Well, I can tell you for sure how it doesn't work. Even though it lists them as "random recipes" the wiki leads players to beleive certain recipes work for certain items. It boggles my mind how often I listen to people chatting around the oven... people with capped or nearly capped synth, discussing what "recipe" they've been using to get ____ (fill in the blank rare synth-exclusive item worth money).
I blame the wiki for this sort of mentality. The "list of recipes" is nothing more than a very short, very incomplete list of results people have gotten in the past. There is no data on how many times a particular "recipe" was tried, and what other items were produced with that same mix of items.
Random synthing is just that: random. Unlike other skills where a recipe of x+y+z=$, synthesis clearly works in a completely different manner. Anyone who has worked on it even a little bit can tell you that putting in the exact same mix of items 10 or 20 times will result in a variety of things, while changing the mix around to different items can end up producing some of the same variety of items.
My theory, based on what I've observed in my own training of the skill to cap, and watching others, is this: when you put three items into the oven, the game takes the average npc gold value of the three items, and uses that as a base. a random variation is applied, which typically results in a lower value, but can uncommonly be higher. Potential items with similar npc gold value form a table of possible results. This table is then weighted by the types of items in the mix... bows in the mix add weight to bows on the result table. Shields add weight to the shields on the result table. Etc. Note that multiple items in the mix of similar type all add weight to those types of items, and with three similar typed items the resulting table is heavily weighted towards items of that time, and more often produces an item of that type than anything else.
We can see this happening in several ways. When you train the lowest ranks, one of the easiest ways to train is kicking posts, buying cheap crystals from Eahba, arrows, paper... random junk that typically has 0-50 gold value. The output of these items is typically other items of similar value. When training off of gathering knives however, the produced items are gathering knives more often than not, but when not typically are clubs, wooden blades, and sticks. fairly rarely will you get something like a small green gem or large nail.
When training clothing requirements, popo's skirts are a popular choice due to their low cost. However, unlike gatheirng knives, skirts drop a wider range of items. My guess is that the 600g average price has a lot more similar value items than the 80g average price, and that of those items, not many are clothing. Mongos traveler suits on the other hand are bit pricier, but perform more stably in terms of producing clothing items.
So my "recipe" is any three items, with the following guidelines to help improve your odds: average npc gold value of the three items equals or exceeds that of the finished item (preferably exceeds it by a significant amount; have not tested if there is a point of "going too high" or not). Include if possible 1 or 2 items that share some kinds of type similarity (again, what exactly qualifies for one type or the other is not fully expored out yet) or 3 if you can still maintain a high average.
The last bit of advice is repetition. Even with the perfect set of synth materisl, you're still likely to need several attempts to get the item you want.
Copied and pasted, this seems like a good start for personal research~