5 beats 4 in iceland, turn #1: http://WarLight.net/MultiPlayer.aspx?GameID=2647315

7 beats 6 in austria, turn #1: http://WarLight.net/MultiPlayer.aspx?GameID=2651392

I seem to be seeing this more. Wonder if Fizzer changed anything in the way luck works?

I wondered the same thing, since I've seen more 2v2 and 1v1 succeeding lately. I've also noticed more 3v2 winning, but that could all just be my perceptions.

interesting. correction on my first post, it's turn #2 in first game, not turn #1

I have also seen some bizarre fluctuations in luck of late. Hopefully it's purely subjective.

i saw 1 year ago, when 10 beat 10

I saw 1 beating 50 some years ago, but it might have been Jackie Chan, I'm not sure

i once saw 2 beat 3 once.

Ironheart - no you didn't.

Everyone else - I wager it's simply bad luck and coincidence, nothing more.

i did i really did

No, you really didn't.

|>"Each army that attacks has a 60% chance at killing one defending army"

@Iron:
You might have *seen* it, sure, but it just didn't *happen*. Possible causes for seeing it anyway include just not paying enough attention (it was a 3vs3, one attacker got killed, you saw 2 armies move in), sleep deprivation or any number of chemical "goodies" some people (no idea whether you are among them) subject their body to.

According to the game rules, even at 100% luck (or 0% luck and 100% offence kill rate), in order to beat X defending armies, you will always need, at the very least, X attacking armies; if the number of attackers is lower than the number of defenders, the attack fails, *by definition*. (For completeness' sake: there are lots of cases where even X vs X attacks cannot possibly succeed either.)

As you might remember from the [What are your most improbable failed attacks?](http://warlight.net/Forum/Thread.aspx?ThreadID=3153&Offset=20) thread, I worked on it quite a bit (arrggh, should finish it... :s ), so I really do know what I'm talking about.

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@Everyone:

Human intuition and statistics are a terrible combination. A great example of just how badly human intuition stinks when probability is involved is the [Monty Hall problem](http://en.wikipedia.org/wiki/Monty_Hall_problem). Or, as the (pen and paper) role players amongst you know: "A fifty-fifty chance never happens; a one-in-a-million chance is a sure thing!".

There are a number of reasons why you might *think* more attacks are succeeding that "should've failed". The most important one is observation bias combined with psychology.
Let's say you toss a fair coin 16 times. On average there "should be" one string of four heads in a row. Your feeling tell you this is weird (it has a 0.5^4 = 6.25% chance of happening when you toss a coin four times in total; for comparison, at 75% luck, 60% offensive kill rate, 7vs6 has a 9.98% chance of succeeding). However, you might well shrug this off as "weird things happen", or simply not notice it happening at all (probably more likely with weird attacks than with coin tosses).
On the other hand, if you toss a fair coin 64 times, you expect four strings of four heads in a row. But, if that happens, you are (1) far less likely to "shrug it of", you can't accept that something that weird should happen "that often" (that's psychology for you; in a sample size four times as large you don't accept "unlikely events" will happen four times as often) and (2) you are far less likely to overlook the occurrence in the first place.

*(Disclaimer: I just got back from an all-night film marathon; it's 5:30 AM and I'm tired as hell. The above prose is probably rather badly written and I wouldn't recommend copying any of my calculations onto a statistics test... However, I'm pretty sure I didn't mess up so badly that the general idea I'm trying to convey is invalid.)*

I think there is something to this conspiracy, I had a game yesterday where a 10 killed 8 with 7 remaining armies. It was the deciding factor in the game :/

played a game with my hand today, he also thinks that something has changed. he saw 4 kill 4 2x in 2 days.

This is a testable hypothesis. Set up a practice game, and keep having say a 10 attack a 7 (doesn't really matter, but large enough to make a purty histogram by the end). Keep doing it and record it each time how many armies those 10 killed. Repeat maybe 100 times. Make a histogram of the results. Compare it to what the analyzer says should happen. Should be close. If not, the great luck conspiracy caper of 2012 will be well underway.

i had a case today where 3 armies killed 2 with all two spare
i don't know whether that is anomaly or just cos there was a fair chance of it happening though

|> Make a histogram of the results. Compare it to what the analyzer says should happen.

Unfortunately that is utterly pointless. The analyser uses the exact same code as the game engine itself (this has been stated on multiple occasions by Fizzer). The analyser comes up with its **estimates** by simply simulating the attack a lot of (1000??) times and simply counting how often the attack succeeds. In other words, what you're doing is essentially manually simulating a run of the analyser. Even if the calculation / code / whatever *did* change, this experiment will not confirm it.

If you want, you can use my analyser (link below) which actually calculates the success chance. When I first wrote it, it either agreed with the WL built-in analyser fairly closely, or it disagreed (but only in cases where the built-in analyser was known to get it wrong; the reason I even started that little coding project).
If it suddenly starts disagreeing with the built-in analyser now, that would be an indication something has changed. Note, if you find such a disagreement, please post number of attackers, number of defenders *and* offence kill rate and luck percentage (if it happens to be an X-vs-X attack, equal numbers of attackers and defenders), you should also include the *defence* kill rate.

***Warning:** as pointed out by Fizzer the last I posted this link, you're downloading executable code; essentially you are blindly trusting me to not have put any viruses or other nasty stuff in there.* (If you have even a tiny bit of programming experience, you don't have to trust me; [here](http://warlight.net/Forum/Thread.aspx?ThreadID=3153&Offset=19) is the important part of the code; feel free to copy-paste it into your own program.) If you choose to trust me, you can download my analyser [here](http://dl.dropbox.com/u/12477348/AnalyserGUI.exe).

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@Arun:
Do you mean three attackers kill two defenders and only lose a single army themselves? That is a combination of 3-killing-2-(or-more) and 2-killing-1. Assuming 60% offence, 70% defence and **100%** luck (that's a bit easier to calculate :p ) that works out to:

60% * 60% * 40% * 2 nCr 3 = 0,432
60% * 60% * 60% * 1 nCr 3 = 0,216
70% * 30% * 1 nCr 2 = 0,42
( 0,432 + 0,216 ) * 0,42 = 0,27216

For **0%** luck (also easy to calculate) the result is:

3 * 60% = 1,8 -} 80% chance of killing both defenders
2 * 70% = 1,4 -} 60% chance of killing one attacker
0,80 * 0,60 = 0,48

So at 100% luck that's better than a 1 in 4 chance and at 0% it's virtually 1 in 2; either way not exactly "extraordinary" if you ask me. (A 1 in 4 chance is flipping a coin twice and having it come up heads both times, a 1 in 2 chance is flipping a coin once and having it come up heads.)

Well, using the warlight analyzer, with the settings from your games (75% luck, 60 and 70 kill rate on offense and defense respectively) a 5 has a 27% chance of taking the territory from a 4. A 7 has a 10% chance of taking the territory from a 6. Not really that unusual, when you take the probabilities. For the 5,if you did it 100 times, 27 of those times, it would take the territory (just using the percentage). For the 7 over 6, it would happen 10 out of every 100 times.

We would probably see 5's beating 4's, and 7's beating 6's (and the like) more often if we actually attempted them. We just know instinctively that most of the time it would not work,and that we would need more troops for it to have a better chance, so thats why it seems like such a surprise when it did happen.

You know that saying: an army of donkey led by a lion is better than an army of lions led by a donkey?
Don't forget that the armies were led by me :P:P:P:P:P


On topic: as the guy b4 me said, 10 percent chance. Unlikely but not impossible.

i meant that the 3 didn't lose any armies

|> i meant that the 3 didn't lose any armies

Seriously, the math isn't that hard (especially since you only need to slightly modify what I gave above).

60% offence, 70% defence, 100% luck:

60% * 60% * 40% * 2 nCr 3 = 0,432
60% * 60% * 60% * 1 nCr 3 = 0,216
30% * 30% * 1 nCr 2 = 0,18
( 0,432 + 0,216 ) * 0,18 = 0,0317447424

~= 1 in 30

60% offence, 70% defence, 0% luck:

3 * 60% = 1,8 -} 80% chance of killing both defenders
2 * 70% = 1,4 -} 0% chance of killing zero attackers
0,80 * 0,00 = 0,00

Can't happen. Then again, since you didn't specify otherwise, I assume you were playing at default (75%) luck, where (I assume) the value would be much closer to the 100% luck value than it is to the 0% luck value.

I don't know about you, but I do quite a few 3-vs-2's, since if we only consider the chance of the attack succeeding, ignoring how many attackers survive, it isn't all that bad (68,40%). Doing something a lot means you will sooner or later run into it working out in an unlikely way, that's inevitable.