Subject

[Math, Transparency] Lootbox unit pricing explained - Update Gems & HotM added

### Inquiry

An Australian inquiry into lootbox in game ( see Notes ) discussed several tactics loot boxes use the hide the cost of acquiring a virtual item.

### Currency

There are many reasons virtual premium currencies are used, but one unintended consequence is to hide the real world price. Instead of $3.74 USD per Epic summons lootbox, it is 300 gems.

#### Grouping items

There are many reasons to simplify listed odds. But one unintended consequence is to hide the odds for acquiring a desired virtual item like Boldtusk or Vivica.

### Probability

Most users do not have a good grasp on probability, even the users that do, can have trouble understanding the cost of a desired virtual item like Boldtusk or Vivica.

### Lootbox unit pricing

One proposal in the inquiry was a cash value assigned to each virtual item using the 99% threshold. If 100 users spend $ X USD, each, then 99 of them will acquire the desired virtual item. So Boldtusk would be $1,616+ USD and Vivica would be $22,967+ USD.

This is similar to items at the food store having X USD per pound, or Y USD per quart, or $ Z USD per 100 count. This lets you compare lootbox pricing by generating a single simplified cost.

When displaying a possible prize, displaying the lootbox unit pricing would allow users to make a more informed decision. This would also allow users to shop around between different games with micro transactions.

### Epic summons

Lootbox unit pricing for Epic summons

USD | Gems | Hero | Hero | Hero |
---|---|---|---|---|

$467+ | 37,500+ | Hawkmoon ( red 3* ) | Gan Ju ( yellow 3* ) | |

$587+ | 47,100+ | Tyrum ( purple 3* ) | Valen ( blue 3* ) | |

$707+ | 56,700+ | Belith ( green 3* ) | ||

$1,291+ | 103,500+ | Wu Kong ( yellow 4* ) | Rigard ( purple 4* ) | Kiril ( blue 4* ) |

$1,312+ | 105,300+ | 5* HotM | ||

$1,616+ | 129,600+ | Boldtusk ( red 4* ) | Melendor ( green 4* ) | |

$22,967+ | 1,841,100+ | Vivica ( any color 5* ) |

### Leveling

In Empires, lootbox rewards are unleveled.

Another unit cost would be the leveling cost per hero using only Epic Summons.

Example

$ X USD using Epic Summons to level a 5* 1.1 hero to 5* 4.80 .

### Notes

## Click for notes

### Math

300 gems per Epic summons / 400 gems * $4.99 USD = $3.74 USD

From a bug with red troops, and from long term tracking of red heroes, we know rarity is determined first, then color, then specific hero.

4x 3* heroes= Red, Yellow

5x 3* heroes= Blue, Purple

6x 3* heroes= Green

4x 4* heroes= Blue, Purple, Yellow

5x 4* heroes= Red, Green

4x 5* heroes= all colors

Posted summons odds

3*= 0.72

4*= 0.265

5*= 0.015

3* heroes= 0.72 / 5 colors = 0.144

0.144 / 4= 0.036

1- 0.036 = 0.964

log ( 0.01 ) / log ( 0.964 ) = 125

Check 0.964^125= 0.01

125 * $3.74 = $467

0.144 / 5= 0.0288

1- 0.0288 = 0.9712

log ( 0.01 ) / log ( 0.9712 )= 157

Check 0.9712^157= 0.01

157 * $3.74 = $587

0.144 / 6= 0.024

1- 0.024= 0.976

log ( 0.01 ) / log ( 0.976 )= 189

Check 0.976^189= 0.01

189 * $3.74= $707

4* heroes= 0.265 / 5 colors= 0.053

0.053 / 4 = 0.01325

1- 0.01325= 0.98675

log ( 0.01 )/ log (0.98675 )= 345

Check 0.98675^345= 0.01

345 * $3.74= $1,291

0.053 / 5 = 0.0106

1- 0.0106 = 0.9894

log ( 0.01 ) / log ( 0.9894 )= 432

Check 0.9894^432= 0.01

432 * $3.74 = $1,616

5* heroes= 0.015 / 5 colors = 0.003

0.003 / 4 = 0.00075

1- 0.00075 = 0.99925

log ( 0.01 ) / log ( 0.99925 )= 6,137

Check 0.99925^6,137= 0.01

6,137 * $3.74 = $22,967

Edit:

Hotm

0.013 odds

351 summons

351 * $3.74= $1,312

FIN