In a greater effort to avoid finals, I am attempting some more math.

I noticed that the Rune Golem is very dependent on rune coins, and their performance can really suffer with bad luck. The Greyhaven Channeler is an interesting upgrade that allows you to reroll 2 coins out of the 5 (4 really, considering one has two identical faces) and I wanted to know how big a difference he makes.

Since Natural Energy has 3 coins and you can only reroll 2, I had to make a rather strange truth table to get the probabilities, and so I'm not entirely sure I got the numbers right, please let me know if you have an idea.

Numbers in blue are iffy.

Ok so here is coin averages per turn and per game, with and without rerolls. Note that the rerolls improve the averages of what you want while possibly lowering the averages of the result you are rerolling. Also note that stable benefits the least because only 1 coin to reroll, while unstable benefits the most because exactly two coins having 2 symbols each.

I was looking at just this thing earlier last week, and I think I ended up with similar numbers. Although natural energy presents some problems for the math, I think you're likely close enough to draw good ballpark figures, at least ones that will help you make decisions. for example, I've heard 80% offered as a reliability threshold, and 90% even better, but from 87.5 to 95.7% to have one natural energy is pretty high regardless. I think what the data really shows is that if you're fishing for particular results, you're getting good improvements on getting runes that you want. For 50 to jump to 73.9% and for 12.5 to jump to 30.4% are pretty high chances of getting higher levels of natural runes. For stable to jump from 50 to 75 is pretty big.

The only other thing I might try is figuring up the basic probabilites per turn over the course of a game, and the improvement over the course of the entire game by being able to reroll runes. That's a much more complicated question, because you might want to fish for different runes in different situations and you might have changing rune priorities over the course of the game. We are talking a 50/50 coin flip per roll. I bet the overall effect would be pretty substantial, and I bet these upgrades are a bit underrated, at least from what I've seen out of board play so far. I see Malcorne's bequest, but not much of the others.

A problem with calculating improvement over an entire game is the fact the natural energy eats into stable and unstable energy and vice-versa, so the better you do with one the worse you do with others.

I might give it a shot later and try to figure the total number of a specific rune's increase over an entire game.

4 hours ago, hamooding said:

I might give it a shot later and try to figure the total number of a specific rune's increase over an entire game.

Not counting potential rethrows, expressed in the form of natural/stable/unstable:

Update with averages per turn and per game with rerolls, and goddamn does Unstable benefit, a full 50% increase.

The benefit is exactly the same with Malcorne's Bequest when it comes to Unstable energy, and is absolutely amazing if you do not care for Natural energy.