Solution to Re-Rolls in a Full Availability ARAM

So there's apparently been some serious consideration for making all champions available to all players. However, there's the issue of Reroll Credits.

My proposal is, instead of having up to two Re-Rolls, you now get to choose between three options:

http://i.imgur.com/MFTosS5.png

This retains the informed choice that veteran players currently have (with a free reroll every game); while removing some of the intimidation-factor for newer players (who currently get rerolls rarely, but only have a pool of ~20 champions).

Options:

• Each player picks concurrently. In a no-duplicates system, this would require rolling 30 unique champions at the start of each round. This is not preferable for a system that promotes champion trading.
• Each member of the team now picks sequentially, but the picks are rerolled each time. This reduces the number of excluded champions from each player's roll, but still doesn't promote trading - since there could be two good picks in one person's roll.
• Each member of the team now picks sequentially, and the two options the previous player didn't choose will carry over. This is my preferred option, as well as the option with the least favourable odds (since 2 bad picks stick around).

New featured game modes:

• Same-team duplicates are enabled and have slightly higher odds of occurring. The team all pick concurrently, but all the available choices are presented (i.e. you can see all 15 options, 3 per player, and can build your comp accordingly).
• Random Draft. Standard Draft turns (1-2-2-2-2-1), but the two teams share the same pool of five random champions. The pool is not refilled until all picks are locked (so in a 2-person phase, you still only get 5 choices between you) and any champion your team does not pick is presented to the enemy.