# The Balance and Bravery Patch decreases the expected epics per run

Let’s do the math using Harvestshield Mountain as an example.

`Previously, the rewards were 3 epics for 6, 5 for 12, 2 for 18, 1 for 19 and 20 for 20.`
`P (getting an epic per run) = 1 - (5/6) * (10/12) * (15/20) = 0.479 or 48%.`
`You had three times to roll 6, two times to get 12 and 1 time to get 18, 19, 20. So if received an epic you would expect it to be in a ratio of 3:2:1:1:1.`
`You would expect triplicate 6's once every 240 times you rolled a 6 on the 6 die, double 6's 13% (1 - (11/12*19/20)) of the time you rolled a 6 on the 6 die, and a double 12 5% of the time you rolled a 12 on the 12 die. So we can increase the value of the 6's and 12's by adding the rate for duplication.`
`die roll value = [ratio to be expected] * [epic number] * [duplicate modifier] / [sum of all ratios]`
`6 die value: 3 * 3 * (1.13) / 8 = 1.27125`
`12 die value: 2 * 5 * (1.05) / 8 = 1.3125`
`18 die value: 1 * 2 * 1 / 8 = 0.25`
`19 die value: 1 * 1 * 1 / 8 = 0.125`
`20 die value: 20 * 1 * 1 / 8 = 2.5`
`Summing up the values we get the number of epics we receive on average if we rolled an epic: 5.45875`
`Multiplying that by the probability of getting an epic, we get an expected number of epics per run of:`

2.6 epics per run using the previous system.

Now we can do the math for the new reward system

`P (getting an epic per run) = 1 - (16/20) * (16/20) * (16/20) = 0.488% - so we're slightly more likely to get an epic now.`
`You have three chances to for each of 10, 14, 18 and 20. If we received an epic we'd expect it to be in a ratio of 1:1:1:1.`
`You expect triplicate rolls once ever 4000 times and duplicate rolls once just a hint less than 10% of the time. For simplicity sake, I'll increase the value of the rolls by 10% across the board.`
`die roll value = [ratio to be expected] * [epic number] * [duplicate modifier] / [sum of all ratios]`
`10 die value: 1 * 1 * (1.1) / 4 = 0.275`
`14 die value: 1 * 2 * (1.1) / 4 = 0.55`
`18 die value: 1 * 4 * (1.1) / 4 = 1.1`
`20 die value: 1 * 10 * (1.1) / 4 = 2.75`
`Summing up the values we get the number of epics we receive on average if we rolled an epic: 4.675`
`Multiplying that by the probability of getting an epic, we get an expected number of epics per run of:`

2.1777 2.2814 epics per run using the current system.

So based on my math (which I admit may be in error), it looks like it’s actually a nerf to the expected value of the number of epics, if you could consistently unlock all the dice. If anyone feels like running through a simulation to test whether my math is correct, I welcome it.

I was just noticing this also. It seems like less rewards per run unless you roll multiples

I took the possibility of double dice rewards into account in my calculations. Your expected value (i.e. the average over infinite runs) in epics has decreased even with duplicates. I haven’t done the math for the other challenges yet, but I believe it should be similar since the rewards are all ratioed similarly.

In summary, this update was nice if you couldn’t clear all of the bosses, but is about a 20% nerf in epic collection rate if you could.

What’s worse is the update notes are worded to make it seem like it’s improving the in-game economy for the player, when it really is a stealth nerf to it.

It’s worse: it also nerfs the gold payout. Sharpstone Keep used to be a slight net positive gold payout. Given enough runs, you could slowly make some gold. Now, it’s basically a wash. After putting in the new numbers, after 1000 runs, my simulation shows I’d be up 3850 gold. So, that is a net average gain of 4 gold per run. And yes, my sim takes into account possible multiples of dice.

I don’t have the numbers of what the old payout was, but I know it was way better than 4 gold per run.

Edit: my numbers above we’re assuming that if given a choice, I’d take the epic gear if it dropped at the same time as gold. If you took gold every time, a 1000 run sim yielded 10525 gold, or about 10.5 gold per run. I think that’s still not as good as before this latest update.

If memory serves, Harvestshield mountain used to give 1500 gold for 14, 1250 for 13?, 750 for 8, 250 for 1 and 7. I’m not sure exactly what 13 was; I know it was less than 1500 because it didn’t follow the pattern from Hidden Forge and Frostsilver Mines.

This. If it’s better if you can’t clear all the bosses, it adds up with the free challenge being the hardest one. But 3-dicing is less valuable and gold returns are minimal, so right now I don’t know what to grind/farm because gold is so gosh darn important. Before you could farm gold by grinding -paid with gold- challenges, now I don’t know…

But now that the sale system works properly picking a reward with tones of commons will net good gold eventually also.

Also for all challenges are shorter now for the tougher ones, so you can do more in the same amount of time.

Forge and Harvestshield both reduced from 12 to 9.

Heartcoil from 15 to 9.

This means I can run much faster and easily make up for the small rate drop.

Plus with 3 D20 the odds of getting shut out for an entire reward cycle is way down. Before I had weekends where I ran 40+ times and never got the D20. Now your almost assured to get some along the way. It’s a smoother route to rewards, instead of long runs to feast or famine.

Admittedly when harvestshield had a good reward for 6 that was always my favourite, and that’s gone. Overall I still think it better for the reasons I stated above.

Don’t you now have a better chance of getting epics now that if you can 3 20’s , before you had no chance of a 20 unless you could clear all 3 bosses. So I think you get better stuff now even if it’s not quite as many at once

Oof, looking at the newest event, the gold 2x in sharpstone. Looks like that got nerfed even harder.

The worst rewards for 2x golds used to be a wash with spending gems on the lowest gem to coin conversion (60 gems = 1000 golds).

Now, the worst golds roll is 2x 25 = 50 golds, for 5 gems. Or 60 gems = 600 golds.

Granted, i didn’t look to see if there were more gold rolls, and do the full “expected” math compared to before. But having low rolls = a guaranteed loss means i likely won’t use anything but the free attempt on special challenge events, for a bit.

Admittedly, this is a single data point, and your mileage may vary. However, I just finished the event after 9 runs for a total of 6300 gold. (And the first one was free.). So, 8x5 = 40 gems spent on 6300 gold, plus 16 rares and 50 commons.

As I said, only 1 data point. I got 3 20’s in 9 runs. That’s WAY better than the odds would normally suggest, so I’ll consider myself lucky.

What also bugs me about the decreased rewards, is that combined with the fact only your furthest challenge is free really hinders me at the moment XP-wise as well.
I literally finished Harvestshield a day before the patch and I can’t for the life of me or my characters pass the 5th room. That means I get only one die, and 2 more experience doing that than I get completing Sharpstone, and about 30 less than what I get for completing Frostsilver.

I personnaly ran the event about 35 times. i got the 20 dice 2 times, the 250 a couple of times.
But mostly, the amount of gold / return per run was horrible.

5gems is ~ 100gold
yet, rewards for roll 1-6, 8, 9 is a straight lost at < 100
and, 6, 10, 11 is even.
It makes that 8/20 rolls are gains.
I might have been the unluckiest player, but i kept rolling 1-6 the entire time.
Even when i got my first 20 (2000g) i did the math on the amount of runs i did, and i was soso even at that point.
At the end of it, i was, AM at a lost. It costs me over 17 000 gold to run this to get my completed status. Yes i did get some gear on the side when money rolls didn’t occur, but it’s pretty low.

I prefer running harvestshield mountain. for 250gold i roll VERY often in the higher 15+
I’ve actually got the 17 and 16 about 4 times each. Now THATS a gain. 1250 gold, or 75 gems (1650gold) for a meager cost of 250gold.

TL,DR: Caught a mistake in OP’s math. Reduction in epic rewards/run balanced by decrease in gold/run and time/run with free runs and reduced dungeon length. It’s a game have fun!

There’s some fuzzy math going on in OP. It doesn’t affect the numbers for the old system much. I calculated 2.58 epics per run for that system. But the new system is slightly more generous than OP’s math would suggest. Primarily, the assumption that the ratios of results will be 1:1:1:1 is false because the die rolls that award more epics will be favored; in cases where more than one distinct epic die roll is showing, the player will pick the die with the most epics.

So the math for the new system will look like this:

{20}: 10 * (3/20) = 1.5 epics/run
{18}: 4 * (3/20 - 3 * (1/20 * (1 - 19/20 * 19/20) + 3/8000)"" = .543 epics/run
{14}: 2 * (3/20 - 3 * (1/20 * (1 - 18/20 * 18/20) + 6/8000)"
" = .2445 epics/run
{10}: 1 * (3/20 - 3 * (1/20 * (1 - 17/20 * 17/20) + 9/8000)"*" = .1095 epics/run
Total = 2.397 epics/run

By these numbers, the epics/run has been reduced by ~0.18 or about a 7% reduction, considerably less than “20%.” (OP’s numbers, in fact, reflect a 16% loss.)

But I think many people are putting too much emphasis on rewards/run and ignoring the increases made to the runs/resources. The three hardest challenges have been shortened, reducing the resource of time invested per run. The free run is now the highest unlocked challenge, reducing the investment of gold as a resource. I personally, even with the shortened dungeons, could probably only manage 10 runs of HSM every 5 hours if I was pushing it and ignoring more of the responsibilities I’m already ignoring when I play this game. At that point, the gold cost would be 93.9 gold/epic, the cost under the old system was a flat 96.9 gold/epic. I would need to do 15 or more runs in 5 hours before the gold cost would be more than the old system (97.3 gold/epic). And even if I do run HSM 15 times, Ludia has cut out 45 rooms for me.

Don’t get me wrong, Ludia’s still a money-hungry company and I won’t pay them a dime. I just like to give credit where it’s due. I have yet to look at the math for gold and gem payouts per run, but my gut reaction is that whatever the decrease, it’s probably compensated by them finally fixing the equipment economy to make those huge stacks of commons and rares actually worth something. Of course if they’ve used the fixing of a bug that was keeping us from obtaining gold as justification to nerf the gold and gem rewards of challenges, I would probably take umbrage at that.

“*” The last terms of the last three probability calculations (within the widest parentheses) are corrections for the second term. The results in which 2 of the specified die roll and one higher epic die roll are showing (i.e. {18, 20, 18}) have each been subtracted twice by the second term. The third term adds one of each of them back in.

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I’m not a very good data point because of this roll either:

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Yes just I noticed an error with my calculations for probability of duplicates rolls. I didn’t square a term. It should be (1 - (19/20)*(19/20)) and I used (1 - (19/20)).

This was unintentional and I was going to update the OP to correct this error but it’s been a busy day. I’ll get around to it once I get a chance to sit down.

EDIT: So I sat down and took a look at Drizzle’s math. It’s much more elegant than my approach, so I’m happy to adopt it as correct.

I’m also just a single data point, but I’m just over halfway completing the coin challenge and I’ve already spent more gems compared to the completing the same challenge before the update. (Notice the cost has gone up from 3 to 5 as well?) In order to get as much epics on a 20 roll as before, you need to roll a 20 twice. I haven’t hit it once. I am sure I’ve rolled more than 60 dice now, including my free challenges or grind challenges…

I got really lucky then, because I scored so many epics during the Farideh challenge. I basically can level up Farideh’s epic armor from 1 to 4, now just need the gold lolol

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It works better, but not “properly” as I just noticed that I have a ton of gear that hasn’t ever been listed in the store. I also saw in another thread, an issue about trying to sell off max gear:
https://forum.ludia.com/t/re-selling-extra-gear-unable-to-sell-maxed-lvl-gear/97656/2

Hopefully the store cycles through these excessive amounts of gear so that they can be sold off.

I still can’t believe there are players at max level and max gear level already in this game, damn. Congrats killers!

If anyone likes, I can upload all of the dice I get after i complete each run. I take a screenshot each time.