Rng is a very simple concept. So is probability. Odds of the voidfang being sold four times in a row is exactly how he put it. If a number lower than 0 is multiplied by itself it becomes lower. Example: you have .5. You then multiply that by itself. So half of .5 would be .25. This is just done four times over with .1666. And by the way, your attempt to scare me with large words doesnt work and makes a fool of yourself.
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You really have no clue how rng works. There is more then one step to how rng works and that changes the math completely. With Xur it is slightly different then the normal rng for killing a mob or end game rewards. 1 step is to see what kind of gear it will be, I.E helm, chest, gloves, primary, special, or heavy 2 step is after the gear type is set, which piece of gear it will be. So the OP is incorrect in how he is doing his math, he is basing everything off of a single rng roll, which is incorrect.
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And, im sorry, do you have any proof of this? The odds are the same anyway. You have a 1/3 chance to get chestpiece, and 1/2 of getting voidfang. 1/3 X 1/2 is 1/6. That results in the same number of odds. And, do tell me of how I dont know RNG