quickly, introduce new ridiculous factors into your bloated, farcical anecdotal equation

It definitely is farcical, by the basest meaning of the word. You would think someone would bother to run a trending program on their seed before releasing it to the public. This is why people use rotating modified feeds of the system clock to generate seed numbers, to avoid the ridiculous problems a set seed creates.

before you lose even more face...on the internet, of all places!

I can't lose face on the internet. Personas are made and discarded with ease, so a name means nothing but what people think it means. You seem to value them highly, which is sad.

The latter is not only more consistent with reality, but inherently more rewarding. Or "profitable", if you prefer.

Incorrect on the first count. But you could actually make the argument that being in the dark is more 'profitable.' People who have poor understandings of reality tend to be happier, whereas people who have good understandings of how the world works tend to be more prone to depression and insanity. So you it's probably better that you don't look behind the curtain.

 

[Kilo24]

Personally, I think that most of the people who complain about probability in X-Com either don't know about the seed being saved or they fall prey to the biases that get associated with probability. Seriously, we're really bad about thinking about probability intuitively - it's the whole reason casinos can make money at all. You'll ignore your own good luck and only pay attention to the times when your luck turns bad.

Note how few people come in saying "I hit all of my 55% shots for the whole mission! 20 in a row! This game's RNG is screwed up!"

But I wouldn't be surprised if there was some screwiness to the RNG as displayed; Firaxis has been known to play around with displayed probabilities when they think it will make a better game (look up Sid Meier's talk on "Everything You Know is Wrong": he talks about altering the RNG based on the history of battles). That being said, I'd doubt that it they would have tweaked it to quietly screw over the player - frustration is far more likely to result than any gain.

 

[Keoul]

I don't know much about chance but this pretty much sums my reaction to games with "chance"

Spoiler

Cause really at the end of the day you're going to hit and you're going to miss.

 

[simmeh]

snip

snip

sounds like the way Fire Emblem does it to me... i ran it on an emulator once (i owned the actual game too so it was technically legal. pipe down...) and hit/miss was always the same when i made the same move after loading a savestate. and i rock at Fire Emblem so XCOM should be a cakewalk for me. i havn't got it yet but i want to.
of course, i never made an attack in Fire Emblem that had below an 80% hit rate.

I'll just jump in here for a slightly tangential comment.

Yes, XCOM uses a seeded random number list that it draws from every time it needs to do a calculations, just like most Fire Emblem games (the two on the NES and the first one on the SNES don't do this, actually). And yes, in both games when you reload a save file or state, it reloads that same seeded list, so performing the same actions will always have the same results.

However, in Fire Emblem (at least in the GBA titles) the accuracy shown is actually lying about 97% of the time. The game doesn't use a single number for accuracy, but two, and averages them together before comparing it to the hit percentage. This results in actual chance hit being different from the displayed chance to hit (source: http://fireemblem.wikia.com/wiki/Accuracy). 70% to hit is actually 82%, and 10% may as well be 0 (it's actually 2%). The displayed chance to hit is only correct in three instances: 0%, 50%, and 100%.

I would assume this was done to help the player and make them forget about their own confirmation bias, as player characters often have 70%+ chance to hit while enemies are often sitting at 30-40%. So, just be warned that you'll probably be missing more of those 80% chances to hit in XCOM than you would in Fire Emblem.

On another interesting note about Fire Emblem, you can actually still manipulate the RN system rather easily if on an emulator, because the arrow that shows up when you move your characters around uses some of the numbers from the list if there are multiple paths it can take over the terrain.

 

[Octorok]

The impact of luck on XCOM has been grossly overstated by people who are frustrated with a poor grasp of the mechanics.

Although I wholeheartedly agree with this statement, I do think that the game could be a little less obtuse with letting the player learn about new threats. I think that when people believe the game has cheated them, their frustration is not entirely unjustifiable.

Earlier today I encountered my first downed UFO with two Sectoid Commanders. Not being entirely familiar with their mechanics, my senior team member got Mind Controlled and I lost half the team (1 Squaddie, One Major, who was my only Support, and One Captain, my only senior Assault.). Afterwards I felt really rather angry, like I had not entirely deserved that kind of penalty simply for not knowing something I couldn't have known.

For comparison's sake, the mission before, I lost a veteran Major Assault I'd had since Day 1 because I made the wrong tactical call and only two of my Squad were in a position to fight 3 Chrysalids in a tight corridor. The loss hurt, but I understood that it was my mistake, and I never felt cheated by the game.

On my next UFO encounter (which I fought with a squad of Rookies/low levels incidentally), I was aware of the "rules" about Sectoid Commanders. So I set my team up in such a way that the turn I triggered them, I could bring down the maximum firepower at the minimum risk. I took some wounds due to some interfering Mutons, but the scrap ultimately went my way.

So, while it is definitely true that the complaints of XCOM being "unfair" are mostly a feeling that the game is unfair, this is in part the game's fault for not doing a great job of letting the player know the mechanics of new enemies/situations.

I do enjoy a game that lets you discover things for yourself, but it really does sting when you take a hit to your squad due to ignorance of mechanics you've never encountered before, especially if you've sunk 10 or 15 hours into a game.

Of course, with all that said, learning about and then overcoming new threats is deeply satisfying (and the game is made up of those amazing/tragic moments), but did it have to cost me my only damn Support?!

 

[twistedsquare]

2. While reading it I went along all those calculations that are done so well and then the writer became an idiot. He/she rounded 0.333 and 0.966 to 34% and 96% respectively. Both are amusingly wrong.

This is slightly late, but I thought I'd explain this. I'm the author of the original post, and while often an idiot, not in this case

As you say, the boundaries of where rapid fire are useful came out to 0.333 and 0.966. Therefore, you should only use rapid fire above 0.333 chance and below 0.966 chance. XCOM only displays whole number percentages for chances, so you just need to know which integer percentage is for normal shot and which is for rapid fire. So for 33% you should use a normal shot (because 0.330 0.333). Similarly, at 96% you should use rapid fire, but at 97% you should use a normal shot again. So as the article says, you should use rapid fire for 34% to 96% inclusive. It's not about rounding, just about thresholds.

Although as others have pointed out, rapid fire can actually get to 100% accuracy too. When it does, rapid fire at 100% is equivalent to normal shot for 100% (if you only need to hit with one shot), but rapid fire at 99% is still worse than normal shot at 100%.

 

[zumbledum]

And then of course we have the issue that actually the probability of anything happening is zero or 1 as there is nothing that is actually random. its our ignorance that makes it appear to be a spread of possibilities.

 

[Dr.Panties]

*Pedantic, useless dissection of a supposedly offensive post*

Did you really just question both my grasp of reality and sanity, whilst simultaneously maintaining the existence of this [80 shot/100% miss] probability seed? And did you really just state that you aren't complaining about the RNG being unfair, and then go on to state that it is poorly implemented?

Hey, one more...did you really just presume that I attribute an unhealthy value to online personae? After your continued insistence that this "Unlucky XCOM Unicorn" scenario is real?

Why, yes. Yes, you did. Wow. That's like...an unstoppable force meeting an immovable object- the former being reality, and the latter being your ego.

Another poster accused you of lying, and then I did. But perhaps "delusional" is the more appropriate term here. In this instance, the "curtain" to which you refer is transparent.

 

[AD-Stu]

If we make 20 shots and assume 50% hit chance, we would expect aproximately 10 hits and 10 misses. Even if we get exactly 10 hits and 10 misses it's possible to get results that feels very non-random. A few examples where H is a hit and M is a miss:

HHHHHHHHHHMMMMMMMMMM

HMHMHMHMHMHMHMHMHMHM

HHHHHMMMMMHHHHHMMMMM

In all examples there is a perfect 50% distribution between hits and misses, but it would feel very wrong and 'non-random' in a game. The last outcome is probably the closes to what happens when random number generators in games gets criticized for being broken.

It's very hard to tell what an acceptable random outcome must look like, but we can often instinctively tell when something isn't right. Our brains instinctively pick up on those patterns, and often pick up on patterns that isn't even there. Sometimes it's broken and sometimes we just imagine that it is.

I'd say that most of the time we just imagine that it is.

This is an interesting discussion to me because it's one that I've had dozens of times over in a completely different context - with poker players. A lot of poker players (particularly new online poker players) will complain that the game is obviously rigged because they lost three hands in a row where they were a favourite to win. Turns out the game is never rigged and mostly they're just experiencing selective recall or they aren't using a big enough sample.

In the above examples the idea is much the same, it really is all about player psychology and expectations. What you're talking about is essentially no different to flipping a coin 20 times. Pretty much everyone knows that the odds of a fairly flipped coin coming up heads are 50%, but they wouldn't necessarily expect to get exactly 10 heads and 10 tails in a series of 20 flips. It's only over runs of hundreds or thousands of trials that you'd expext to see the results start to really even out.

If players expect every second shot to be a hit just because the chances are 50% then it's almost certainly their imagination that is at fault, not the RNG.

 

[Mycroft Holmes]

Did you really just question both my grasp of reality and sanity

Most people have poor understandings of reality. It's not really much of a badge of dishonor. Without checking the post, I don't recall questioning your sanity. But then again you are arguing on the internet in defense of(to prove) something you repeatedly say you don't care about. So ya know, connect the dots.

whilst simultaneously maintaining the existence of this [80 shot/100% miss] probability seed?

This was already discussed in an earlier post which you clearly did not read. Par for the course I guess.

And did you really just state that you aren't complaining about the RNG being unfair, and then go on to state that it is poorly implemented?

Yes, and do you really think that those are mutually exclusive things? Man the more you talk...

Something is fair if it is done in perfect parody. If for example the number seed always returned values of 10% on a scale of 100%. Then every single shot with a 10%+ chance would hit and every single shot below would miss. This is a perfectly fair system as it is handled equivalently for both the NPCs and the player controlled units. It is however an extremely poorly implemented system as it essentially ignores or rather sways the probability by not being an even distribution of variables.

Do you understand the difference? If so you should be able to understand why a 'more normal' distribution than my '10% rule' can still be fair but poorly implemented. It's like the base rules of Nomic. You can't say they are unfair because everyone does the same thing with the same dice; but you can say they are shitty rules. The only difference is this is better dressed up and the dice is prone to giving extremely improbably number trends.

Hey, one more...did you really just presume that I attribute an unhealthy value to online personae?

I wouldn't call it unhealthy, but you do seem overly concerned with it. We assume of others what we assume of ourselves.

After your continued insistence that this "Unlucky XCOM Unicorn" scenario is real?

I prefer the truth to being popular.

Also I have no idea what Unlucky Unicorn means but it's apparently a shirt on snorg tees.

Why, yes. Yes, you did. Wow. That's like...an unstoppable force meeting an immovable object- the former being reality, and the latter being your ego.

The reality of the situation agrees with me and I have very little ego to speak of.

Another poster accused you of lying, and then I did. But perhaps "delusional" is the more appropriate term here.

I know exactly what happened. You however are merely postulating on it and becoming extremely defensive when told that you're wrong. I have my senses and my observations to guide my experience. You only have your compulsion to jump the the defense of a corporation, and your ego insisting that you have to win an argument on the internet despite having no facts to know either way what the truth is.

In this instance, the "curtain" to which you refer is transparent.

Then send me the reverse engineered code, since you would have to have it to understand the mechanics behind the game and thus see through the curtain. Because either you have it, or you don't understand how metaphors work, or you're lying and don't at all know how the game is coded and functions and are merely trying to win an argument about something you have no evidence on and no understanding of.

 

[BloatedGuppy]

I wouldn't call it unhealthy, but you do seem overly concerned with it...

You however are merely postulating on it and becoming extremely defensive when told that you're wrong...

...and your ego insisting that you have to win an argument on the internet despite having no facts to know either way what the truth is...

...are merely trying to win an argument about something you have no evidence on and no understanding of.

Not that this is likely to have an impact with you, but you can't keep drifting in for the last word whilst simultaneously accusing others of being unable to let things go/fixated on winning an argument. The same goes for Panties. You can cultivate an air of impartial, condescending neutrality all you want, it's a good way to "win" a debate. Sort of the civilized man's "U mad bro". But if you continue to respond like clockwork every single time he pokes you, you're not exactly holding yourself above the fray.

Also I have no idea what Unlucky Unicorn means but it's apparently a shirt on snorg tees.

I have to admit this was pretty funny though. Bravo!

Another poster accused you of lying, and then I did. But perhaps "delusional" is the more appropriate term here. In this instance, the "curtain" to which you refer is transparent.

I highly recommend letting this go. He's going to calmly deny fabulation until you put your head through the wall. Even if this went on for another 50 posts and he fell to his knees and said "YES I WAS EXAGGERATING" no one is going to show up at your door with a prize. Best case scenario, you get another infraction.

 

[Dr.Panties]

You know what? I'm not even going to bother.

 

[Kopikatsu]

I read through most of the math given in this thread and this is what I got out of it:

 

[Bostur]

I'd say that most of the time we just imagine that it is.

This is an interesting discussion to me because it's one that I've had dozens of times over in a completely different context - with poker players. A lot of poker players (particularly new online poker players) will complain that the game is obviously rigged because they lost three hands in a row where they were a favourite to win. Turns out the game is never rigged and mostly they're just experiencing selective recall or they aren't using a big enough sample.

In the above examples the idea is much the same, it really is all about player psychology and expectations. What you're talking about is essentially no different to flipping a coin 20 times. Pretty much everyone knows that the odds of a fairly flipped coin coming up heads are 50%, but they wouldn't necessarily expect to get exactly 10 heads and 10 tails in a series of 20 flips. It's only over runs of hundreds or thousands of trials that you'd expext to see the results start to really even out.

If players expect every second shot to be a hit just because the chances are 50% then it's almost certainly their imagination that is at fault, not the RNG.

I'd say you would be perfectly right about that. That was not I was refering to however. If the coinflip resulted in 8 heads and then 12 tails I'd say there was something odd going on. It can happen but it would be extremely rare. The statistical distribution is stil close to 50/50 that is not unusual, but the order of the outcomes is what would make it rare.

If I play a poker game and get 2-3-8-9-10 three times in a row, I would say that the deck needs to be shuffled. There is no need for a thousand samples to be suspicious about a random outcome like that. If I get a losing hand three times in a row however, that is perfectly normal.

In XCOM if I miss 2 95% shots in a row, and the aliens then miss a 95% shot, and I miss a 95% shot again the turn after that would you really dismiss that as just a coincidence?
That did happen to me. I know Guppy don't like anecdotal evidence, sorry about that. But anecdotal evidence is pretty much all we have.

A more common occurence in XCOM is several turns where most 50% shots are missed (on both sides) followed by several turns where most 50% shots hit. It is that kind of distribution of numbers that I don't think is suitable for a game like XCOM.

I don't claim that the game of XCOM is rigged. All i claim is that software random number generators are generally unreliable and only works in specific contexts.

Edit: Retracted some nonsense in the last paragraph.

 

[Loonyyy]

I read through most of the math given in this thread and this is what I got out of it:

"The fucking NUMBERS". God Black Ops had the most hilariously stupid story. I wasn't sure whether to laugh or feed Sam Worthington to a crocodile. So I watched Rogue instead (He gets ate).

Random Number generators are hard to judge-what appears to be non random is equally likely to be chosen by a RNG as a really fucked up sequence.

For a 50% hit miss, HHHHHHM, or MMMMMMH is equally likely, though trends with greater distributions of one or the other are less likely, you're more likely to encounter a mix. The saved seed makes most tests invalid, you can only test by checking every shot over an extended period. Very few people actually do this, they cite short periods where everything went wrong. Which you would expect to happen with an RNG. I'm highly disinclined to think that the RNG in a game is broken when it seems more likely that short term bad-luck streaks are being extrapolated to mean a failure. Over a long enough period of time, the thing will tend to the mean, but you're going to miss 90% hit chances, and hit 10% ones.

And that shouldn't be a suprise. Yes, your particular outcome is unlikely people-but they're all very unlikely. It's how random distrubutions work. The unlikeliness of your outcome does not discredit the RNG, unless your set outcome occurs repeatedly, with an identical seed, repeatedly in the game (I don't mean upon loading the saved seed, obviously). If you miss 80 shots, and then later in the mission you miss 80 shots, and the probabilities were ALL THE SAME and the RNG spat out THE SAME OUTPUTS I might believe that the RNG is favouring unlikely outputs. But getting seemingly nonrandom strings doesn't discredit it. Game over.

As many have said: The game is about mitigating risk. By choosing the strategies most likely to succeed, you minimalise the probability of failure. That's the game. I really need to get paid soon so I can afford it, looking very forward to it.