First off, well said, Argothair. If I were going to be a proponent of LL, that would sum it up. I also agree with the sentiment that rolling for large battles is time consuming, though I turn into a dice-rolling robot when it’s my turn, and everyone involved goes into a calculation trance to get that shit done as quickly as is humanly possible. If I were at a table where this was not the case, I can imagine I’d go crazy.
On the other hand, at my table, we play with a range of people. I recently moved a great distance away from the old group, so most of my physical people are only on their 0th through 6th game ever. Still far too early to propose low-luck in my opinion–even if I were to consider suggesting it.
As far as online with people I used to play with back home, we always have done, and will likely continue to do, dice games for anything competitive.
For theory-craft and screwing around with what-ifs, however, we always did/do LL. And actually, usually branch at decisive battles (because it’s easy to do in an electronic format). One branch where the results were subpar but not disastrous, one where the results were exactly average, and one where the results were slightly better than average. This turns into a fractal of “wasted” time, yeah, but it lets you see how the game could evolve from turning points depending on how well you bounced through a particular fight. If you have the time, it can help you plan not only if a strategy is worthwhile, but what can be done immediately afterwards depending on the results.
If you’re in the thick of a real game, the dice are an equalizer of sorts. Yes, you can drop to a mathematically negligent chance of winning in only an hour or two of play (if you’re doing something overtly risky or have exceptionally bad luck), but that’s part of the challenge: adapting to what happens to you. In LL, you can plan everything to the letter nearly. In dice games, as calvinhobbesliker said, you must actually play differently at certain times, because you need to overkill battles that you need to win. It also leads to situations where that one frenchman that runs headlong into three italians (to take the 1/6 chance to soften them up before a US landing, for instance) can actually win. This is a fantastic thing to see, and much drinking is done when it occurs.
We also are usually very respective (yet reluctant, mind you) to throw in the towel. If it’s 3v2 or what have you, and everyone on one side and at least half of the people on the other agree there is nearly no chance for one side to continue, we shake hands, and if it’s early enough, set it all up again.
I think dice are just more fun.