Edit: TL,DR: Don’t listen to the complainers. Sharpstone is still safe to grind for gold and gems, in fact it’s better than before!

I have already addressed the complaints to the “nerf” to epic rewards in challenges here: The Balance and Bravery Patch decreases the expected epics per run:

Now I would like to address the issue of gold and gem rewards brought up in several threads. At first, I was also skeptical, concerned that Ludia would use the correction of the equipment buyback algorithm as a justification for reducing the expected rewards from challenges. Fortunately for us, the math does not bear that out, in fact this update has been a boon to challenge rewards! First lets look at the old 1d6+1d12+1d20 system.

(Before I get into this, a few assumptions: 1. Epics are more desirable than gold or gems. 2. Gems(G) are worth 20 gold(gp) based upon the 500 gems for 10000 gold purchase in the store. 3. Rares and commons are less desirable than gold or gems.)

The rewards break down like this:

{20}: 4 epics * 1/20 = 0.2 epics/run

{14}: 300 gp * 1/20 = **15 gp/run**

{13}: 200 gp * 1/20 = **10 gp/run**

{15}: 9G * 20 gp/G * 1/20 = **9 gp/run**

{8}: 150 gp * ((1/12+1/20) - (1/12 * 4/20) = **17.5 gp/run**

{9,2}: 3G * 20 gp/G * (1-(1-(1/6+1/12+1/20)) * (1-(1/12+1/20))-1/6 * (1-(1-5/20) * (1-1/12))-2/12 * 5/20-2/20 * 1/12+7/1440-6/1440) = **17.5167 gp/run**

{7,1}: 50 gp * (1-(1-(1/6+1/12+1/20)) * (1-(1/12+1/20))-1/6 * (1-(1-7/20) * (1-3/12))-2/12 * (1-(1-1/6) * (1-7/20)) - 2/20 * (1-(1-1/6) * (1-3/12)) + 24/1440 + 6/1440) = **10.743**

Total gold and gems/run = **79.759 gp/run**

Seems like a lot, eh? And yes, those calculations were a bear. Now let’s take a look at the new, 3d20 system.

When addressing the question of epics/ HSM run i used the following equations:

The probability § of obtaining a result of a value “n” where n is the rank of desirability in descending order (i.e. n=1 for the most desirable die roll, n = 20 for the least desirable die roll) can be expressed as:

P = 3/20 - 3/20* (1 - (21-n)^2 / 20^2) + 3(n-1)/20^3

Where the first term identifies the odds of the roll appearing, the second term corrects for the chance of obtaining a better die roll in the same result, and the third term adds back in results that were removed twice by the second term. Factoring out 3/20 affords:

P = 3/20* (1- (1-(21-n)^2 / 20^2)) + (n-1)/20^2)

Distributing -1 to the second term causes 1 - 1 to zero out and 1/20^2 can be factored out, resulting in the following expression.

P = 3/8000 * ((21-n)^2 + n-1)

Applying this formula to the new SSK rewards looks like this:

{20}(n=1): 2 epics * 3/20 = 0.3 epics/run

{16}(n=2): 15 G * 20 gp/G * 3/8000 * (19^2 + 1) = 40.725 gp

{17}(n=3): 250 gp * 3/8000 * (18^2 + 2) = 30.5625 gp

{11}(n=4): 6 G * 20 gp/G * 3/8000 * (17^2 + 3) = 13.14 gp

{12}(n=5): 100 gp * 3/8000 * (16^2 + 4) = 9.75 gp

{6}(n=6): 3 G * 20 gp/G * 3/8000 * (15^2 + 5) = 5.175 gp

{7}(n=7): 50 gp * 3/8000 * (14^2 + 6) = 3.7878 gp

{1}(n=8): 2 G * 20 gp/G * 3/8000 * (13^2 + 7) = 2.64 gp

{2}(n=9): 25 gp * 3/8000 * (12^2 +8) = 1.425 gp

Total = **107.205**

This is a **114%** return on your investment in gold! More if SSK is still your free dungeon. (If you’ve made it to the forums, chances are it’s not, but still.) Aside from the raw totals, a few interesting trends become apparent. In the old system, the lowest 4 values {1,2,7,9} contributed 35% to the total gold and gem rewards, whereas in the new system, the lowest four values, contribute only 12%. In the old system, one felt that they had to take all of the gold and gem rewards, or at least be forced to make the hard choice between gold and a desirable common or rare, because even the low results had a large impact on resource income. In the 3d20 system, however, the player can eschew rolls of 1 and 2 for the trash rolls they are and still earn over 100 gold per run. One can even ignore rolls of 6 and 7 and still earn 94.1775 gold per run. Of course if you’re still angry over how they “nerfed” the gold and gem rewards, you could ignore all gold and gem rolls except 16, 17 and 12. The sums of these will get you about the same payouts as the old system.

In higher dungeons, the returns on gold investment will go down with the addition of epic rewards. Some back of the envelope calculations suggest an 11% decrease in relative gold and gem rewards for the addition of each epic slot to the rewards table. While this is an unfortunate consequence of having better options (read: champagne problems), the addition of epics to the old system was even more disruptive to the gold and gem rewards because they were on smaller dice than the d20.

This, *in addition to* the fixing of the equipment economy, greatly drives the incentive for players to grab more commons and rares, possibly finding new combinations of abilities, new uses for “trash” commons, (I’m personally looking really hard at the rogue common pants plus epic wondrous item with the epic or legd. weapons for crazy crit fishing.) and overall fun of the game. Which I suspect is what the devs were intending with this update.

In summary, Update 10 was not “good” for people who “can’t three dice their hardest dungeon”, nor was it “good” for “free players” or “paid players” or “subscription players” or “players with two heads and purple spots.” It was just good.