Aganju: if the randomness is not good, it slowly makes a different game out of Backgammon - for example, if there are less doubles, or incorrectly often two doubles in a row, you can adjust your strategy to take advantage of it.

I suspect that any such effect would have to be quite sizeable for it to change people's strategy. Their strategy can be highly resistant to change even when you teach them to improve their game.

Aganju: It is still a fair game, but it is not 'standard' Backgammon anymore.

Aganju: However, I found a high chance of reproducing your opponent's roll by clicking in specific sequences. So when the game comes up, and he had a 5-5, and I want one too, I do that sequence of clicks, and have a higher-than-1/36 chance to get it too (it does not work all the time, but maybe 1:3; still, pretty useful feature); whereas if he has 1-2, I will not do that typically.

I'd say that if you're doing that then it's still standard backgammon but it's no longer a fair game. :-/