Here's a simple tip I thought I'd share. This tip is REALLY basic, but it helped me visualize odds.

When I progressed beyond the bare basics of backgammon I learned that it was useful to know the odds of getting hit, or hitting someone, or coming in off the bar, or similar situations. I learned how to count up these odds, and knew that there was an 11/36 chance of rolling one specific number, and a 20/36 chance of rolling one of two specific numbers, etc. The problem was that although I had a general idea of what something like 11/36 or 20/36 meant, it was still a little fuzzy in my mind's eye. However, I found a way to visualize these fractions so that they became crystal clear.

I divide the fraction by 3 and then visualize the result as time on a clock. So 27/36 would become 9/12 and thus 9 o'clock (in practice I just divide the top number by 3). When you can't divide the numerator evenly you will be left with either 1 or 2 left over and these would correspond to 20 minutes or 40 minutes respectively. For example, 19/36 would be 6:20 (i.e. 20 past 6), and 11/36 would be 3:40 (but visualize on a clock with hands). Now my mind's eye has a very clear reference for the odds of a roll.

I don't know if that helps anybody else, but it helped me. I also haven't seen this tip in print anywhere, so I thought I'd throw it out there.

I like it!

I've never seen this anywhere else either.

Beautiful!