The random element in backgammon is inconsequential: a good player will always beat inferior players over several games. What makes good players good is not that they know how to win when they have a good roll but the fact that with regular throws, each of their move is optimal, which guarantees a win over the duration of the entire game.
The same could be said of poker, where the element of chance appears to be huge but which doesn't matter over many games.
Backgammon: the best way to want to kill yourself. I was playing a 21-game match against someone on the Internet, it was 17-16 for him, but I was in a very good position and I doubled and he (incorrectly) accepted. I was about to build a 5-prime between my 4 and 8 points when he got a lucky roll, hit two of my blots and closed off his home board. He won a gammon and the match. One lucky roll, 1/36 chance and I go from still being in the match to being a 3% dog.
Bridge is a game of short-term and long-term memory, strategy (in long matches), tactics, deduction, induction, risk assessment, hidden information, and finally a strong test of character, and your judgment of the characters of others. Unlike chess it does not seem to have a "limit" where you stop getting smarter and start merely learning more about chess. There's a reason it's the favorite game of some of the world's smartest and richest men.
Another nice thing about bridge is that most tournaments are open, and even if flighted you're almost always given the option of "playing up". I, as a serious amateur have had the chance to play against probably 3 of the top 10 players in the world, and anther 10-15 that are probably top 100. I'm not talking exhibition games either, like a chess simul, but actual tournament play.
I played a lot of bridge through High School, tournaments, etc. I think it can become very robotic once you are just following conventions and can count cards without difficulty.
I think there is much more depth than your're giving it credit for - you can work on developing your own conventions, and there are many advanced play techniques - ever heard of a mandatory false card?
Nope, what is it? Nothing shows up in my Google searches other than plain old "false cards", which are fairly obvious. I don't remember bothering to name such a thing.
Basically the idea is that you assume you have, say, QT doubleton in a suit, dummy has J9x, and declarer is presumed to have the rest of the significant cards in the suit - perhaps the suit opened.
Declarer leads the A, parter plays low, dummy plays low. Do you discard the Q or the T?
Since you have to discard a non-small card declarer will know you have either a singleton, or QT doubleton, because with any other holding you'd play something else. If you have T singleton, there is nothing declarer can do about it except lead small to dummy's J at trick 2. However, if you can convince declarer you have Q singleton, the right play is to hook the 9 in dummy. Thus, playing the Q at trick 1 is a mandatory false card - discarding the ten will never gain, discarding the Q puts declarer on a genuine guess.
At very high levels, this gets further randomized because declarer will pickup on the Q likely being a MFC, and thus work to otherwise resolve the guess and get it right (e.g. play other suits and using deductive reasoning from that. - so at very high levels the winning strategy is actually to make the MFC most - but NOT ALL - the time, at random.
Right, this just seems like basic card tracking and reasoning, which is fun when figuring it out, and then not fun once it becomes routine. When you present a situation with only two options and one is worse than the other, you will have a hard time convincing me there is a lot of depth.
On the other hand, for the declarer it is just business as usual: you try to navigate the tricks making as few guesses as possible. At some point realize that seeing the Queen doesn't always mean a singleton, so you put that in the "guess" category, but the actual process isn't effected.
If you're doing that routinely, and actually getting it right, you could make a good living playing professionally. Either you were very, very good, or there was a lot of depth you were missing out on.
I take your point, and I'm enjoying discussing this. I was never all that good, although we did find the time for a dozen hands or so a day for months at a time. I just remember being bored by the "deeper" things, which my friends (those who were much better players) found interesting. Which is mainly to say, as the OP was bored by go, he may also be bored by bridge.
Backgammon is also very rich also, although there is a random element there which, depending on your preferences, is either a good or bad thing.