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Full disclosure, this is not D&D related, but it does relate to dice and probabilities.
I've been playing a LOT of backgammon lately on my computer, and I got to thinking: would the game play slower or faster if instead of using 2d6 you switched to 2d4?
I mean, obviously you're giving up the 5s and 6s. But you are also increasing your chances of rolling doubles from 1 in 6 to 1 in 4.
I haven't done any math yet, but it is an interesting problem.

So from what ove read, mind you I dont play a lot of backgammon, you are right about your chance to roll doubles. I've noticed though that changing the dice to d4 impacts a lot of the rules and strategies. It will be easier to move twice for sure because of the doubles, but you also reduce your bar rolls from 1-6 to 1-4. Which will make blots much more powerful in the long run because it will be harder bear off any tokens that got blotted. Lastly, it severely limits legal moves. d6 allows you to potentially access a third of the board. D4 limits you to only a sixth of the board. That is half the board lost with changing the dice.

I'm a maths and probability nerd, but have never played backgammon. A quick google tells me that movement is as follows:
- roll two dice, and get to move that many spaces (with the two dice being allocated to two separate pips, or both to the same one)
- doubles means you get to move that amount 4 times (ie. doubling the total movement)

On that basis, the average number of total spaces moved per turn is:
- 4.83333 with D6s
- 6.25 with D4s

So yes the D4s would result in an increased total number of moves.

Whether that is better or worse for the game, I don't know, as I don't know how that would interact with any other movement restrictions (because I don't know the rules other than the quick googling I just did).

Happy to share my calculations, but I'm not sure if there's a good way to file share on here. But, my methodology was to simulate all possible rolls for 2D6 and 2D4; calculate the actual total moves from each possible roll (eg. rolling 1,1 = 4 moves, 1,2 = 3 moves, 1,3 = 4 moves, etc.) and found the average for each of the 2D6 and 2D4 scenarios.

Sorry, I'm afraid I'm neither a math nerd or a backgammon player.

Ditto... if I knew more backgammon I could work by old math skills but I it would be hard as I am no math nerd...

I'm a probability nerd, myself, but it has been so long since I've had to do the math/formula end of probabilities that I was dreading the process.
So you, Lyrwick, have confirmed my suspicion that the the rolls will be higher.
I guess now it becomes a question of strategy. A big part of the game is evaluating risk. The backgammon board consists of 24 "points," bars on which pieces can be placed divided into four quadrants. The goal of backgammon is to move all of your pieces from their starting positions into your home quadrant, then to move them off the board, with movement each turn determined by d6 rolls, while your opponent does likewise with their pieces. You have to move a piece the entire amount on each die (except at the end when bearing the off the board). The starting positions of each player's pieces mirror those of the opponent, and the two players move in opposite directions. Conflict arises because if a point is occupied by a single piece, and your opponent lands on that point, your piece is taken off and has to transit the entire board, while if you have two or more of your pieces on a point, that point is said to be "covered" and therefore off limits to your opponent. So it is important to evaluate the risk one is taken prior to leaving a single piece vulnerable. All of this mental arithmetic would have to be adjusted if a different die were used.

I got hooked on backgammon a little over a year ago, on a four-hour flight where a computer backgammon game was part of the in-flight entertainment suite. Now I play pretty much every day. I also got hooked on Texas Hold-em poker, which I also play on the computer very often and have gotten pretty good at, but I'm smart enough to know not to play it for actual money.

Oh, here, play some backgammon for free: http://www.247backgammon.org

I had a four games in one in gameboy, chess, reversi, checkers and backgammon... I never understood the backgammon but of course I was never explained how to play, maybe if I just follow someone playing, but now I understand better how its played based on what ya say.

Now why have i never thought of that before?

I've been playing forever, to include a few variations of the game. I may have to try this as well as with other dice.

Why not roll 1d6:

1-3: This move is determined by 2d4
4-5: This move is determined by 2d8
6: This move is determined by 2d12