Odds on rolling specific colours on a 6-link

Some time ago I learned the hard way how many chromes it can take to try and roll off colours on an item - and that was just on a four link pair of boots!

I'm looking to buy a 6-link Lightning Coil and am mulling over which way to go as far as buying one. There's only one or two out there with my preferred colours of RRRRBG, so I was wondering what the odds would be of simply buying one of the cheaper ones and hitting it with chromes to get the colours I need. Given that the suit is Armour/Evasion based the odds would be pretty good on getting any combination of red and green I might want relatively easy, while getting the one off-color blue thrown in would doubtless stretch the odds out a bit (I use it for Concentrated Effect). If need be I could live without the blue socket and just go with four red/two green or five red/one green, so the question is what the odds might be on getting either of those two combos? Anyone have any idea on the odds? I mean, I can work out the odds in purely mathematical terms with all things being equal, but obviously given the weighting system used here for specific gear and colours that doesn't apply. Not really knowing what the weighting formula is doesn't help either.

Assume both red and green have same probability. Then use chromes on a 4 socket lightning coil to test the hypothesises blue p = 0.20 and blue p = 0.10. That way you can find out what is most likely to be the proper blue p and then do math to calculate the 6-socket case.

You can always resell the 4 socket lightning coil, so the cost involved in testing would be the chromes, net loss when you resell and time.

Well no, you don't need to use an LC - any four socket item that's evasion/armour based would do the trick. But the mathematics also plays out differently. On a four socket item with only the two colours mentioned in question, and everything working truly to random, only five combinations come into play. That's a miniscule sampling that in no way could indicate the probabilities on a six link. But of course there's a third colour, blue, which gives 15 combinations - unweighted. But because there is a weighting system in place that does have a distinct bias against off colours the odds go up dramatically of specific combinations that involve that specific color. To the best of my knowledge no one really knows what the formula is, thought it would certainly help matters - very early on in my experience of the game and before I learned about the bias, I blew around two hundred chromes, more out of sheer stubbornness than anything else, trying to get a four-socket pair of armour-based boots to turn all blue - and failed! That at least indicated how heavily weighted the bias is.

So no, I'm not going to blow a pile of chromes pointlessly on a tiny sample base trying to work out the variables, when it theoretically should be possible to do the math on paper, at least on the basis of some good guestimates on the weighting system being used. I know there are people out there who have put some effort into that side of things, and it was mainly to them that I was addressing the question.

RRRRBG on coil won't be that hard, few hundred chromes max. It's just 1 off, but chroming hybrid items is generally quite hard.

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timbo1959 wrote:

Well no, you don't need to use an LC - any four socket item that's evasion/armour based would do the trick.

The probabilities depend on the stat requirements for the item. (Higher dex requirement => higher odds of green sockets)

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On a four socket item with only the two colours mentioned in question, and everything working truly to random, only five combinations come into play. That's a miniscule sampling that in no way could indicate the probabilities on a six link.

The socket colors are rolled independently. Each chromatic orb on a 4S spent gets you four data points.

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timbo1959 wrote:

There's only one or two out there with my preferred colours of RRRRBG, so I was wondering what the odds would be of simply buying one of the cheaper ones and hitting it with chromes to get the colours I need.

Rolling one off-color on a 6-socket Lightning Coil is not challenging at all. If the odds of getting an off-color socket were only 10%, for example, you'd have about 50% chance of at least one showing up on each roll. Getting just one green socket, however, may take a few dozen rolls, as there are only 5 out of 32 red-green combos that produce that result.

Well put it this way - if 300 to 400 chromes would pretty well guarantee getting the combo I need than the investment is worth it if I can pick up the LC cheap enough. I guess the insanity would be in trying to get 4 - 5 blue sockets on it! Now THAT I would like to see in terms of how many chromes would be needed, especially after my efforts with the boots.

Still, it would be nice to know how the weighting functions in exact detail, because it would make it that much easier to work out the statistics and probabilities on specific outcomes and thus the merits one way or the other of pursuing particular objectives. In real life there's basically nothing you can't break down on an actuarial basis but in the wacky world of Wraeclast things get a little more nebulous.

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timbo1959 wrote:

Well put it this way - if 300 to 400 chromes would pretty well guarantee getting the combo I need than the investment is worth it...

You will likely have enough Chromes left over to trade in for an Exalt.

Great, that's all I needed to know. Appreciated.

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timbo1959 wrote:

Great, that's all I needed to know. Appreciated.

Also a tip is to make a chrome lottery. Lotteries are an important economic tool for any seasoned veteran.