A player posted his recent gambling results in an eventually successful effort to obtain the ultra-rare legendary gloves, Tasker and Theo. How long did it take? How many other legendary gloves did he get in the meantime? Here are some extrapolated Gambling Odds for Diablo 3 Legendary Items:
36,000 total blood shards spent. 112 legendary gloves dropped
Recall that Legendary Drop Rates in Diablo 3 work with the game first deciding on a legendary (including set) of an item type, and then selecting one of the possible legendary/set items of that type for your character, all of which are weighted. This guy was playing with a Witch Doctor, and since legendaries via gambling are always Smart Drops, you see the 2 WD set gloves, but you do not see any gloves from other the class sets. (You will get those once in a while from monster drops, via the ~15% of items that are non-smart drops).
As for item frequency, the legendary items of each item type in D3 are classified as common, uncommon (1/2), rare (1/4) and ultra-rare (1/10). These frequency figures match those odds quite nicely, with the Pride of the Invoker, Helltooth, Jade Harvester, and Gladiator Gauntlets all roughly the same drop rate. St. Archew’s Gage is the only outlier, since it’s common like the others. Magefist is uncommon for a Witch Doctor, and should roll about half as often as the most common ones, which it did. There aren’t any rare type gloves with 1/4 rarity for the WD, and Frostburn and TnT are both ultra-rare, at 1/10th the drop rate of the common ones.
As for the overall legendary rate, that’s useful data as well. Gloves cost 5 shards per gamble, so 36,000 / 5 = 7200. Divide that by the 112 legendaries he got and that’s 1 leg for every 64.3 gambles, for a 1.5555% legendary gamble rate.
Obviously this isn’t the final scientific rate, because RNG, but extrapolting from that gives us some useful figures:
This assumes all items are weighted the same in legendary gamble rate, and that there’s no “mercy” gamble success counter. I wouldn’t be surprised if there are some oddities like that, such as slightly higher legendary gamble rates for more expensive item types? It would be fascinating to compare these to other gamble charting results, especially of item types other than armor.
Finally, casual players might gape at the idea of ever earning 36000 Blood Shards, but Shards are quite common at the high end. Rift Guardians on Torment 1 drop 50ish, and on Torment 6 they cough up around 100 each time. Since really well geared characters can do T6 as fast (or faster) than more casual players can clear T1, the shards can really stack up at the highest levels of play.
Update: Literally while this post was being written a new Patch was being applied, with big changes to gambling:
While Kadala is doing a great job of giving players more control over finding specific items, we felt the current experience was a bit cumbersome and inconvenient. As a result, we’re working to reduce the frequency at which players need to run between Kadala and the Blacksmith to salvage unwanted items
This sadly invalidates all of that useful data collected above, though it should improve the overall experience? We need data for the new system, though! Anyone who gets some gambling in the new patch, please record your total legendary per shards spent, and share the results!