The base rate of receiving the thread is 1/10. To mitigate bad luck, the rate is scaled linearly with the number of raid completions, up to a maximum of 3/10 upon completing 15 raids.[1] Once the player gets their first thread, the drop rate is decreased to 1/50.[2][3]
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References
^Jagex. Mod Ash's Twitter account. 15 May 2023. Archived from the original on 5 August 2023. Mod Ash: "[(...) The bad luck protection for jewels. Does it cap out at 90 or 270 raids? I.E. 60x1,5 or 180×1,5. (...)] I think it's 1.5 x 180 like you said, so 270 - if I'm reading my colleagues' code directly. (...)"
^Jagex. Mod Ash's Twitter account. 5 May 2023. Archived from the original on 5 May 2023. Mod Ash: "[Can you confirm the drop rate of the Thread of elidinis after getting the first one? Is it 1/10? I haven't seen a single duplicate thread for almost 200 raids after losing it.] No, if I'm reading the loot code correctly (which isn't a sure thing, as it isn't something I ever worked on myself) it changes to 1/50 after you've had one of those."
^Jagex. Mod Ash's Twitter account. 24 April 2023. Archived from the original on 6 May 2023. Mod Ash: "I'd wonder if that 1/10 advertisement was massively over-simplified. It looks to me like it's affected by whether you already have the jewels, as well as whether you already had a thread (moving the chance to 1/50 as you say)."
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