So, there are some assumptions in this thread. But hopefully, I've kept track of them well enough that you can follow along. @Sofaking and I were chatting yesterday about the odds of finding specific items in Cardhunter (among other things), and I got to working out some of the math. Here's what I did: I made a spreadsheet figuring out the odds that any given one of those legendaries would drop over days of farming, using the handy function that figures out that kind of probability. There are around 42 tokenless legendaries. You also don't see a few legendaries in every mission, but you do see a few of the higher-level, blue token legendaries on the missions you're likely to run (because almost all of them are level 6 or 7, so again, it about evens out (as we're just ballparking, here). Given that, I set the odds at about 1/50 of any given legendary dropping, because that's nice and round. Sofaking told me he averages about 1 legendary per day of SP farming, so I set the time interval to 1 day - each row on the sheet represents a new day of Cardhunter-ing. Conveniently, this also syncs up with the daily deal's time cycle, so I added a column representing the odds of getting any specific item from the daily deal. Then, to be thorough, I also added in the odds for Randi's every seven days. Both of those odds are taken from the total set of all legendaries that can be dropped normally - Base, both expansions, and AA - and so they're probably more useful to people who aren't just looking for specific tokenless legendaries. Then, I took all these numbers, and, like mathematicians do, mashed them all together in a horrible display of fraction-on-fraction violence. This gave me my fourth and fifth sets of odds, a measure of your odds of finding that one legendary over a full week of Daily Deals and a Randi's, and the odds you'd have if you were ALSO grinding that whole time (which I titled "Balls-to-the-wall odds", because that's clearly where they are at that point). The DD + Randi's section is calculated by taking the Randi's odds, and factoring in each new day of Daily Deal as it happens, which is why it seems to jump a bit more dramatically at the beginning of each new week - that Randi's infusion of 10 more Legendaries into your chances. Balls-to-the-wall is just that with the farming odds factored in. Finally, I took your chances of getting any given item, and factored in how many items there are to get. The result is a VERY rough estimate of how many items you're likely to have left to find. It's inaccurate on the low end and high end, but is a pretty good guideline for the scale of how long it takes to find forty-odd items in the game. Some interesting finds: A Parry succeeds 83.33 percent of the time. One at least one of two parries succeeds 97.22 percent of the time. That means your odds of a single parry failing are 16.66%, and your odds for two parry fails in a row is 2.77% You are "Parry Fail" unlucky if you haven't found your item after about 90 days (3 months) of pure grinding, approximately 43 Randimars (or 301 days), or far more than a year's worth of Daily Deals (estimation says 460 days, didn't want to ctr-v and check). Checking both DD every day and Randi's every week, it's about 175 days (about a week under 6 months) to get to Parry Fail levels. If you go Balls to the Wall, you get to Parry Fail about day 60, or two months. You hit DOUBLE Parry Fail levels around 180 days (again, just under six months) of pure grind, or after about 120 days (four months) of BALLS TO THE WALL. A perfectly lucky individual (we'll call them Smitty) will complete their task in 14 days, with the coming of their second Randimar's. A perfectly unlucky individual (we'll call them Boxbot) will never complete their task. Fortunately, we're not that guy. That guy is just terrible. A perfectly average person will probably get all 42 items in about 215 days of pure grinding, about (I'd guess) a year and two months of combined Randi's and DD, or 150 days of balls to the wall. Not bad. Now, some meta-stats: I am 100% done with spreadsheets for at least a few days - that was so much math. I spent maybe 3 hours putting this together instead of sleeping or playing cardhunter. Sorcererers are the best clan and this is a true fact supported by all of math. I have a real-life copy of the above statement signed by the abstract concept of math itself. No you can't see it. Yes, it's totally real, just like that collage girlfriend I had while I was in high school. Just trust me, okay? EDIT: Does someone want to summarize this in a way that ISN'T full of snark? I'm really not up to that.
Somewhere I have done also some math. Lets try to find that. Got it: Your numbers are 175 days for finding a specific item in Randis or DD with a 83.33% chance, while I calculated 293 for 90%. I have my data here and it says 206 days when you check both for a chance of 83,33%. I calculated with the 0,77% mentioned above. What is wrong in my calculation? Pure Grinding is doing every league and getting an epic in every league? Also doing the Loot Fairy?
"Pure grinding" in this case, means "playing enough games to average a total of one non-treasure legendary a day from low level SP maps", so of the sets of data, it is probably the least useful for calculating item-finding odds in general. Maybe after I've recovered a bit, I'll go back and add a MP column, see what your odds are for just playing MP games... but Sofaking doesn't really run MP games, so the numbers from that wouldn't have been representative of his experience, which is what I was trying to simulate. I can't speak to your calculation, but here's how I did mine: I went to neoncat's utility analysis on Stexe's site, and put in my info, checking the boxes for Base, both expansions, and AA (but not holiday items, treasure, or promotional items). It said I had some number out of 248 legendaries. So presumably, I have a 1/248 chance of getting any given legendary in the daily deal, and similarly, a complicated to write chance of getting one of ten items in Randi's (because randi always gives you 10 different legendaries, the odds are a little different). Randi's odds are: SUM of 1/248 (odds of finding your specific item in the first slot) + 247/248*1/247 (odds it wasn't in the first slot times odds it's in the second slot) + (246/247*247/248)*1/246 (odds it wasn't in the first or second slot, but in the third slot) + (245/246*246/247*247/248)*1/245 (odds that it's not the first, second, or third, but the fourth)... and so on, all the way up to slot ten, which is + (239/240*240/241*242/241*242/243*243/244*244/245*246/247*247/248)*1/239 It turns out the sum of all that is about 0.04092218751 (at least as far as google sheets is concerned - it rounds a bit). Both of these numbers are a little inaccurate in the long term, as the number of legendaries fluctuates with time, as Holiday items are added and removed from the pool, but in the end that was too complicated to account for so I just calculated based on the rough number of general-access legendaries. I plugged both those numbers into the function, which spit out the odds you see in the sheet. I then took the two sets of odds for any given day - lets call the DD odds D, and the Randi odds R, which my original formulas express as a fraction of 1 - and plugged them into the following equation: (1-D)*(1-R) = the odds that neither Randi's nor the Daily Deal gave you the item in questions. So 1-((1-D)*(1-R)) = the odds that at least one of them did. As for factoring in the fact that Randi's only changes once a week - that was pretty easy. DD odds would increase once a day, while Randi odds only iterated once every seven - you'll notice how in the spreadsheet, there is only one Randi's odds entry every seven rows. So while over the course of a week, the chance that you would see a specific legendary in the DD would slowly increase, the odds you saw it in Randimars would stay the same. A full week of formula looks like this: 1-((1-D1)*(1-R1)) 1-((1-D2)*(1-R1)) 1-((1-D3)*(1-R1)) 1-((1-D4)*(1-R1)) 1-((1-D5)*(1-R1)) 1-((1-D6)*(1-R1)) 1-((1-D7)*(1-R1)) and then next week, you'd use R2 and D8 to D14 instead. All this means I calculated that you'd have 90% odds at around day 229, assuming you did nothing but check Randi's and the DD every day. Given that, and assuming that my calculations are right and yours are wrong (which may not even be the case), I'd guess that you overestimated the odds of finding something in Randi's by just a bit. That's definitely the most complicated part of that mess, and the easiest place to make a mistake. The other place I'd check is how you combined the odds - its possible you might find a difference in our methods there as well that could lead to the difference in results. Hopefully that makes sense!
Huh. Well, as someone who's largely self-taught at math, that's an interesting thing to learn. Does that work for all fractions? Oh wow, seems to! Neat trick! But the rest of what I did checks out? Re-reading things, the likely difference is that you used a higher total number of legendaries. Whoops. Can't believe I overlooked that. Math is hard >.<
Randi's odds are: (number of legendary slots in RR)/(Total number of legendaries available) (what you wrote, essentially). You'd only need to mess around with more complicated stuff if they could be duplicated.
I'm realizing that now I have a history of finding the long way to the right answer when it comes to math.
May I ask what your B column is? Also, what is that L column supposed to represent? Is it over a certain level range or something? Edit: Sorry, L is the tokenless legs, should have read more carefully.
Column B is the specific odds that that day of grinding low-level missions is the one that gives you the legendary you need, expressed as a fraction of 1. To get a total percent chance of success (Represented by column C), I multiply the result from B by 100 and add that to the sum of the previous day's total chance of success (one square above, in Column C).
I calculated with one epic chest per day. Which is also not very accurate. With now four leagues a day you have easily the chance to grind three epic chest per day and a lot more rare chest while doing that. That is the difference. Somehow I got there a wrong number. That explains the difference. But the chance of having 'all' items needed for mp are unfortunatly much lower. With all I want to reference to all for a specific build. The builds with mages and buff priest you will not reach fast as you need some legendaries four times. But even the priest and two warrior builds are hard to complete, as the priest needs a lot of legendaries. A typical mp warrior build needs 3 legendaries on the warriors and 6 legendaries on the priest. This makes 12 legendaries (not taking into account that the priest has 2-3 of the same legendary). The chance to complete your build after 3 month are 83.33% ^ 12, which is 11.21%. To be parry unlucky to not get your build complete you have to grind 16.66% = 88.79% ^ x month which are log _88.97%(16.66%) = log (16.66%) / log (88.97%) = 15.33 month or one year, three month and ten days. Uff, a lot of time as we all need how often parry fails. Lets see how long a DarialStorm like mage deck will take to complete. 7 legendaries on the priest, 4 legendaries on the mages. (Not taking into account the 4x1, 3x1, 3x2 legendaries.) This makes log(16.66%)/log(100-83.33^15) = 26 months. Luckily he uses Sensate's Ring and not Asmod's Telekinetic Chain. The perfect burf build I have in mind would need 7 legendaries on the mages. It will take 47 month for just beeing parry lucky to accomplish that build.
Remember that the math I did was just for grinding out tokenless legendaries via targeted farming. If you're opening up league or MP chests, you could get any of the whole level range of legendary items when one finally does pop up. Also, Legendary-free warriors can be very powerful. I ran a team of two warriors and a priest into the high 1700's, and there were only two legendaries in my loadout, both on the priest. I lied - apparently I'm not done with spreadsheets. Edited the sheets to include a MP/League column assuming you get about 1 legendary every day (of any level, not just of the range you're looking for), and a new Bonus Column showing Balls To The Wall plus MP/League. It looks like it cuts almost a month off your time... but it still takes about half a year to get that full set. It's also interesting to note that if you've spent a half-year grinding out a new legendary every day you'd have about 180 extra legendaries of various kinds, twice that if you also got one from MP and League chests too.
You mean something like my 20 Staff of the Misanthropes, 15 Unholy Nimus and 15 Staff of the Inferno?
Something like that. At least that's how it seems to go. I've never been able to average a legendary per day, but I'm happy for anyone who does.
