I’m just a casual player, so I don’t have tons of data, but I did go through most slots and tried to get 200+ gambles on each (didn’t make it with weapons or amulets). Below are my results. Odds = odds of getting this many legendaries or fewer assuming a 20% legendary rate (computed using BINOM.DIST(legendaries,gambled,0.2,TRUE) in Excel). Unless indicated otherwise, gambles all occurred on my main, a Necro.
Slot Gambled Legendaries Success_rate Odds
Helm 201 44 21.8% 77.8%
Boots 237 26 11.0% 0.015%
Belt 200 31 15.5% 6.3%
Pants 200 44 22.0% 78.9%
Shield 207 47 22.7% 85.5%
Gloves 202 43 21.3% 71.1%
Chest 209 22 10.5% 0.018%
Shoulders 204 38 18.6% 34.9%
Bracers 215 34 15.8% 7.1%
1-hand Weap 43 11 25.6% 86.5%
Quiver 201 40 19.9% 52.8%
Orb 221 29 13.1% 0.50%
Mojo 210 58 27.6% 99.7%
Phylactery 209 40 19.1% 41.8%
Ring 223 23 10.3% 0.008%
Amulet 41 9 22.0% 70.4%
Ring(Wiz) 122 7 5.7% 0.001%
Helm(Wiz) 64 13 20.3% 59.8%
From this, and from reading what other people have posted, I am pretty convinced that Boots, Chest armor, and Rings are either not doubled, or were doubled but started at a lower legendary drop rate. (Since nobody has ever postulated that these slots drop legendaries at half the rate of other slots, I’m more inclined to believe that the buff just isn’t working on these slots.)
Orbs seem low, and Mojos seem high, but those numbers aren’t so far out of the realm of possibility that I’m convinced anything is amiss there.
Bottom line, I would avoid gambling rings, chest armor, or boots.