> For the complete documentation index, see [llms.txt](https://polars-io.gitbook.io/polars-public/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://polars-io.gitbook.io/polars-public/business-model-1/betting.md).

# Predictions

White or Black

*The price of polar tokens is consistently influenced by the results of various events in which there are opposing sides. One opposing side randomly ends up on the White Team side, and the other opposing side falls on the Black Team side. If the White Team wins, the WHITE token will rise in value and the BLACK token will fall in value. Conversely, if the Black Team wins, the BLACK token will go up in value and the WHITE token will go down in value. But the cumulative collateral of the two polar tokens will remain unchanged.* 

The formula for calculating the change in the price of polar tokens contains several basic parameters, including **Collateral for WHITE token**, **Collateral for BLACK token**, **Aggregate collateral for WHITE and BLACK tokens**, **Minted WHITE tokens**, **Minted BLACK tokens**,  **Basic volatility** and **Popularity** **Coef**. 

**The WHITE token collateral** is the amount of the underlying asset (For example: BUSD) that users paid when purchasing WHITE tokens from the Prediction Pool. 

**The BLACK token collateral** is the amount of the underlying asset (For example: BUSD) that users paid when purchasing BLACK tokens from the Prediction Pool. 

**The aggregate collateral** of WHITE and BLACK tokens is the aggregate amount of the underlying asset (For example: BUSD) that users paid when purchasing WHITE and BLACK tokens from the Prediction Pool. 

**Minted WHITE tokens** is the number of WHITE tokens generated by the Prediction Pool as a result of users purchases.

**Minted BLACK tokens** is the number of BLACK tokens generated by the Prediction Pool as a result of users purchases.

**Basic volatility** is the percentage of the winning and / or losing team's price change, excluding the Popularity Coef. For example: **5%**. 

**The Popularity Coef** is the value multiplied by the Basic Volatility for the winning or losing team. This ratio reflects the difference in the collateral of the WHITE and BLACK token in relation to each other. To calculate it, it is enough to divide the collateral of one token by the collateral of another.

$$
WhitePopularCoef=BlackColleteral/WhiteColleteral
$$

​If the WHITE token users bought more, and its collateral is greater than the BLACK token collateral, then the WHITE Token Popularity Coef will be less than 1, and the BLACK Token Popularity Coef will be greater than 1.

$$
WhitePopularCoef=900000/1000000=0.9<1
$$

$$
BlackPopularCoef=1000000/900000=1.111>1
$$

​The platform has 2 options for Popularity Coef influence, one of which is selected when creating a Prediction Pool:

* **Option 1.** Popularity Coef affects the Basic Volatility of the winning team (And the Basic Volatility of the losing team remains unchanged)
* **Option 2.** Popularity Coef affects the Basic Volatility of the losing team (And the Basic Volatility of the winning team remains unchanged)

At the moment, we have given priority to the first option, so we will use it in further examples and formulas.

### Change in prices of polar tokens

In order to calculate the future price of polar tokens if any of the teams win, we need to understand how the collateralization will be redistributed between WHITE and BLACK tokens. To do this, we need to add BasicVolatility \* PopularityCoef to the collateral of the winning team, and subtract BasicVolatility from the collateral of the losing team. Further, it remains to divide the new collateralization of polar tokens into Minted Tokens and we will receive a new price of polar tokens.

$$
NextWinnerPrice=NewWinnerTokenCollateral
/MintedWinnerToken
$$

#### Let's look at the calculations using an example

Start WHITE Price (BUSD): **0.55**

Start PLACK Price (BUSD): **0.46**

Start WHITE Collateral (BUSD): **110000**

Start BLACK Collateral (BUSD): **98000**

Minted WHITE tokens: **200000**

Minted BLACK tokens: **213043**

Basic Volatility: **5%**

> **Let's see how the price of polar tokens will change if Black Team wins. First we calculate the new BLACK price, then we calculate the new WHITE price.**

*<mark style="color:purple;">#NewBLACKPrice</mark>*

**Calculating Popularity Coef for BLACK:**

$$
BLACKPopularityCoef=110000/98000=1.1224
$$

**Now calculating new Black Collateral:**

$$
NewBLACKCollateral = 98000+98000*0.05*1.1224=103500
$$

**Calculating New BLACK price:**&#x20;

$$
NewBLACKPrice = 103500/213043=0.485817
$$

*<mark style="color:purple;">#NewWHITEPrice</mark>*

**Calculating New WHITE Collateral:**

$$
NewWHITECollateral = 110000-110000\*0.05=104500
$$

**Calculating New WHITE price:**&#x20;

$$
NewWHITEPrice = 104500/200000=0.5225
$$

#### Total, new prices for polar tokens:

WHITE Price (BUSD): **0.5225** (-5%)

BLACK Price (BUSD) **0.4858** (+5.6%)

Now users can freely buy and sell polar tokens at new prices in the Prediction Pool. This process is cyclical and most likely has no end.

> **If the result of the event turns out to be a draw, then the price of polar tokens in this cycle will remain unchanged.**