## Heart’s Desire in Rise of Kingdom

Which event should you choose to use your **Sovereign Keys**? Read on to find out!

Below is my detailed analysis to help guide your decision.

## Legendary Tavern

**Event Rules:**

**Legendary Tavern**is a**46-days**event, where you can use**Sovereign Keys**to open chests for rewards including Legendary Commander Sculptures. There is a**cap of 2,000 chests that can be opened each day**.- Once your
**Sovereign Keys**are fully expended in the event, you can use**Gems**to open chests in the event. - Every 10 times you open a chest, you are guaranteed 1 x Legendary Commander (i.e. 10 x Sculptures) or Legendary Commander Sculpture.
- Guaranteed reward of 10 x Sculptures of your choice of one Legendary Commander for every 200
**Sovereign Keys**used in event. Note that you must use 200 keys before the event expires, as the count will be reset once the event expires. - If you obtain from the chest a Legendary Commander (or its Sculptures) that you have already Expertised, the reward will be converted to
**Legendary Marks,**which can be exchanged for items in the event**Exchange Shop**.**Basically, you can exchange for one Universal Legendary Commander Sculpture (what most RoK players call a Gold Head) in the Exchange Shop for every Sculpture of an Expertised Commander you get from the event chest.** **Rewards and their Probabilities:**

## Heart’s Desire

**Event Rules:**

**Heart’s Desire**is a**5-days**event, where you can use**Sovereign Keys**to open chests for rewards including Legendary Commander Sculptures. There is a**cap of 100 chests that can be opened each day**.- Once your
**Sovereign Keys**are fully expended in the event, you can use**Gems**to open chests in the event. - Choose 5 Commanders (“
**Choice Commanders**“) at the start of event, for a chance to obtain Legendary Commander Sculptures of your Choice Commanders with each**Sovereign Key**used.**Note: You cannot change your choice once selected.** - Every 10 times you open a chest, you are guaranteed 1 x Legendary Commander (i.e. 10 x Sculptures) or Legendary Commander Sculpture of your Choice Commanders.
**Note: Although this rule applies in both the Legendary Tavern and Heart’s Desire events, it is actually not the same value to you! This is because the Sculpture you are obtaining for every 10 keys used is for your Choice Commanders! The sooner you Expertise a Commander, the greater is its strength and utility to you.** - If you obtain a Legendary Commander (or their Sculptures) during this event for a Commander that you have already Expertised, it will be automatically exchanged for
**Sovereign Keys**.**Note: Choosing an Expertised Commander as your Choice Commanders in this event is not a good idea.**As I will show later in this post, the average Sculpture you can get from each Sovereign Key used in the Heart’s Desire event is 0.42. Therefore, using 1 Sovereign Key to obtain 0.42 of an Expertised Commander Sculpture to exchange for 0.42 Sovereign Key is a bad idea. **Rewards and their Probabilities**(Note that the probability of obtaining Sculptures of every Commander in the Heart’s Desire is the same. This is not the same case in the Legendary Tavern, which seems to assign lower probabilities for Commanders that are released in the game later than others.**Therefore, choosing the Heart’s Desire event should give advanced RoK players an advantage in developing the newest Commanders in the game**)

## Methodology

First things first, let me clarify the method used in my analysis. As we are dealing here with probabilities and different possible rewards, I have used the “**Expected Value**” formula, which is commonly used in statistics and probability analysis.

You can refer to the following links for an explanation of the method:

## Analysis of Expected Value from Legendary Tavern event

First, let’s look at the scenario whereby we do not prioritize any Legendary Commanders and are happy to obtain Sculptures for any Legendary Commander featured in the event.

Probability of obtaining a “10 x Sculpture” reward: 0.979%

Probability of obtaining a “1 x Sculpture” reward: 32.226%

Assuming I use 200 **Sovereign Keys** in this event, my expected value (in terms of Sculptures) is as follows:

Expected Value = 200 x 0.979% x 10 + 200 x 32.2265% x 1 = 84

Recall that the event rewards you with a chest containing your choice of 10 x Sculptures for every 200 keys used:

Total Expected Value from event in Sculptures = 84 + 10 = **94**

Now, let us consider the scenario whereby we prefer to obtain Sculptures for 5 selected Commanders (“**Choice Commanders**“). What is the Expected Value from the Legendary Tavern in this scenario? We consider this scenario in order to make a like-for-like comparison with the **Heart’s Desire** event.

**Note:** Highlighted in **red** above are the 5 Choice Commanders that I have chosen for the **Heart’s Desire** event. You can choose any 5 of your liking.

Probability of obtaining a “10 x Sculpture” reward (Choice Commanders only) = 0.133%

Probability of obtaining a “1 x Sculpture” reward (Choice Commanders only) = 4.44%

Assuming I use 200 **Sovereign Keys** in this event, my expected value (in terms of Sculptures) is as follows:

Expected Value = 200 x 0.133% x 10 + 200 x 4.44% x 1 = **12**

Recall that the event rewards you with a chest containing your choice of 10 x Sculptures for every 200 keys used:

Total Expected Value from event in Sculptures = 12 + 10 = **22**

Now, let us take a look at the Expected Value from the **Heart’s Desire** event.

## Analysis of Expected Value from Heart’s Desire event

Probability of obtaining a “10 x Sculpture” reward: 0.975%

Probability of obtaining a “1 x Sculpture” reward: 32.255%

Assuming I use 200 **Sovereign Keys** in this event, my expected value (in terms of Sculptures) is as follows:

Expected Value = 200 x 0.975% x 10 + 200 x 32.255% x 1 = **84**

## The Verdict

Event | Expected Value (number of Sculptures) | Average number of Sculptures obtained from each Sovereign Key used |
---|---|---|

Legendary Tavern(200 Sovereign Keys) | At least 22(Choice Commanders) | At least 0.11(Choice Commanders) |

Heart’s Desire(200 Sovereign Keys) | 84(Choice Commanders) | 0.42(Choice Commanders) |

Legendary Tavern(200 Sovereign Keys) | At least 94 (Any Commander) | At least 0.47 (Any Commander) |

- From the above, we can clearly see that the
**Heart’s Desire**event is a much better event to use your**Sovereign Keys**to develop your Choice Commanders. The potential reward in Sculptures of Choice Commanders is almost**4 times higher**in the**Heart’s Desire**event as compared to the**Legendary Tavern**event. - Note that the above figure calculated for average number of Sculptures obtainable from each Sovereign Key used in the
**Legendary Tavern**event is based on a spending of 200 Sovereign Keys to obtain the guaranteed 10 x Sculpture chest.**If you use less than 200 Sovereign Keys in the Legendary Tavern event, your Expected Value will only be 12**, which gives you an average of 0.06 Sculptures from each Sovereign Key used. - Notice I used the words “
**at least**” in the Expected Value from**Legendary Tavern**. This is because you can potentially achieve a higher Expected Value in**Legendary Tavern**due to**Legendary Marks**(if you have 1 or more Expertised Legendary Commanders that is featured in the**Legendary Tavern**event).**Each**Expertised Commander you have increases your Expected Value by between 2 and 9 Sculptures, and average Sculptures per Key by between 0.01 and 0.05 (there is a range here because there are different probabilities to obtain Sculptures for different Commanders). - Unless you spend money like a Whale in RoK, most of us work with limited resources in the game, and should focus our resources to Expertise our selected Commanders. My recommendation would be to go with the
**Heart’s Desire**event to spend your precious**Sovereign Keys**.

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Check out my other event guides **here**!