Spiral Knights - Something I've been wondering for a while (Forge related)

Something I've been wondering for a while (Forge related)

17 replies [Last post]

Sun, 10/20/2013 - 02:47

Gyrruss

I'm not sure if I may be the only one, but I can't seem to trust Medium setting on forges. The 70~80 percentage it tells me feels like a lie; the main reason is that most of the time I get successive failed forges, 3 to 5 failed forges in a row. I've also taken an observation where the Minimum setting feels more reliable; the expectancy of failure is high, however I usually get successful forges from it. And Max will always be Max. So I'm not even sure that the percentages are right, or maybe my luck is just upside down in a sense.

But I can't be the only one with this sort thing... right?

Sun, 10/20/2013 - 03:06

Heroshian

4* forging is bugged so that

4* forging is bugged so that medium almost always fails. All others are apparently accurate.

Sun, 10/20/2013 - 05:01

Hexzyle

Hmmm. I wonder if they confused the "Percent chance of success" with "Percent chance of failure".

Sun, 10/20/2013 - 06:54

Iamnoone

The forge is crap. The

The forge is crap. The percentages stated are a lie.

I have only forged 5*'s. Lowest amount of crystals in = zero chance of success. Medium mount in = you're lucky as heck if it ever works. Maximum amount in doesn't actually mean absolute success. I have failed more times than succeeded at that 100% chance of success.

The forge is gambling for children.

Sun, 10/20/2013 - 06:59

Thunder-The-Bright

Iamoone, you can't fail at 100% success. I heated up 7-8 weapons not counting star levels and it never happened to me.
screenie or it didn't happen.

Sun, 10/20/2013 - 08:36

No-Thanks

100%

Attempt stuff, that promises 100% success
Succeed
????
Profit

Sun, 10/20/2013 - 10:21

Alphappy

Never forge less than maximum. It's not only a huge waste of crystals in terms of the levels you (might) get, but you also forfeit any chance at the forge box.

Sun, 10/20/2013 - 10:34

Exerpa

1/3 crystal cost - less than

1/3 crystal cost - less than 1/3 chance of success - no chance of prizes. Whats the point?

Nuke the 1/3 option.

Sun, 10/20/2013 - 10:52

Jendar-Nox

...

I often succeed when forging 4* items on medium. Theory of probability is a curious thing.

Mon, 10/21/2013 - 09:23

Aiden-Curry-Puff

Statistics. Expected returns

Statistics.

Expected returns is the probability multiplied by the cost. I think. I forgot most of this as soon as I graduated. Oh screw the terminology, I'm pretty sure now that's not right.

Anyway.

1 success * 30% = 0.3
1 success * 70% = 0.7
1 success * 100%=1.0

Divide that by the cost. Now you have 0.3, 0.35, and 0.33

For those chances, those are the theoretical average amount of success you could buy with one unit of crystals.

I think.

That's not at all the result I was intuitively expecting.

There's a formula you can use to find the expected number of tries to get one success 95% of the time you do that many tries in a gemetric probability sequence. Or something. Look it up if you want.

I hated statistics, so don't trust me too much.

Mon, 10/21/2013 - 09:32

#10

Bopp

not hard to work out

Aiden-Curry-Puff, the calculation you were doing is not a bad idea. But we need to know how many fire crystals are needed to achieve the 30%, 70%, and 100% chances. Then we can compute expected cost.

Mon, 10/21/2013 - 09:38

#11

Khamsin

1/.3, 2/.7, 3/1 = 3.33, 2.86, and 3 times the base amount of crystals.

So the first craft makes zero sense. Higher cost, higher risk, no extra rewards.

The 70 and 100 are comparable, but the 100 is less risky, and you have a chance of forge prize boxes which contributes to its cost effectiveness.

Mon, 10/21/2013 - 09:41

#12

Culture

Hmm

I think someone gathered the number of crystals needed at each level and put it on the Heat page.

There was an online calculator I used to use to determine time to success with levels of confidence for events with fixed probability... now I can't find it.

Mon, 10/21/2013 - 10:06

#13

Aiden-Curry-Puff

We don't need the number of

We don't need the number of crystals since it's always a multiple of the minimum.

So max is always 100
med is 80, 75, 70
and low is 40, 30, 20

It seems I lost my life so this is the relevant math.

We're looking at a binomial probability i.e. only two outcomes (succeed or fail)

Now if you're repeating the same thing over and over at the same prob level (max med low) until you succeed, you can use a geometric probability distribution to throw out the numbers you're looking for. It so happens the mean of this distribution is given by mean=1/p

Which actually makes things really, really easy.

100 = 1 expected try * 3 units = 3 units for success
80 = 1.25 expected try * 2 units = 2.5 units for success
40 = 2.5 expected try * 1 units = 2.5 units for success

100 = 1 expected try * 3 units = 3 units for success
75 = 1.33 expected try * 2 units = 2.66 units for success
30 = 3.33 expected try * 1 units = 3.33 units for success

100 = 1 expected try * 3 units = 3 units for success
70 = 1.4286 expected try * 2 units = 2.8571 units for success
20 = 5 expected try * 1 units = 5 units for success

Weird. So TL:DR theoretically the medium option is always "cheapest". However it becomes more expensive at higher levels. And the lowest option is always "most expensive" and becomes even more so more rapidly than medium.

Don't gamble.

http://math.tutorvista.com/statistics/geometric-distribution.html
http://stattrek.com/statistics/dictionary.aspx?definition=geometric_prob...

Mon, 10/21/2013 - 10:20

#14

Sirius-Voltbreaker

You must also take into consideration that the amount of crystals needed to forge is changed along with the ratio and percentages used to forge. I might not have tested correctly, but the percentage of suceeding changes every 5 levels and the crystals needed changes every two.
EDIT Well I should've read aidens posts because it actually makes much more sense.

Mon, 10/21/2013 - 10:32

#15

Momofuku

what?

Easiest way to think about it is in terms of expected cost.

Cost to level up / Probability = expected cost to level up

Where you can think of "expected cost" as "how much you expect to pay in order to succeed"

Easily pictured with two examples:

3x cost has a probability of 100%. Thus 3x / 100% = 3x ; which makes sense, since you never have to spend more than 3x fire crystal for the 100% level up
Suppose 2x cost has a probability of 50%. Thus 2x / 50% = 4x ; this makes sense because on average, you will fail just as many times as you succeed (coin flip). Thus, you will spend an average of 4x fire crystals to gain a level.

Thus the approach to calculate expected cost in #11 is correct.

You get the same numbers as #13, but there is no reason to overcomplicate things and bring in additional probability theories when the math is pretty straightforward.

Mon, 10/21/2013 - 10:50

#16

Aiden-Curry-Puff

Um.

Well the fact that you get the same numbers should tip you off to the fact that it's the exact same probability theory. The numbers would be different if it was a different theory.

If you expand out your formula you'll get this.

Chosen Cost * Expected number of tries = expected cost for one level up

And since expect. #tries is the inverse of the probability of success.

We're back to cost/probability = average cost per successful forge.

If you read my post fully, I did say the math works out to be ridiculously easy. It looks complicated because I cited some research because I like seeing the full picture and recording my thought process. And it's a useful record to myself if I ever wanted to crunch something weird. Like the odds of succeeding twice if you repeatedly forged at low chance 10 times in a row. Though I have no idea why I would ever do that.

But we're arguing exactly the same theory/point, so we're in agreement really.

Mon, 10/21/2013 - 10:58

#17

Aiden-Curry-Puff

Using the Data

I should probably warn people that they should make sure they know what they're doing if they come across these numbers.

If you were looking at

80 = 1.25 expected try * 2 units = 2.5 units for success
40 = 2.5 expected try * 1 units = 2.5 units for success

you might think it doesn't matter which of the two you choose, assuming you had 2 units to burn.

It actually does. Forging twice at minimum 40% would actually give you a 64% chance of succeeding on either try. For that price you could have an 80% chance.

ref: 0.64 = 0.4 + 0.4*0.6

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Something I've been wondering for a while (Forge related)