> For the complete documentation index, see [llms.txt](https://doc.cryptostone.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://doc.cryptostone.org/crypto-stone/crypto-stone-wp-cn/xi-you-du-yu-shou-cang/31rarityscore-yu-probabilityrarityindex.md).

# 31. Rarity Score 与 Probability Index

CryptoStone 使用两个指标来量化每颗宝石的稀有度。

| 指标                       | 目的                 |
| ------------------------ | ------------------ |
| Rarity Score             | 用户可直观理解的 0\~100 分数 |
| Probability Rarity Index | 基于实际发生概率的数学稀有度指标   |

## 31.1 Rarity Score

$$
\text{Rarity Score}
===================

\text{Pool Supply Score}
\+
\text{Weight Score}
\+
\text{Color Score}
\+
\text{Clarity Score}
\+
\text{Cut Score}
$$

分数分配如下。

| Attribute         | Max Score |
| ----------------- | --------: |
| Pool Supply Score |        20 |
| Weight            |        20 |
| Color             |        20 |
| Clarity           |        20 |
| Cut               |        20 |
| Total             |       100 |

Pool Supply Score 基于每种宝石的 Max Supply 计算。该项目并不是为了让某一种宝石自动获得更高稀有度的奖励。相反，Max Supply 越低的矿池会获得越低的基础分数，使其更难达到高等级最终结果。

$$
\text{Pool Supply Score}
========================

15 + 5 \times
\frac{\text{StoneMaxSupply} - \text{MinCollectionSupply}}
{\text{MaxCollectionSupply} - \text{MinCollectionSupply}}
$$

基准值如下。

* MaxCollectionSupply = 220,000
* MinCollectionSupply = 110,000

Pool Supply Score 使用 15 到 20 之间的固定值。

| Stone      | Max Supply | Pool Supply Score |
| ---------- | ---------: | ----------------: |
| Diamond    |    110,000 |              15.0 |
| Emerald    |    120,000 |              15.5 |
| Ruby       |    130,000 |              15.9 |
| Sapphire   |    140,000 |              16.4 |
| Pearl      |    150,000 |              16.8 |
| Garnet     |    160,000 |              17.3 |
| Amethyst   |    170,000 |              17.7 |
| Aquamarine |    180,000 |              18.2 |
| Spinel     |    190,000 |              18.6 |
| Opal       |    200,000 |              19.1 |
| Topaz      |    210,000 |              19.5 |
| Zircon     |    220,000 |              20.0 |

例如，Diamond 的 Max Supply 为 110,000，因此拥有最低的 Pool Supply Score。Zircon 的 Max Supply 为 220,000，因此拥有最高的 Pool Supply Score。因此，在 Diamond Pool 中获得 Epic、Legendary、Genesis 会更困难。但这样挖出的高等级 Diamond Gem NFT 同时满足低供应量与高等级两个条件，因此可能在市场中形成更高的收藏价值。

这一结构并不是用简单分数固定矿池之间的优劣，而是将各矿池发行量差异反映到最终等级难度中。供应量较低的矿池更难获得高等级结果，供应量较高的矿池相对更容易。

## 31.2 Probability Rarity Index

如果说 Rarity Score 是面向用户的直观比较指标，那么 Probability Rarity Index 则是基于各属性发生概率的数学稀有度指标。

Gem NFT (`g`) 的属性组合发生概率 (`P(g)`) 定义如下。

$$
P(g) = P\_{\text{stone}} \times P\_{\text{weight}} \times P\_{\text{color}} \times P\_{\text{clarity}} \times P\_{\text{cut}}
$$

由此计算概率型稀有度指标。

$$
\text{Probability Rarity Index} = -\log\_{10}(P(g))
$$

该指标用于显示某个 Gem NFT 的属性组合在统计上有多稀有。

Rarity Score 用作最终等级计算的用户友好标准。基础等级区间如下。

| Final Tier | Rarity Score Range | 角色                 |
| ---------- | ------------------ | ------------------ |
| Common     | 0 \~ 34            | 最常见的宝石群，基础收藏层与精炼材料 |
| Rare       | 35 \~ 50           | 比普通挖矿结果更稀有的中间收藏层   |
| Epic       | 51 \~ 74           | 用户可感知为有意义成功的高等级区间  |
| Legendary  | 75 \~ 89           | 非常稀有的高价值收藏区间       |
| Genesis    | 90 \~ 100          | 反映极端属性组合与最高分的顶级区间  |

当 Pool Supply Score 15\~20 与 Weight、Color、Clarity、Cut 分数表共同适用时，该区间目标是平均每挖出约 36 个 NFT，可期待 1 个 Epic 或以上结果。实际结果会因随机属性组合与矿池供应修正值而变化。

CryptoStone 同时使用 Rarity Score 与 Probability Rarity Index，为收藏者提供直观分数体系与基于数据的可验证稀有度体系。


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