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Seeking input on UV calculations

4 replies [Last post]
Mon, 03/28/2016 - 19:29
Ultimaximus's picture
Ultimaximus

I currently have a Winter Grave with ASI High on it. However, since my default loadout already gives me max ASI on all guns, I figure having CTR or even Damage vs Gremlins would be more helpful. Since it feels bad to just throw away ASI High, I figured I should just roll these as a 2nd UV. However, I got into a debate with a friend about some calculations I was doing.

I figure that since there's 7 different UV types I can get on a gun other than ASI, and I only want 2 of them, the chances of succeeding are 2/7 or 28.5% on the first roll, ~50% on the second roll (5/7 * 5/7 = 25/49), and ~63% on the third roll. My friend is saying that there's no way the odds can be this high, so I went and looked into it in-depth from a mathematical perspective. I made this quick write-up, and I wanted to see if anyone had any input on it. Am I horribly wrong? Is my math sound? Does SK have hidden biases (like that rumour that if Punch gives out a good UV, he won't give out another for some amount of time or rolls for that particular Haven instance)?

https://docs.google.com/document/d/1izr1JK6uX2tPhIYuFxU05jGUazOpcB9W5Cpc...

Sorry if it's hard to read, it's just a single-draft quick write-up I did

Mon, 03/28/2016 - 19:41
#1
Bopp's picture
Bopp
obligatory

You may want to read this:

http://wiki.spiralknights.com/User:Jdavis/UVs#Second-UV_Strategies

It tells you how to put a second UV on an item that already has one UV. The guide as a whole is unfinished, but this section is solid.

I figure that since there's 7 different UV types I can get on a gun other than ASI, and I only want 2 of them, the chances of succeeding are 2/7 or 28.5% on the first roll, ~50% on the second roll (5/7 * 5/7 = 25/49), and ~63% on the third roll. My friend is saying that there's no way the odds can be this high

Assuming you lock the first UV (and you'd be crazy not to), the chances are 1 / 7 for getting the second UV. But it is probably +1, not the +3 or +4 you were hoping for. After that it just gets worse. Let me know if I've misunderstood you.

Mon, 03/28/2016 - 22:01
#2
Ultimaximus's picture
Ultimaximus
P = 1, T = 8, 2 / (T - 1)

P = 1 since I don't care for the strength of the UV, and T = 8 since I'm using a gun. The probability of getting the type I want changes from 1 / (T - 1) to 2 / (T - 1) since there's two types I'll be happy with. Concretely, originally the chances are 1 / (8 - 1) = 1/7, but now the chances are 2 / (8 - 1) = 2/7.

The way the author gets the final value of C2 * (T - 1) / P from the proposed series is beyond me, since I dropped out right before that class, so I'll calculate it manually. I do indeed get a number that asymptotes towards 525kcr, which means that I did it correctly (I also get similar results to the chart when I change P to 0.34 for Med and Higher or T to 4 for shields).

When I use my modified equation SUM-K (1 - 2 * P / (T - 1))^K * 2 * P / (T - 1) * C2 * (K + 1), then I get 262.5kcr... which is just half of our previous value <_<

That's about 3.5 Punches, which according to my graph is a ~68% chance of succeeding.

EDIT: Oh I didn't even realise that you were the author of that page

Tue, 03/29/2016 - 06:52
#3
Bopp's picture
Bopp
oh, sorry

Sorry, I somehow missed that there are two UV types (CTR or gremlin) that you would find acceptable as your second UV. Yes, that completely changes the calculation.

Yes, you have a 2 / 7 chance of getting one of those two UV types. The expected number of rolls is therefore 7 / 2. Each roll costs 70,000 crowns. So your expected cost is 245,000 crowns.

There are other aspects of the problem that you might compute: how unlucky you'd have to be to spend such-and-such, etc. I haven't checked your 68% figure.

Mon, 04/11/2016 - 20:36
#4
Ultimaximus's picture
Ultimaximus

It took a total of 11 rolls. That's 825,000 crowns. Eggghhhhh. I know it's all averages, but the results with SK's RNG I've had over the years is just so discouraging.. Failing 10 rolls is a 3.39% chance..

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