Probability in Games (XCOM)

[kyoodle]

I have a hard time believing the numbers given in XCOM are the actual odds. As a little experiment I took every shot around 25-30% mark that I could on classic difficulty. After about 30 shots not a single one had connected. I guess I should never play the lottery

As someone else also said the chance of hitting an alien within the next square seems far to low, how often would trained soldiers actually miss a shot when the target is within a couple of metres of them? Unless we're going into several decimal places those shots should be 100%.

 

[BloatedGuppy]

http://www.escapistmagazine.com/forums/read/9.391083-X-com-isnt-hard-its-stupid?page=4#15748158

This post best explains my feelings on the matter.

And for those who don't want to read it. I missed about 80 shots in a row all of them above 50% some as high as 95%. Even if we assume all the shots were only 50% coin flips. Given a normal random math distribution the statistical probability should be .0000000000000000000000008272% that such a series can occur. Which is a ridiculously low probability that if 5 million people buy x-com and shoot at 1 enemy every 20 seconds nonstop every day. It should take them 15,220,700,000,000 years(over 15 trillion years of playing this game) before they encounter such a series. If the % to hit listed is the real % to hit and the mathematical distribution is mathematically normal(IE numbers below 50% come up as often as numbers above 50%.)

Take 5 different people together. You could have one that has 0% accuracy, one that has 25% accuracy, one with 50%, one with 75%, and one with 100%, which would combine to be a 25% accuracy average.

The mathematical average for that series is 50% not 25%.

http://www.basic-mathematics.com/finding-the-average.html

0+25+50+75+100=250
250/5=50

You were reloading and attempting the same shot with the same guy again and again, weren't you?

I mean, reading that post, that's what it sounds like you were doing.

Ah, here we go:

I missed about 80 shots over 6 turns trying to kill a tier 1 floater.

6x6 = 36, so there was COPIOUS reloading going on here. I expect reloads and re-attempts on bad shots accounted for about 90% of your missed shots.

You ARE aware that XCOM does NOT regenerate the random seed on a reload right? So you weren't missing "80 shots in a row". You kept replaying the same miss over and over again.

You then go on to speculate the game is racist in terms of how it determines psionic ability, which was particularly amusing, but I digress.

 

[Naeras]

The RNG is actually one of the main reasons I didn't buy XCOM. I still don't think it suits turn-based combat, or any kind of combat where there aren't a lot of small random rolls going on at the same time. There's nothing more frustrating than playing solidly and still getting killed on a 0.4% chance (which happened to me on the final mission in Fire Emblem, btw, and it was rage-inducing). Often times games like this will end up punishing you for making good tactical decisions because the dices didn't like you. And that's freaking dumb.

And just to illustrate my point on how much I hate RNG: it's the sole reason I don't like Black Isle RPGs. =/

 

[BloatedGuppy]

The RNG is actually one of the main reasons I didn't buy XCOM. I still don't think it suits turn-based combat, or any kind of combat where there aren't a lot of small random rolls going on at the same time. There's nothing more frustrating than playing solidly and still getting killed on a 0.4% chance (which happened to me on the final mission in Fire Emblem, btw, and it was rage-inducing). Often times games like this will end up punishing you for making good tactical decisions because the dices didn't like you. And that's freaking dumb.

And just to illustrate my point on how much I hate RNG: it's the sole reason I don't like Black Isle RPGs. =/

There is no single dice roll that can screw you if you're "playing properly" in X-Com. Or I wouldn't be running Iron Man games on Classic with zero casualties past the 2nd month. Eventually the dice would catch up to me.

It would take a spectacular run of bad luck to even lose, say, one Major or Colonel. It would be the culmination of a series of bad decisions compounded by bad rolls. At which point you've still lost 1/6th of your force. Which, if you've "played properly" at the strategic layer, is replaceable.

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

 

[Naeras]

There is no single dice roll that can screw you if you're "playing properly" in X-Com. Or I wouldn't be running Iron Man games on Classic with zero casualties past the 2nd month. Eventually the dice would catch up to me.

It would take a spectacular run of bad luck to even lose, say, one Major or Colonel. It would be the culmination of a series of bad decisions compounded by bad rolls. At which point you've still lost 1/6th of your force. Which, if you've "played properly" at the strategic layer, is replaceable.

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

I haven't heard anyone complain about the mechanics or RNG, so that's not what influences my buy here. What influences it is quite a lot of bad experience with RNG throughout my 10-15 years of playing RPGs and strategy games. The aforementioned Fire Emblem-example was just one of them, but it illustrates the my issues fairly well.
Now, if XCOM doesn't allow people to get insta-gibbed from single crits or whatever, that's definitely better than a lot of other games, but I still get ticked off when my 95% accuracy shots miss. It goes the other way as well: I get annoyed, not delighted, if I make a mistake and the enemy can't punish me for it because the dices favored me.

I don't feel the RNG adds anything to turn-based strategy at all: compare it to something like Company of Heroes, where the RNG doesn't matter nearly as much because the amount of shots fired is so high that you'll almost always see the result close to the actual probability(unless we're talking countersnipes. Fuck countersnipes). In turn-based strategy, you do risk missing several shots in a row even if you're very likely to hit, which obviously will influence your game plan heavily. Sure, you can adjust to it, but I still find it ridiculously annoying when it happens.

I'd much rather see the accuracy percentages done as damage modifiers rather than as dice rolls here, in which case I'd probably pick up the game.
..and, speaking of which (and because I'm too lazy to check it, going to bed now), do you know if there actually are any mods that turns the RNG into damage modifiers? :V

 

[FoolKiller]

This was a good article on probability in gaming, using the new XCOM as an example. This was a hot button issue on these forums a week or so ago in which a demographic of individuals was yowling about the cheatin' ways of random, so I thought I'd share it here.

http://sinepost.wordpress.com/2012/10/26/probability-in-games-xcom/

This part in particular amused me...

Your shot either hits or it doesn?t, and then damage is randomly calculated thereafter. But the key thing is whether the shot connects. Waste your chances with 25% shots, and you?ll soon get overpowered. It?s better to maneuver around, destroy the aliens' cover, and then shoot with an 85% chance. And when it misses, you can exclaim stupid things like "My 85% shot missed! What?s the chances of that!" (Spoiler: 15%).

So I read the article and a couple of things occurred to me.

1. We assume that the programmers did a good job of setting the game to reflect the mathematics involved. We already know that the good folks at Gearbox didn't know what they were doing mathematically when they created the Bee in Borderlands 2.

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.

Overall I don't like it when random chance affects the outcome that much. It is irritating because I like my hard work to pay off.

 

[BENZOOKA]

I'd rather keep the frustration from low chance disappointments, like in live poker, away from entertainment media, like video games.

 

[cojo965]

This is exactly what I want to know .

I can't see it, the image isn't working.

 

[Mycroft Holmes]

:words:

I wrote out a huge post and then googled something by accident thus deleting everything I had written. Started writing again and made the same dipshit mistake. I wrote all my work in the post but luckily saved a text file with end percentages so I can reverse engineer it pretty easily but I'm sick of showing my work on the math. So you can run the numbers for yourself if you want to dispute them.

I know about the saved seed numbers. I never reloaded. I'm not retarded. Every class in the game but support can fire twice per turn(Not once). So your math isn't even close to accurate on the shots fired. Research makes reloading weapons almost not required later in the game. And I was being generous on the to hit percentages. I fully remember and took note that I missed 9 shots at 90% and another shot at 95%. And the bulk of the shots were in fact made at 65%+. I was simply being generous to XCOM while still proving my point that their random number generation is borked. Which is why you see things like lopsided distribution of psionic abilities.

Using a less high total but much more highly accurate hit percentages for high ranking officers at close range(that much more closely matches the reality) we get .00000000000000000000000000000034% which is even worse % than my previous number run at 50%s. So again, I was very much favoring X-COMs shit number generator with that post, because it's probably a great deal worse than I said it was.

If we use your excessively conservative estimate of 36 shots which is less than my 3 HWs and sniper working alone were capable of around 48 shots in that period of time. So we take your 36 put the shots I fully remember percentages on in, and then assume the overly generous low of 36(with a low 50% to hit) shots made we still come up with .0000000000000000074499% for an average math distribution. Which to put back in perspective:

1) if 1 shot occurs every 20 seconds, it should take 12 minutes to finish out the whole series.
2) .0000000372528% is the percent chance of that happening if 5 million people complete one series of 36 shots for a normal math distribution.
3) 26,000,000 is the number of series that those 5 million people would have to complete for once such chance to occur again given a normal distribution where 50% really is a 50%.
4) As noted before it takes 12 minutes to finish such a series. And ergo to complete 26,000,000 series it would still take nearly 600 years.

So by my conservative estimate it would take trillions of years. By my accurate estimate it would take even fucking longer. And by your super (excessively to the point of being ridiculous) conservative estimate it still should take 593.6 years for 5 million people playing the game nonstop to run into that same set of circumstances if the distribution is actually evenly distributed so that each 50% to hit is actually 50% to hit, and a 90% is actually a 90% to hit.

So it's an outlandishly poor number generator any way you slice it.

 

[BloatedGuppy]

I know about the saved seed numbers. I never reloaded. I'm not retarded. Every class in the game but support can fire twice per turn (Not once). So your math isn't even close to accurate on the shots fired.

So in this hypothetical scenario where you're firing at a basic floater, you're using heavies with bulletstorm, assault with rapid fire, and snipers with double tap. And in 80 consecutive shots (some as high as 95%!) they all missed! Remarkable! Without any reloading either. That is a truly legendary run of bad luck.

I'm not even going to beat around the bush and be sarcastic, really. There's no point. You seem like a nice guy. You clearly enjoy math. I think that's great. All I can say is my anecdotal experience (which is easily repeatable) does not match up with yours, and that the scenario you are presenting is so hilariously outlandish that I really can't come to any conclusion other than you are completely full of it.

I'm not even going to defend the number generator, because I couldn't tell you a good one from a bad one. Maybe it's terrible! I wouldn't know. I do, however, feel completely comfortable in the knowledge that this bullshit scenario never actually occurred. But who knows! Anything is possible I guess.

You can reply, if you want, it doesn't really matter. I think you're lying. At one point I might've conceded it was a bug, but your defense of it has been so ludicrous that I simply can't come to any other rational conclusion. You can say "Sir I protest" or "You are a jerk" or whatever fills your boots, but it's really a waste of time. And I think we've wasted enough of each others time at this point. I see us on the opposite side of a great expanse. On your side, the magic number generator is booga booga terrible and makes the game unplayable and your crack team of colonels cannot kill a floater through a billion rounds of combat, and you TOTALLY PARSED THE NUMBERS FOR REALS. And on my side the game plays pretty much like you'd expect it to. Maybe your game is broken! Maybe you got the cheap Slovakian port, instead. Who knows. This was a fun read though, thanks. I'm laughing pretty hard, and everyone needs a good laugh, and I'm being 100% serious when I say I appreciate it. It's been a long day.

 

[Mycroft Holmes]

:words:

Ok bro, enjoy being wrong. I agree though: it is a 'hilariously outlandishly' bad number generator.

 

[Tallim]

Did he actually collect data on hits and misses to see if the reported % was a plausible figure for the actual underlying probability? Firaxis are notorious for thinking about probability displayed on screen in psychological terms. In other words considering lying about % chances to win to confirm faulty expectations of success or other reasons.

There was a guy on the official forums for XCOM who parsed hundreds of shots. Average predicted accuracy was 67%, his results were 66% (decimal places excluded because I can't remember them). If you're curious about bias, the guy running the experiment posted it in his thread...where he'd originally blasted the game for deceptive accuracy numbers after a bad run of luck on 50 shots.

Where you will run into trouble with XCOM is if you are save scumming, because the game does not regenerate its random seed on a reload. So if you miss a 95% shot on your first attempt, you'll miss it on every subsequent attempt too no matter how often you reload.

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.

That has nothing to do with Fire Emblem, that's because you are using savestate which will save all the internal configuration of the game including the RNG state so of course it will be the same.

 

[kyoodle]

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

Isn't that just the other side of the RNG argument though? Someone has a run of bad luck and assumes the game is cheating, someone else has a run of good luck and assumes they're playing skillfully.

I pretty much gave up on classic when the first outsider turned up. Even when I placed my soldiers to it's flank or behind it the percentages wouldn't go above 42%. After 8 or 9 shots at around 40% missed I moved the last man to the square immediately behind the outsider for a measly 52% chance that also missed.

My main gripe there is the strangely low odds of getting a hit but even accepting those percentages the total party wipe had far more to do with bad luck than bad judgement.

 

[Dr.Panties]

:words:

Ok bro, enjoy being wrong. I agree though: it is a 'hilariously outlandishly' bad number generator.

I'm also calling massive bullshit on your "scenario". It's just so utterly ludicrous, and such a blatant fabrication. And it's all just to "win" some ridiculous, untenable assertion that you have made in an online forum. Pathetic.

 

[BloatedGuppy]

Isn't that just the other side of the RNG argument though? Someone has a run of bad luck and assumes the game is cheating, someone else has a run of good luck and assumes they're playing skillfully.

I pretty much gave up on classic when the first outsider turned up. Even when I placed my soldiers to it's flank or behind it the percentages wouldn't go above 42%. After 8 or 9 shots at around 40% missed I moved the last man to the square immediately behind the outsider for a measly 52% chance that also missed.

My main gripe there is the strangely low odds of getting a hit but even accepting those percentages the total party wipe had far more to do with bad luck than bad judgement.

The thing is, I'm not claiming I have mad skillz or anything. I'm just claiming that with a better understanding of the mechanical fundamentals of the game came a very easily correlated success. If I'm having a run of luck, it is bordering on the extraordinary, since it has persisted through 3 full length Iron Man Classic campaigns and one full length Iron Man Classic Marathon campaign. We're not talking 80 consecutive shots here, we're talking 8,000. At which point is a sample size sufficient to rule out luck?

I've already discussed elsewhere that there is a span of time in the game where luck does play a substantial role, and that is the pre-sergeant game. I think Thin Men probably represent too steep an increase in challenge from Sectoids, at a time when people are just feeling their way into the game. And surprise surprise, 90% of the complaints about "unfair randomness" come from the first month or two, usually with rookie or squaddie heavy units engaging basic level aliens.

I don't have an issue with people questioning elements of the game's design, it ain't perfect. I do have an issue with people making unsubstantiated claims that the random number generator is screwing them, because they are always 100% anecdotal. I have a particular issue with Mycroft Holmes because the fable he's concocted is so ridiculously stupid it beggars belief, and when called out on it instead of having a laugh and admitting his hyperbole he just dug in deeper.

At the end of the day though, it doesn't really matter. If people want to believe that cameras steal their souls, and rabbits feet make them lucky, and random number generators have it in for them specifically, they are free to do that.

 

[Zhukov]

Huh, this could be interes... Arrgh! Math! Make it stop!

Anyway, my RNG experience in XCOM has been a smooth one. Usually hit high probability shot, usually miss low probability shots. Occasionally miss a shot that I was counting on to hit, occasionally pull off a shot that I was only doing for lack of any other options.

People seem to forget that "95% to hit" also means "1/20 chance to miss".

Might restart the campaign on Classic. Normal Iron Man (I hate that term) is proving a bit of a pushover.

 

[BloatedGuppy]

Might restart the campaign on Classic. Normal Iron Man (I hate that term) is proving a bit of a pushover.

There's a missing difficulty step between Normal and Classic IMO. Normal is "easy" and Classic is "hard" in traditional gaming parlance.

Hehehehe...Captcha is "real hoopy frood".

 

[GloatingSwine]

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.

 

[WoW Killer]

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".

 

[Mycroft Holmes]

I'm also calling massive bullshit on your "scenario". It's just so utterly ludicrous, and such a blatant fabrication. And it's all just to "win" some ridiculous, untenable assertion that you have made in an online forum. Pathetic.

Your disbelief is irrelevant to what happened. I don't win assertions, I merely explain things to other people. It's your choice to profit by that explanation or not.