With Heroes of the Storm 2.0 released tomorrow, Reddit user SirLancelittle1 has done a great job of knuckling down on the Loot Chests players can purchase or be awarded. With many veteran players receiving bags of Chests tomorrow, it's important to know how to maximize your returns. With that in mind, here's what SirLancelittle1 found out (full text below) - we think as many people as possible need to know this before opening their crates. 

Loot Chest Reroll Summary

1. Keep any chest containing a rare or better item you like.

2. Reroll chests no more than twice

3. Keep common chests if the chest has 2 rares or 1 epic/legendary (regardless of duplication)

4. Keep rare chests if the chest has 3 rares or 1 epic/legendary (regardless of duplication)

5. Keep epic chests if the chest has 2 rares, 2 epics, or 1 legendary. Don't reroll if you are short on gold (but you probably won't be)

FAQ

What if I run out of gold?

Based on my calculations you will earn gold for rerolls at about the same rate you earn loot chests to spend it on so this won’t be a problem. If you are low on gold, remember that rerolling two different chests is more efficient than re-rolling a single chest twice. The order to cut back on rerolls is: Start by keeping all epic chests, then 2 rares in a rare chest, then 1 rare in a rare or common chest.

Should I spend my gold once 2.0 hits or should I save it for later rerolls?

Based on my math you shouldn’t have to save gold. Put aside enough gold for your legendary rerolls then open and reroll your common/rare chests first (it will give you a better idea of your duplicate situation). If you have enough gold left over you can reroll your epic veteran’s chests on release. I recommend no more than 2 rerolls. If you have 500g/chest you should plan on rerolling 50% of them once and 25% of them twice. If you have 250g/chest you should plan on rerolling 50% of them once.

Should I use my gold on heroes or loot chest re-rolls?

Wait til after 2.0 to buy heroes since you will get a ton of free ones. Then, open veteran loot chests before spending your gold to see if you get any in chests (saving enough gold in case you don’t get them). After the 2.0 release, the odds of getting heroes is about 2% per reroll which means you would have to spend, on average, 12k gold to get an extra hero via re-rolls and would, usually get a hero worth 2-7k. This means you should definitely spend your gold directly on any heroes you want and only use gold for rerolls once you want skins/mounts/etc more than any remaining hero.

What if I want to craft a specific item? How do I maximize my shards?

In the long term you will maximize your shards by following the rules listed above. This will maximize your item rarity which, in the long term, will net you the most duplicates at higher level which will maximize your shards. If you really want some shards now (at the cost of shards later), consider the following re-rolling rule of thumb. If you have a collection of size X%, your average common chest will contain X shards (for example 10% = 10 shards). You can, on average, increase the shard count in that chest by rerolling if you are less than that number.

How much gold do I need when 2.0 hits? To follow the epic loot box plan shown above you need an average of 750g/box. If you have less than this you will have to be more selective about rerolls. Post 2.0 your steady state income should allow you to follow this plan.

Summary of Work

The following is my logic behind the above statements. I needed to determine was the ratio of gold/xp you would earn going forward so I could know how much gold you could afford to spend on loot chests. Furthermore, I need to determine the reroll chances to determine the approximate line where rerolling was worth it.

On average you earn approximately 100k experience per game (40k for an AI game). 25g/game or 10g/game versus AI. As a result our our gold per xp is 25g/100k xp for QM or AI.

Team League + 50%

Play with Friends +75%

Stimpacks +150/100 g/xp

Bonus 500g/5 levels = 100g/1200k = 8g/100k (16g/100k at low level)

Daily quests are worth 369g/day on average.

1.2 Million xp/level at high level. 100k-1100k xp/level from 1-10 (600k average).  

Based on these numbers a player maximizes their gold/experience by playing low level character in solo-QM/AI with a stim pack. A player maximizes their experience/gold by playing 5-man Team League with no stim pack on a high level character. This allows us to approximate our boundaries and determine about how much gold/loot chest we will earn. I included hero league as sort of a middle ground.

Math

QM + stimpack (low): 1.5 * 25g/100k + 16g/100k = 53.5g/100k = ~320g/level

QM + stimpack (high): 1.5 * 25g/100k + 8g/100k = 45.5g/100k = ~546g/level

Hero League (low): 25g/125k + 16g/100k = 41g/100k = ~246g/level

Hero League (high): 25g/125k + 8g/100k = 28g/100k = ~336g/level

5-man Team League (low): 25g/225k + 16g/100k = 27g/100k = ~162g/level

5-man Team League (high): 25g/225k + 8g/100k = 19g/100k = ~229g/level

Furthermore, if you complete all of your quests you will earn, on average, 135k/year from quests alone. Last year there were 15 new heroes released. This means if you want to buy all the new heroes once they drop to 10k, you will need to spend all of your quest money and then some on heroes. However, you will likely get a couple free heroes from loot chests or promotions so this may cancel out. However, if you buy all your heroes using real money you will have an additional ~400g/day to spend on rerolls. From a practical standpoint you probably only be earning 1 loot chest per 5-12 games (5 games at high level 5 man team league, 6 games at low level, 6 games at high level with stim, 12 games at high level no stim). So you will have an extra reroll relative to the rest of us.

Based on the numbers above you can see players will have between 200-500g per loot chest for rerolls with most players somewhere in the middle. So, how can we use this information to maximize our rerolls? We could try to write an equations but there are enough variables it is easiest to just look at some examples. Let’s look at 4 cases  

Case 1: Reroll bottom 50% of chests regardless of cost

50% - keep

25% - reroll once and keep

12.5% - reroll twice and keep

6.25% - reroll thrice and keep

6.25% - reroll thrice and stuck

Expected reroll cost is (250*.25+.125*750+.125*1750) = 375g/chest. Expected value is 93.75% we get an above average chest, 6.25% we get a below average chest. Expected chest value is (.9375*7.5 + .0625*2.5) = 7.2.

Case 2: Reroll bottom 50% of chests no more than twice

50% - keep

25% - reroll once and keep

12.5% - reroll twice and keep

12.5% - reroll twice and stuck

Expected reroll cost is (250*.25+750*.25) = 250g/chest. Expected value is 87.5% we get an above average chest, 12.5% we get a below average chest. Expected chest value is (.875*7.5 + .125*2.5) = 6.9.

Case 3: Reroll bottom 75% of chests no more than twice

25% - keep

18.75% - reroll once and keep

56.25% - reroll twice

Expected reroll cost is (250*.1875 + 750*.5625) = 469g/chest. Expected chest value is (8.75*(.25+.1875) + 5*.5625) = 6.6.

Case 4: Reroll bottom 75% of chests on your first reroll, 50% on your second, and 25% on your third.

25% - keep (top 25% value)

37.5% - reroll once and keep (top 50% value)

28.125% - reroll twice and keep (top 75% value)

9.375% - reroll thrice

Expected reroll cost is (250*.375+5750*.28125+1750*.09375) = 469g/chest. Expected chest value is (.25*(7.5+10)/2 + .375*7.5+.28125 * (2.5+10)/2 + .09375*5) = 7.2

As you can see between cases 1 and 2, rerolling a third time is basically not worth it. Your expected chest values goes up by only a small percentage but your expected cost goes up by 50%. Furthermore, being super picky actually lowers your expected value because it increases the odds you end up re-rolling too much and are stuck with a bad chest. Finally, case 4 tries to balance the cost with the how good the chest is but ends up showing similar results to case 1 but with a higher cost.

From these tests you can see our basic rule. Reroll chests if you think you have a greater than 50% chance of upgrading but no more than twice. Luckily this expected 250g cost matches our expected gold earned (with a little extra to help pay for heroes since quests don’t quite cover it).

Now you might be thinking, this assumes that most loot chests contain an item of value. What if only the top 5% of chests contain something we care about and the other 95% are basically garbage… Well in this case we don’t really have to do math because you will basically always end up stuck. You will need to reroll as much as possible and spread your gold out as evenly as possible (rerolling two different chests is cheaper than rerolling one chest twice).

Loot Quality Section

So… how can we evaluate whether or not a chest is in the top 50%. Well one thing that really helps is our chest rarity odds:

Odds of a single item (remember 4 item/chest)

This means that a common chest only has a (.71^4) = 25% chance of coming up all commons and a (.71^3*.2 * 4 permutations) 29% of 4 commons and a rare. In other words we have a 46% chance of something better than 4 commons and a rare. If we re-roll on that boundary, the expected cost is now 280g/box (46% chance of no re-roll, 25% chance of one re-roll, 29% chance of two-reroll)

We don’t know how rare chests work for sure. There are two likely options. One option is that it rolls a common chest and if none of the items are rare (25% chance) it upgrades one. The other option is that 1 of the items has a different percentage table (with no commons). This actually makes big difference because in the first case you have to roll 2 rares out of 4 items to get two rares while in the second case you only need to roll 1 rare in 3 items to get two rares.

Case 1: Only 1 rare = 54%. Exactly two rares = 15%.

Case 2: Only 1 rare = 33%. Exactly two rares = 28%.

Case 2 is obviously better for us (and I think is more likely) but we have 31 or 39% chance of better than 2 rares (case 1 or 2 respectively). It may not look like a good deal to reroll two rares (< 50% odds) but consider the following (even with case 1). A reroll of rare chest containing 2 rares will on result in an average chest containing 1.1 rares, 0.28 epics and 0.08 legendaries. On average this means a reroll is worth -.9 rares but + .36 epics/legendaries. If you consider epics/legendaries worth at least 2.5x what a rare is worth, this is a good deal. In case 2 it is even more obviously worthwhile with a reroll of a 2-rare rare chest netting us 1.5 rares, 0.28 epics and 0.08 legendaries. The expected cost using this plan is 337g/box (39% chance of no reroll, 24% chance of 1 reroll, 37% chance of 2 reroll) .

Epic chests are weird because they cost twice as much to re-roll. One might imagine this means we should save our gold to reroll common chests since we can re-roll twice as many. However, based on our math from above we are rerolling 54% of common chests at a cost of 250g/chest and rare chests at a cost of 340-380g/chest. Given our expected of earnings of 200-500g/chest we probably have extra gold. While we could use this to try to re-roll more common chests, keep in mind we are already rerolling those chests an average of 1.1 times. As a result, rerolling a common chest with that extra gold will, on average, already be the same cost as rerolling an epic chest for the first time. So we might as well plan on re-rolling some epic chests. Keep in mind that only 1/25 chests will be epic so the added cost is very small.

For epic chests there is a 35% chance of 3 commons and an epic and a 30% chance of 2 commons, and epic and a rare. Similar to the logic for rares this means we could maximize our value by rerolling in these two cases. The expected cost is 745g (35% no reroll, 23% 1 reroll, 42% 2 rerolls) but spread out over 25 chests means we only need to earn 279g/box for our overall loot chest plan to work (this assumes 1/25 epic at 745g, 1/10 rare at 337g, rest common at 250g).

Shard Section

Okay, so what about shards. Should you keep duplicate items, or re-roll them? This depends on lot on two factors. What percentage of the collection do you own and how much do you care about specific items. Obviously, if you own most of the collection you will usually get shards and your only goal should be to maximize their rarity (as we did above). Likewise, if you really want to craft a couple of items and don’t care about 95% of items, maximizing your shards is the best way to get what you want (so you shouldn’t reroll duplicates, because a higher level non-duplicate is actually worth less to you than a lower level duplicate). Finally, If you just want as many items as possible, you should still aim for higher rarity since a duplicate epic = any rare you want.

This means the only question we need to ask is, if I got a chest meets our re-roll criteria from above but contains a bunch of shards, should I keep it (assuming short term shards is my main objective)? Assuming I own 20% of the collection, a common chest will contain an average of 22 shards. At 10% of the collection, a common chest will contain an average of 11 shards. This gives us a quick rule of thumb: If I only care about short-term shards my reroll criteria for common chests becomes re-roll (up to twice) if the number of shards is < % of the collection I own.