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Sorcerer's Homecoming: Elusive Daily Exclusive

Lady Croft

Seeker
I realize it's free (actually, I do buy diamonds), I realize it's just a game...

I had 3500 sorc's points... and it was the day for the Unexpected Morning... so, I thought, I should get a few with that many points! I only need 2, 3 would be nice and 4 would be very helpful.

At the end of my 3500 points, spent on low medium and high turns, guess how many Unexpected Mornings I had won?
NONE.

Disappointed? Nah, not in the least. Scratching my head at the numbers game so should have got at least ONE out of that amount? Nah, of course not. :/
Really? None at all? How come? That's 100 goes (194 if I only did the 18p ones). So I got a load of other stuff; great... but it makes no sense at all to receive no buildings whatsoever.
... Sigh...
 

Gargon667

Mentor
I realize it's free (actually, I do buy diamonds), I realize it's just a game...

I had 3500 sorc's points... and it was the day for the Unexpected Morning... so, I thought, I should get a few with that many points! I only need 2, 3 would be nice and 4 would be very helpful.

At the end of my 3500 points, spent on low medium and high turns, guess how many Unexpected Mornings I had won?
NONE.

Disappointed? Nah, not in the least. Scratching my head at the numbers game so should have got at least ONE out of that amount? Nah, of course not. :/
Really? None at all? How come? That's 100 goes (194 if I only did the 18p ones). So I got a load of other stuff; great... but it makes no sense at all to receive no buildings whatsoever.
... Sigh...
It is highly unlikely, but obviously not impossible :) Which of the beacons did you choose? Not saying that it is your fault, for that amount you should certainly have gotten a daily prize, no matter which ones you choose, but it does help to pick the right ones if you want the daily prize next time.
 

Sir Derf

Artisan
The beacon with the lowest probability still had a 6% chance of giving a Daily, the odds only go up from there.

Even picking that lowest 100 times, you would have expected about 6 Dailies.

What are the odds to get 100 non-Dailies from a 6% chest?

(0.94)^100 = 0.00205, or 0.2%, or 1 in 500.

Felyndral currently has just over 43,000 players. About 86 Felyndral players could expect to see the same.

Low probability that it will happen to you. But, it will happen to an impressively large quantity of players who represent a small subset when you have a large enough player base.
 

Pauly7

Magus
That's extraordinarily bad luck, but unfortunately it happens. That's the problem with this style of event. There can be good rewards or you can end up with nothing. In that regard shuffle events have a benefit where you are always going to find the daily after a certain point.

At the other end of the scale, today I started opening beacons and I had absolutely zero interest in the daily prize. I spent 1,800 SK and ended up with 12 Copper Dragons. I'm going to have to open some sort of dragon sanctuary now.
 

Gargon667

Mentor
Wow there are already 43 000? Well anyway say 10% of those actually play the event earning enough to be in such a situation, that is still an impressive 10 people making the same experience :D

Now there´s a math problem for you @Sir Derf: How many daily prizes do the 86 luckiest people get choosing the worst chest 100 times?
 

Sir Derf

Artisan
Before your challenge, I wanted to consider what the theoretically unluckiest player in Felyndral might do.

What is the 1:43,000 player experience?

(0.94)^x=1/43,000

(0.94) ^ x = 2.33*10^-5

log(0.94) * x = log(2.33*10^-5)

x = log(2.33*10^-5) / log(0.94)

x = 172.4

It is expected that 1 player in all of Felyndral could experience 172 unsuccessful Daily attempts from a 6% chest.
 

Lady Croft

Seeker
I tried all different beacons. I varied them as I was also hoping for mana and KP.
Today I found the same with the Copper Dragons; I had 350 points and got all of 1.
Also, I'm not sure if I'm going to get 14 more moves in to get the last set piece with 6 points remaining and whatever I get between now and the event end.
Also, this is Wynyandor, over on Felly and Aren I fared better.
 

Gargon667

Mentor
It is expected that 1 player in all of Felyndral could experience 172 unsuccessful Daily attempts from a 6% chest.
You lost me there, but given the previous result this sounds like a reasonable outcome. But just imagine being that 1 person, even I would sit there screaming at my laptop after 172 unsuccesful tries and I consider myself a patient guy. So I really hope for this one person that there is somewhere a mistake in this calculation.... Then again if I wanted that daily prize I wouldn´t choose the crappiest chest, so I guess I am safe ;)
 

Pauly7

Magus
Today I found the same with the Copper Dragons; I had 350 points and got all of 1.
That one is just slightly unlucky. If you opened the best beacon for dailies every single time (the 32 beacon) then it should, on average, cost 236 SK. If you constantly opened the worst beacon for dailies (the 80 beacon) then it is likely to cost you 325 SK to get the daily.
 

Gargon667

Mentor
I tried all different beacons. I varied them as I was also hoping for mana and KP.
Today I found the same with the Copper Dragons; I had 350 points and got all of 1.
Also, I'm not sure if I'm going to get 14 more moves in to get the last set piece with 6 points remaining and whatever I get between now and the event end.
Now that is really a rather normal outcome. 1 for 350 is more or less what you would expect, or let´s say 2 would have been extremely good luck ;)
 

Sir Derf

Artisan
Now, as to your challenge...

First of all, the question is either "How many does the 86th luckiest person get?", or "At least how many do each of the 86 luckiest people get?".

Having said that, let's dive in...



(0.06)^x * (0.94)^(100-x) = 0.002

log(0,06)*x + log(0.94) * (100-x) = log(0.002)

log(0.06)*x + log(0.94)*100 - log(0.94)*x = log(0.002)


x * (log(0.06) - log(0.94)) + 100 * log(0.94) = log(0.002)

x * (log(0.06) - log(0.94)) = log(0.002) - 100 * log(0.94)

x = (log(0.002) - 100 * log(0.94)) / (log(0.06) - log(0.94))

x = (-2.69 - (-2.69)) / (-1.22 - (-0.027))

x = (-0.011755) / (-1.194977)

x = 0.0098


Well, that doesn't make sense.... Gonna have to ponder this a little bit...
 

Sir Derf

Artisan
Hah, forgot the Combinations. Think I need to add a (100!) / ( x! * (100-x)!) to the above. Ick.

Gonna bust out a spreadsheet on this one. Back in a few.
 

Sir Derf

Artisan
Well, that did it.

(0.06)^x * (0.94)^(100-x) * 100! / (x ! * (100-x)!) = 0.002

Grand Prizes DailiesOddsPlayers
0​
0.21%​
88​
1​
1.31%​
564​
2​
4.14%​
1782​
3​
8.64%​
3716​
4​
13.38%​
5751​
5​
16.39%​
7048​
6​
16.57%​
7123​
7​
14.20%​
6106​
8​
10.54%​
4531​
9​
6.87%​
2956​
10​
3.99%​
1717​
11​
2.09%​
897​
12​
0.99%​
425​
13​
0.43%​
183​
14​
0.17%​
73​
15​
0.06%​
27​
16​
0.02%​
9​
17​
0.01%​
3​

So, the 6th 86th (or 88th) Luckiest player from 100 6% chests would expect 14 Dailies.
 
Last edited:

Sir Derf

Artisan
Bear in mind, it is possible that a person could get 100 Dailies from 100 6% chests.

That's a 6.53 * 10^123 chance.

Ah, I love the smell of semi-pointless math in the morning!
 

Gargon667

Mentor
So, the 6th (or 88th) Luckiest player from 100 6% chests would expect 14 Dailies.
If I look at it it seems that 112 people will get 14 or more dailies (btw you called them grand prizes in the table), but I guess that the 88th or whatever it was would be in the 14 dailies group, because only 39 get better than that. right so far so good, but there is one thing I don´t understand, I wonder if you can explain that:

Now the highest probability outcome is 6 dailies, which makes sense since we have 100 tries on a 6% chance, but how come it is nearly as likely to get 5, but much less likely to get 7? Also if I add up all the probabilities below 6 dailies it is much higher than adding up all the probabilities above 6. Something else hinting at 6 not being exactly in the middle... Does that make sense?
 

Sir Derf

Artisan
Yes it does make sense.

To your first paragraph...

6% chance you get it, 94% chance you don't. Not quite even between the two, is it?

Dropping from 6 to 5 means dropping one 6% chance and replacing it with a 94% chance.
Rising from 6 to 7 means dropping one 94% chance and replacing it with a 6% chance.

To your second paragraph...

One-humpy distributions aren't necessarily symmetrical.

By the way, look where the median player falls in this progression, player 21,500. Add 0-5 and you get 18,949. That means player 21,500 is 2,551 into the 7,123, 35% in.

This is not a bell curve.
 

Gargon667

Mentor
Clearly not a bell, well I didn´t exactly expect a bell with having 94 different outcomes on one side of the 6 and only 6 on the other side, so I expected asymmetrical, but I thought the 6 would be at least in the middle in terms of probability. Guess not!
But yes your explanation makes total sense why 5 is more likely than 7 :)
I suppose the only symmetrical distribution would be one of 50% chance one side and 50% the other side, that way both, number of outcomes and probabilities, are the same on each side of the middle.
 

Gargon667

Mentor
btw. sorry @Lady Croft for hi-jacking your thread, this was certainly not what you were going for initially, but of course let´s blame somebody else because Orcs are never wrong!
 

Arnwald

Adventurer
I hate this event. There is absolutely no reason to have T1/2/3 manufactories in the city in the last chapters. Except for events like this, where standard goods need to be produced in every second task.
 

m4rt1n

Mentor
RNG, any outcome is possible, but I love the discussion.

Maybe, some dev is sat in the Hamburg office controlling each outcome individually while having a stein of beer just relaxing and enjoying the controversy.

@Sir Derf out of interest are you the winner of Lotto and Euromillions regularly lol :p