Guessing moves have little to do with luck since its a combination of reading the opponent and doing a risk-reward analysis. Unlike rock paper scissors, there is always a smarter move, the 'luck' moves are about adequately measuring the risk and reward of both your opponent and your situation as well as being able to read his personality to get a feel of which one he is more likely to do.
The best players on this site are able to out predict me in most games I play with them, while players that I think that I am better at this game I am normally able to out predict. I will acknowledge though that there is some luck involved, however as I have alluded in your earlier threads, good players chose their own luck. If you are good enough at the diplomacy aspect, you'll rarely find yourself in a situation where you rely on the luck of strategy to determine your fate. So while there is a luck component, it is rather minimal.
The only board game I know of that has no luck whatsoever is Imperial;
Like diplomacy, there is no dice or anything, its a bigger army always wins.
Unlike diplomacy there is no simultaneous turns, so giving orders never requires guessing. There is a currency aspect of the game and to determine who plays what country people bid on the countries. The object of the game isn't to conquer the world, but to end up with the most money, having your country win on the board will give you money, but you can easily win the game even if your country doesn't.
Its by far my fav board game, and I don't know of any sites that play it online, so I haven't played it in years though.