Thanks for your insight, you're quite the seasoned player and I've read your previous posts on this topic. I'm quite a noob compared to you (Monarch, sometimes Emp player), so please understand I may not have as good an understanding of high level play as you.
Your are welcome. I certainly understand. I've played this game coming on about 13 years now, but I also remember what it was like playing this game before I found this forum and really took steps to learn how to play it. Some good responses so far but I will add my own thoughts as well below. But first I would preface my comments by saying that, if willing, you can learn some things that will totally change your thought process and perspective on the game. These topics are usually discussed over in S&T, which is really where I recommend you spend most of your time in this regard.
Why would you never research IW yourself? I do it all the time, as it reveals Iron for city placement. If you 'lose' on each tech trade, where's the logic in that? I like to keep maths to myself so I can build the Hanging Gardens, by trading it away wouldn't that open up the possibility for the AI to get the Wonder before me?
IW is a very expensive early tech. Also, if you recall my bit on AI priority techs, IW is most definitely a tech the AIs will grab early. A very important concept in this game is the idea of snowballing. Strong early play and better decision making in this timeframe essentially snowballs into more success later. Teching IW is spending a tremendous amount of turns teching something that a) you can easily trade for later b) very likely will get no trade value from yourself. For perspective, it's essentially like creating a huge black hole of turns where you are falling behind and the AIs are happily moving on. The iron resource is usually important but not that important that you need it for city placement early. You will discover it soon enough without wasting turns researching it yourself.
Hanging Gardens is a nice wonder, but its benefit is found when one has a larger empire. Also, I'm not even considering that wonder unless I have stone or I'm IND. Holding Maths with the idea of securing HG is a losing proposition. On higher levels AIs are going to get Maths soon enough anyway, so if you happen to tech Maths yourself you are losing any possible trade value from it by holding on to it. Like most desired wonders, if you really want that wonder, you take steps to build it quickly by setting up whip OF and prepared chops.
"If you 'lose' on each tech trade, where is the logic in that?" Not sure I fully understand this question, but will assume it is about the general fact that trades value does not favor the human. This is true, but you are the human making human decisions. Trades may not be equitable, but you can get a lot of value from a tech by trading it around for stuff. Like Aesths for Alpha, Maths, IW...or first Aesths for Alpha and then Alpha for Maths and IW or something like that (assuming Tech Brokering)
Isn't founding a religion good? You can get the +1gpt Shrine Wonders as well as the Organized Religion stuff. Besides one would have to research it sooner or later to get the +10% Research Monasteries / Organized Religion, so why not get it a little earlier to get maximum benefit? Also could'nt one try "denying" religions to some Civs as they won't benefit from Theo or Organized.
All this stuff you mentioned is considered sub-optimal gameplay. Let the AIs found early religions and spread them to you. Those are hammers and beakers you are not wasting. If you want a shrine go capture someone else's. Founding religions in order to deny AIs civics is just not logical at all and a losing proposition.
You will eventually acquire things like Monotheism yourself for things like OR, but the point here is not wasting precious hammers and beakers in the early turns on things that are really not helping you at all. (Mono is something I'd be willing to trade for)
What is so good about Writing? I often get Bronze Working (to reveal copper and get better mil units), even Iron Working before Writing.
I was just listing some ancient era techs to clarify a point there in no order of preference. BW is most definitely one of my very first techs, maybe the first if I start with the food tech I need. I've already discussed IW, but the idea of IW before Writing is just silliness...ha.
Writing is an extremely important tech and a gateway tech. You want a library in you cap as soon as you can and start running those first coupla scientists.
Why wouldn't you trade to do a backfill instead? I read about the trade caps, still there is a decay where it gets forgotten (1 in 20).
The higher the level the more pressing tech trading is here. You just don't have time to be dealing with AIs that won't trade techs because you've hit the trade caps. It essentially means you will potentially, rather likely, miss out on good trade opportunities for key tech. Don't waste trades on backfilling dinky techs that at this point you can tech in one turn yourself when you think you need them.
Really?! I find Archery just too good to pass up. It's the best defensive tech for 'ages'. An archer on a hill can really hold it's ground for centuries. How do you get by without 'defense'? Wouldn't the AI just declare war and roll your city?
I will caveat the rest of my points, that there are certainly times one might have to tech archery, especially on high levels. If you don't find copper or horses, and it's looking like spawnbusting will be insufficient to hold off barbs due to the land layout, the Archery may be needed. But I avoid Archery like the plague. Archery is a "dead end" tech that has no value at all other than the archer itself, which most often I don't need, or in the case of an HA rush since it is required for the unit.
"Defense" is passive, and passivity is not a great concept for this game. My best defense is offense and archers are not an offensive unit.
Do you trade before being asked / demanded? Is there a difference?
Absolutely! I'm very proactive about tech trading. It's an essential part of the game. Once Alpha is in play I'm analyzing tech trades EVERY turn....assessing trade values and grabbing key techs or gifting stuff at the right point for diplo. With Currency in, I'm frequently looking for opportunity to acquire gold from tech.
Refusing a request or a demand will give a diplo malus, but the main different is that refusing a demand will often have repercussions that the AI will plot on you. Unless the request or demand is ridiculous I will often just accept them for the diplo. Accepting a request or demand will give a 10 turn peace treaty as well.
Some AI are more demand-y than others. Knowing who's who and you can actually setup a resource demand by keeping an extra copy available. For example, Sitting Bull has a high demand factor. Keep an extra copy of a resource available and he will very likely demand it if not already Pleased with you. Easy way to some extra diplo.