When I saw these at first I thought of idioms. When double words are put together, is there always a special meaning? Are there any rules to using double words?
As a complementary to @user3306356 's answer,
there are some variations of 叠词 (I couldn't cover all of them, but I will list out some for your reference :) )
The syntax would be
AA(n.), for example:
吃吃東西 : Eat something
畫畫圖畫 : Draw something
2. Adjective （BAA）
Usually in a form of
紅 has the meaning of RED, however 彤 in
紅彤彤 refers to 丹砂 (a red-color ink), which decorates the adjective
白雪雪, 雪 means
snow, which gives
白雪雪 a meaning of "Snowy white".
There are more than one way to describe a single colour in different context, such as 白茫茫,白皙晢,白花花,白蒼蒼,白皚皚 etc.
3. Adjective/Adverb （AA / AABB）
We can consider words in form of AA / AABB as 疊詞 as well,
For example, 重重疊疊 (Piles over piles) and 彎彎曲曲 (Curvy, in twist and turns)
4. Adjective/Adverb （ABAB / ABAC）
In Chinese language, we also consider the form ABAB and ABAC as 疊詞.
自由自在, however most of them are idioms. We often use double words to emphasize the story itself.
Sometimes, 疊詞 are just used as onomatopoeia (word that phonetically imitates the sound itself)
潺潺, pronounced as 'san san', which imitates the sound of flowing water.
淙淙, reads 'cong cong' also refers to the sound of water
There is a famous poem《聲聲慢》by 李清照(Li Qingzhao), a poet from Song dynasty which starts with 14 words of 疊詞, is a masterpeice of double words.
尋尋覓覓， 冷冷清清， 淒淒慘慘戚戚
Some people tried to translate the lines into English:
尋尋覓覓， I seek in vain, I search in vain;
冷冷清清， Chilled to the bone, all alone;
淒淒慘慘戚戚。 In pain, in tears, unconsolable.
Finally, my answer
So, where does
好事 means "Good things",
連連 means "Again and again" or simply "repeatedly"
It's in a (n.)AA format, which means literally "Good things happens repeatedly" (It's really a good fortune).