> For the complete documentation index, see [llms.txt](https://funarchy.gitbook.io/funarchy/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://funarchy.gitbook.io/funarchy/security-for-prediction-market/trading-mechanism/amm-risks/permanent-loss/unequal-market-state.md).

# Unequal market state

Contrary to scenario A, unequal market state mean that Yes/No shares price are not equal.

{% stepper %}
{% step %}
Liquidity is provided after trading occurs in "Permanent Loss - Market creation stat". (80:20)

* Action: User C provides liquidity of 1,000 USDC.
* LP Position: Temporarily deposit $1000 previously deposited by User A and $1000 added by User C.
  * $$Yes(500 + 1000)$$, $$No(2000 + 1000)$$
  * $$Liquidity Value(1000 + 1000) = 2000$$
  * However, in the current calculation formula, the product of $$Yes$$ and $$No$$ does not equal a constant value.
  * Therefore, since price fluctuations occur when this constant formula is broken, a formula exists to adjust this and calculate how much LP share to distribute to user C. This formula always returns a portion of the $$Yes$$ or $$No$$ shares, which are currently at a high price and thus have a high probability of winning, to those who provided liquidity to adjust the constant.\
    \
    When providing liquidity in an imbalanced market, tokens with high current value are provided together with LP shares. LP shares are tokens that can be immediately converted to USDC later.<br>
  * $$OutcomePriceA$$ : The price of the share with the higher probability at present\
    $$OutcomePriceB$$ : The price of the share with the current lower probability$$OutcomeShareA$$ : Among Yes/No, the number of shares with a higher probability are given to liquidity providers and the remaining number is the remaining number.\
    $$OutcomeShareB$$ : Among Yes/No, this is the share with the lower probability.
  * * $$OutcomeShareA = \frac {OutcomeShareB \* OutcomePriceB} {OutcomePriceA}$$<br>
  * If we consider A in the above formula as having a high present value:
    * $$OutcomeShareYes(x) = \frac {OutcomeShareNo(2000 + 1000) \* 0.2} {0.8}$$
    * $$OutcomeShareYes(x) = 750$$
    * $$Yes(750) \* No(3000) = 1500^2$$
    * The LP share and Yes share returned to user C through the values ​​obtained in this way are as follows:
      * $$Yes(1500) - OutcomeShareYes(750) = Yes(750)$$
      * $$Liquidity Value(1500) -  Liquidity Value(1000)= LPshare(500)$$
        {% endstep %}

{% step %}
**Trading occurs**

* Situation: As time passes and information and news emerge that Trump's chances of winning increase, User B purchases another $1,000 worth of Yes.
* AMM Action: FPMM temporarily provides liquidity to the formula that processes these orders.
  * It must not be broken before $$1500^2$$.
    * $$Yes(1750) \* No(4000) \not = 1500^2$$
  * So, with the information we know, $$No(4000)$$, and the fixed value $$1500^2$$we can calculate the Yes share that will come out later.
    * $$Yes(x) \* No(4000)  = 1500^2$$
      * $$Yes(x) = 1500^2 / No(4000)$$
      * $$Yes(x) =  562.5$$
  * This should leave you with a total of 562.5 Yes shares for a total of $1000.
* LP Position Change:\
  In the end, we give Yes shares to User B, and since the remaining amount should be 562.5, we give $$Yes(1750) - Yes(562.5) = 1187.5$$  Yes shares. In this case, both Users A and B end up losing money.
* Here is the formula for how much money Users A and B lose:
  * $$Yes(562.5) \* No(4000) = 1000^2$$
  * This changes the Yes/No price ratio from 80:20 ⇒ 87:13.
  * User A's loss up to this point can be derived using the following formula.
    * $$V(p) = (\text{YES Price}) + (\text{No Price})$$
    * $$V(p) = \mathbf{2} \cdot \sqrt{k} \cdot \sqrt{p(1-p)}$$
    * *Initial price ratio*: $$V(0.5) \propto \sqrt{0.5 \times 0.5} = \sqrt{0.25} = 0.5$$
    * *Price ratio thereafter*: $$V(0.8) \propto \sqrt{0.87 \times 0.13} = \sqrt{0.11} = 0.3$$
    * $$Ratio = \frac{V(0.87)}{V(0.5)} = \frac{0.33}{0.5} = 0.66 \quad (66%)$$
  * So, User A's funds are reduced from $1000 to only $660.
  * If User B calculates the loss like User A, it is as follows:
    * *Initial price ratio*: $$V(0.8) \propto \sqrt{0.8 \times 0.2} = \sqrt{0.16} = 0.4$$
    * *Price ratio thereafter*: $$V(0.8) \propto \sqrt{0.87 \times 0.13} = \sqrt{0.11} = 0.3$$
    * $$Ratio = \frac{V(0.87)}{V(0.8)} = \frac{0.33}{0.4} = 0.825 \quad (82.5%)$$
  * User B also only has about 82.5% of his initial assets left.
    {% endstep %}

{% step %}
**Market closed and loss confirmed**

* Conclusion: \
  User A, the creator of the market, will have $375 left, which is 2/3 of the 562.5 Yes shares that were initially provided with $1,000.\
  \
  User B receives 750 as liquidity provider, plus 187.5 Yes shares, which is 1/3 of the remaining shares in the pool, leaving only $937.5.
* If there is a 3% fee in the current market, User A will receive $50 and User B will receive $10.\
  Still, User A has $425, and User B has $947.5. Ultimately, liquidity providers have incurred permanent losses.

{% hint style="info" %}
Why does User A receive $50?

The reason is that when the initial transaction was conducted, since A alone provided liquidity, all fees incurred at that time went to A.&#x20;

Later, when User C provided liquidity, the fees incurred in the transaction were taken according to each LP share, so it was $50.

* First transaction: $30 all to A.
* Second transaction: $20 for A, $10 for B.
  {% endhint %}
  {% endstep %}
  {% endstepper %}


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