I thought it would be useful to know the stats in a variety of situations, so I just did a quick calculation on the dice and runes.
Notes about these numbers:
The rerolls are presuming maximizing hits are the primary goal, I realize that is not always the case (like Kari farming for surges)
The game has thresholds where a die getting another hit is pointless, while a reroll to get something else makes the most sense (example, a two threat, 1 reroll reanimate archer unit fires at a rune golem with no armor buff. red gets two hits, blue gets one hit. Better off rerolling for the surge, as 6-4 = 1 wound, as does 4-4)
red die:
0.75 average hits, 62.5% chance of one or more hits
0.25 average morale, 25% chance of one morale
0.125 average surge, 12.5% chance of one or more surges
average hits with rerolls:
with one reroll, assuming reroll when no hits: 1.03125
with two rerolls, assuming reroll when no hits: 1.13671875
with two rerolls, being greedy and only accepting a two faced result for the first roll: 1.140625
blue die:
0.5 average hits, 50% chance of one hits
0.5 average surges, 37.5% chance of one or more surges
0.25 average precision, 25% chance of one precision
average hits with rerolls:
with one reroll, assuming reroll when no hits: 0.75
with two rerolls, assuming reroll when no hits: 0.875
white die:
0.75 average hits, 66.6% chance of one or more hits
0.42 average surges, 33.3% chance of one or more surges
0.167 average morale, 16.7% chance of one morale
0.08 average precision, 8.3% chance of one precision
average hits with rerolls:
with one reroll, assuming reroll when no hits or mortal wounds: 0.104 mortal wounds, 1.125 wounds
runes:
50% chance of one stable rune, 50% chance of two stable runes
25% of zero unstable runes, 50% chance of two unstable runes, 25% chance of four unstable runes
12.5% chance of zero natural runes, 37.5% chance of one, 37.5% chance of two, 12.5% of 3 natural runes
Interesting result, a white die is worse for straight damage then a red if you're attacking something where your threat is higher then their armor (mortal wounds don't multiply with threat, so if threat > armor, mortal wounds decrease damage output)