# What is the value by percentage of Lindel's reroll special ability?

Here is an image of Lindel's card.

After rolling dice ofr an attribute test, you may reroll one die; you must accept the second resul

As you can see his stats are 6, 6, 6, 5. He needs to roll equal or under with 2d6 to succeed on a test. His ability allows him to reroll one of the d6's once after the initial roll.

How much does this ability increase his chances of success?

% of success on a 2d6 test

2 3% 3 8% 4 17% 5 28% 6 42% 7 58% 8 72% 9 83% 10 92% 11 97% 12 100%

Assuming he plays optimally (only rerolling when necessary, and rerolling the higher die), the odds of rolling equal to or less than a given number on 2d6 with one reroll allowed are:

2: 7.4%
3: 19.9%
4: 35.6%
5: 52.3%
6: 68.1%
7: 80.6%
8: 89.4%
9: 94.9%
10: 98.1%
11: 99.5%
12: 100%

Note that this is equivalent to rolling 3d6 and seeing if any two of them sum to the target value (or less). So you can just take the 216 combinations there and check them, just like taking the 36 combinations in the basic 2d6 case and checking those.