> For the complete documentation index, see [llms.txt](https://docs.sugar.money/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.sugar.money/rewards/giveaway/the-mathematics-behind-ticket-valuation.md).

# The Mathematics Behind Ticket Valuation

**Why EV Matters**\
Expected Value (EV) is a core concept in understanding the potential long-term benefits of holding tickets in a rewards-based system. It helps estimate the average value a ticket will return over time, taking into account current platform dynamics.

***

#### Calculating Expected Value (EV)

The expected value of a single ticket depends on two key variables:

* **Available\_rewards**: This includes 85% of platform fees plus some of pSOL mints (post-migration) that are continuously added to the rewards pool.
* **Tickets\_held**: The total number of tickets currently in circulation across all users.

**EV Formula:**

$$
EV\_{\text{per ticket}} = \left( \frac{\text{Available\_rewards}}{\text{Tickets\_held}} \right) \times \text{Multiplier} \times \text{Balancing\_Factor}
$$

Where:

* **Multiplier** reflects any game or user-specific reward multipliers.
* **Balancing\_Factor** is an internal scaling variable (currently set to 0.5) to ensure long-term sustainability.

***

#### Why Holding Tickets Is Strategic

* **Compounding Value Over Time**: Since the EV grows as more users play and contribute to the rewards pool, each ticket becomes more valuable the longer you hold it—assuming others continue to participate.
* **Increased Share of Rewards**: When someone plays before you, they reduce the total rewards available, but also reduce the number of tickets in competition (if tickets are burned or spent), potentially increasing your share.
* **Better Risk-Reward Ratio**: Given that each ticket's EV is around 90% of its cost even in the short term, holding for higher pool accumulation can easily tip the balance in your favor.

***

#### Points allocation

* **Base rate:** Each ticket grants **4 base points**. Your final total is multiplied by the personal multiplier you receive and the amount of tickets you use to play.
* **Time-limited:** This feature (and its point value) is available only during the first season. It may return in the future, but with fewer rewards.
* **Additional incentives:**
  * Although the point amount doesn’t scale with the ticket’s underlying rewards, it still offers a fixed bonus for exchanging tickets.
  * The season-end cutoff encourages users to spend at least some tickets now rather than hoard them.