I would like to add, that for many people including me, who just play every now and then, the gold/win ratio is more important than just the amount of gold you get from a quest. For example a two class win 40 gold quest gives 20 gold for a win, while a 60 gold quest just gives you 12 gold. This is why I like 40 gold quest more than 60 gold ones. It often happens to me that I don't have the time to complete a 60 gold one at one day. And I don't like to miss quests, because my quest log is full.

@Rob That's actually a really excellent point. It might bear you asking and answering a question about maximizing Gold per win.

Answering this hypothetical question would be much more complicated than your calculation, because there are quests which don't need a fixed number of wins to complete. Those you can complete by the way, while doing other quests at the same time. I picket the gold/win ratio, because it was easy to describe. What is actually more important is gold/time.

@freekvd A 33.3% chance of success says that on average one in every 3 picks should be successful. Quests have already been picked once when we get them, and thereby with two more Drops they should resolve to a 60 or 100 Gold quest. Which is why I am only recommending dropping the 50 Gold quests if there is the possibility of Dropping the same quest slot again tomorrow. You'll notice that in the event that there are no empty quest slots I recommend against Dropping 50 Gold quests.

I feel stupid for not considering the amount gained or lost. 42% chance of -10, 33% of +17. And for not carefully reading your entire answer. Thanks for trying to explain.

@freekvd No worries, we have all speed misread an answer. It does probably point to the fact that I should compress and reformat the answer to make it less reticent. Someday...

@Rob great point about gold/win and gold/time. I never drop the non-class-specific questions (Destroy Them All, Only the Mighty, etc) for that reason. You can progress on them in any mode and make progress even in a loss. Also, don't forget that even though it isn't in the quest log, Tavern Brawl is essentially a 100-gold quest that is repeatable every week.

I just realized you're going to need to redo your math. I'm fairly certain you can't get the same quest you just dropped so it would be out of the 8 remaining classes you could get a quest for. So your chances should be out of 35 and not out of 36. Not trying to nitpick, but math is usually pretty absolute :)

@Sorean If you can confirm that with a link I'll rework. I thought that I had that happened to me just this week, though maybe I misread the quest? If it is possible it should happen 1 out of every 36 Drops, or 2.8% of the time, and I must confess, this week is the first time I've seen it and I've definitely dropped more than 36 quests.

hearthstone.gamepedia.com/Quest Under the replacement section. "Players can choose to abandon up to 1 quest each day by clicking the X in the corner of its plaque in the Quest Log, immediately receiving a different, random quest in its place." It also states that you can't get a quest you are presently on. So I would preface your answer saying that the math is based on having no other quests in the quest log unless you feel like doing the math for all the other scenarios too. (That would make this an awesome answer!)

@Sorean I had an exciting (long) weekend, but I finally got back around to updating this. Thanks for helping me make it an awesome answer :D

No problem, I'm a pretty avid HS player and this saved me the trouble of doing the math myself ;)

Is it possible to drop the quest over and over or is there a limitation on the number of drops?

@Don'tclickonmyprofile Yes it is possible to drop a quest as many times as you desire. A quest obtained from dropping another quest is distinct only in the mind of the player. I just completed a quest when it finally went to 60 Gold that I had dropped 5 times :S

@JonathanMee so I could actually drop quests till I eventually get my 100g quest?

@Don'tclickonmyprofile Quoted from the answer: "If there were an infinite number of Quest Slots the right solution would be to just Drop until all quests were 100 Gold quests. But because there are only 3 Quest Slots, shooting to beat the average seems to make the most sense." This average makes sense for a couple reasons, 1. There's a chance that dropping a quest will earn you a quest you can't avoid completing while competing your most valuable quest of the day. 2. While trying to get a replacement 100 Gold quest you may hit a situation where all your slots are 40 Gold quests.

@JonathanMee Well okay, thank you for your response :)

This screws up the math a bit, but you can also only get Total Dominance once every four days (after you complete it). Which was confirmed during the time you could infinitely re-roll quests due to a bug. The Watch and Learn came after that bug so I am not 100% sure about that one.

@Halfwarr That is excellent information. Alas, that would need to go into state as well. And that would greatly complexify the issue. I did most of the math for this by hand. My first step will be to automate this, which in and of itself is an undertaking, so it'll probably be a couple months before I can roll that out, but as you can see from the edit history I'm always working on improving this, so I'll comment back at you when/if I'm able to improve the state again.

@JonathanMee Excellent! Just wanted to let you know. With the new format I wonder if we will get Wild/Standard quests so that could also even further screw the math.

@Halfwarr Yeah I was despondently wondering that myself :( I love(d) HearthStone, so I'm going to have to give Standard a try, but we all know that Wild will collapse under it's unbalanced weight (otherwise they wouldn't have introduced Standard.) When that happens... well, let's just say I'll wait a couple months to see if I want to invest more time into HearthStone.

@Halfwarr I haven't been able to find any confirmation on the 4 day cooldown. I did find a suggested 3-quest cooldown: us.battle.net/hearthstone/en/forum/topic/13681658472#6 Do you have a source on the 4 day thing?

@Halfwarr I was able to find someone claiming to have gotten 2x100 Gold quests in a row it's unclear whether those were the 2 100 Gold quests or the same 100 Gold quest back to back. Of course the counterpoint made in the same thread says there is a 4 quest cooldown based on 2,183 rerolls Incidentally, that seems like too specific a number of rerolls to be the truth... Just sayin.

@JonathanMee I was speaking with personal/anecdotal evidence when the re roll bug was happening I exploited it and could never get the the 100 Gold quest until the 4th day.

@Halfwarr That seems to be in keeping with the suggested 4 quest cooldown. I'll see if I can crunch that info too and let people choose whether they believe in a cooldown. Right now the shear number of combinations overcome Spreadsheets. I'm testing some C++ to see if I can crunch the info... so stay tuned. I'll respond when I have more info.

@Halfwarr So... I wrote some C++ to generate the spreadsheet for calculating with a 4 quest cooldown. It turns out there are 2,088 potential combinations. I'm... not sure how to add this information to the answer. Honestly it's a bit overwhelming cause you need to remember the last 4 quests you've completed to know whether you should pre-drop, post-drop, or not drop quests. In the meantime if you want to look at the code you can find it here: ideone.com/hQbzZL

@Downvoter I'd appreciate a comment as to why this was voted down. I personally feel that this is an excellent answer and I've invested enough of myself in this answer that if you think there's something that can be improved I'd love to jump on it.