Just like the title suggests, I threw together a spreadsheet that shows the probabilities of specific outcomes. Each row is a combination of dice thrown together indicated by the Dice column, ex: 2R1B = 2 red dice and 1 blue dice. Each column indicates the probability of rolling at least the number at the top of the column of that particular symbol, not taking into account counts of other symbols showing, re-rolls due to Precise or multiple ranks, nor abilities.
I don't think this is uncovering anything we didn't already have gut feelings about, but I hope this helps in your mid-game decision making!
EDIT 2017-04-28
I've expanded the program I wrote to make the initial spreadsheet to account for rerolls and extra dice (flanking, upgrades, etc). Since there's now so many conditions I can't fit all probabilities into screenshots cleanly, so I've moved my data to a google doc here . Rerolls were calculated assuming that any die that is not showing the symbol is rerolled.
EDIT 2017-04-29
Added columns for calculating blanks. I chose to keep the reroll logic the same, where it rerolls anything that's not a blank, as I assume blanks were wanted due to upgrades like Reaping Blade.
EDIT 2017-05-02
Added Hawthorne and Ankaur. I don't think their upgrade cards has been shown yet, I imagine Ankaur will add a white die and Hawthorne a red but not sure yet.
Edited by SwagonBallZ