You need 250 points for a reroll actually.
I have made a suggestion in the past to change the amount of points gained and needed which would benefit players who had a lot of champions and would be a slap in the face to those who only owned a few (aka the ARAM accounts).
Never got a response on it however. Made a suggestion similar to the one I made in the past last week but it was downvoted to -2 (old forums) after it had several upvotes so it seems that ARAM account clowns weren't too happy with my ideas (gee I wonder why).
Anyway my idea is something like:
Roll cap changed from 2 to 4
Points required for a roll changed from 250 to 350
Base points gained per game changed from 30 to 16. Points gained are based on the amount of champions you own.
Points per champion changed to the following:
1-10 champions: 0.2 per champion + 16 base
11-20 champions: 0.4 per champion + 18 base
21-30 champions: 0.7 per champion + 20 base
31-40 champions: 1.1 per champion + 22 base
41-50 champions: 1.3 per champion + 24 base
51-60 champions: 1.5 per champion + 26 base
61-70 champions: 1.7 per champion + 28 base
71-80 champions: 1.9 per champion + 30 base
81-90 champions: 2.1 per champion + 32 base
91-100 champions: 2.3 per champion + 34 base
101-110 champions: 2.5 per champion + 36 base
111-120 champions: 2.7 per champion + 38 base
121-130 champions: 2.9 per champion + 40 base
Comparing the current roll system to that of my idea would make it so that the amount of games you need to gain a roll will be equal to the current system once you have ~41 champions (and benefit from that amount onwards) and make it so players with an ARAM acccount will have to play roughly double the amount of games to gain a roll.
Having all champions can be disadvantageous at times (IE: I saved up 2 rolls then get Sejuani. Since we have an Amumu and Shen already I decided to reroll... Got Shyvana and then Skarner) so a roll per game (once you have over 106 champions) makes life a bit easier as well as allowing you to roll for another player.
Again: This was just an idea. I would much rather see ARAM accounts disappear than gain a roll every game instead of every 2 games but something needs to be done.