I was thinking about the chance of get a legendary engram and earn a legendary item when figured out how the drop chance is low, but nothing compared with the drop chance plus the engram chance of earning the desired item.
If you read on some posts, you'll notice the chance of at least 1% of purple engram dropping, the same for earning a legendary item from this engram, so, let's calculate the chance of earning a legendary item:
0,01 (1%) * 0,01 (1%) = 0,0001 (0,01%) or 1 in 10.000 drops.
It's not saying the earned item is the desired item, so, you'll need to divide it with all the slot type of equipment and then divide again with all the legendary items inside that slot type.
0,0001 / 7 Slot Types / 30 (random number of legendary items of that type) = 0,000000476 (0,0000476%) or 1 in 47.600.000 millions.
It's a chance, even if you kill 47.600.000 monsters, your chance of drop one purple engram still attached with the probability of never earning the desired item.
Well, I don't want complain about it, just want show for you how hard is your chance of earn the desired item is at least a real lottery.
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http://www.bungie.net/en/Forum/Post/70451100/0/0/1
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The chance to get a Legendary item from a Legendary engram is not 1%, it is MUCH greater. From my experience, I got Leg 75% of the time. I am including in that 75% the one time I got an Exotic weapon from a Legendary engram. But, in my experience, the 1% figure is to high for Leg drops. When I got the grimoire card for 2500 kills, I forget how many I found (I don't feel like calculating from the figurees I do know), but the Leg Engram drops occurred at a rate of .0016% So, in my experience, the chance of a Legendary engram to drop and then to get a Legendary item is .0012% which is RIDICULOUSLY LOW. Your remaining calculations and reasoning are unsound. There will be more than one item a player would want. Using me as an example, with a Legendary Heavy Weapon Engram, I would want a fusion rifle because I already have a Leg shot gun and an exotic sniper. Any fusion rifle will do, so there is 1/3 chance that I will get what I want. .0012% * 33% = .000396% -blam!-IN RIDICULOUSLY LOW
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Your data is miserably flawed in that you have absolutely zero empirical evidence towards that 1 percent number.