Searching for eggs by: German data* analysed using mathematical expected value
Fast search - 6h (LAST PLACE): 1 = 6%, 2 = 20%, 4 = 10%, no = 64%
0,06+0,4+0,4+0=0,86 egg per search
0,86/6h=0,14(3) per hour ~= 3,44 eggs per day
Medium search - 12h (2nd PLACE): 1 = 14%, 2= 24%, 4 = 28%, no = 34%
0,14+0,48+1,12+0=1,74 eps
1,74/12h=0,145 /h ~= 3,48 eggs per day
Long search - 24h (3rd PLACE): 2 = 37%, 4 = 56%, 7 = 7%
0,74+2,24+0,49=3,47 eps
3,47/24h=0,14458(3) /h ~= 3,47 eggs per day
Very long search - 48h (BEST): 7 = 100%
7 eps
7/48h=0,1458(3) /h ~= 3,5 eggs per day
Those are average values you might expect.
As we see there is not big difference between best and second place and even smaller between 2nd and 3rd, nevertheless we have only few explorers and cannot do hundreds of searches to give theory of probability do all work
so searches with possibility of no eggs at all (6h and 12h) are even less profitable for us.
And beside having better expected value and no risk of getting nothing, longer searches needs less effort.
And one more conclusion: if this event will last three weeks (!) then we have 21days x 3,5 eggs = 73,5 eggs in three weeks...
*http://siedler-vision.de/das-osterevent/