How does the price logic work in detail?

NeoStake uses the Logarithmic Market Scoring Rule (LMSR) mechanism.
Developed by Robin Hanson, it is the most widely used automated market-maker model in prediction markets (Polymarket, Augur, etc.).

1. The Core Formula

The LMSR has a cost function:

C(q) = b * ln( Σ ( e^(q_i / b) ) )

• q_i = number of shares bought for outcome i

• b = liquidity parameter (e.g. 100 or 110 in NeoStake)

• n = number of outcomes

The price for outcome i is derived from the partial derivative:

p_i = e^(q_i / b) / ( Σ e^(q_j / b) )

Interpretation:

• Price p_i is always between 0 and 1 (0–100%)

• All prices always sum to 1 (100%)

• Price depends only on the current inventory of shares

2. Example with 2 Outcomes (YES / NO)

Set b = 100. Initial state: q_YES = q_NO = 0.

p_YES = e^(0/100) / ( e^(0/100) + e^(0/100) ) = 0.5
p_NO = 0.5

Start: 50% vs. 50%

A user buys 100 shares on YES
New state: q_YES = 100, q_NO = 0.

p_YES = e^(100/100) / ( e^(100/100) + e^(0/100) ) = e^1 / (e^1 + 1) ≈ 0.731
p_NO = 0.269

Effect: YES price jumps to ~73%, NO drops to ~27%.

3. Trade Costs

The cost of a trade is the difference in the cost function:

Cost = C(q_new) - C(q_old)

Example: buying 100 YES shares with b = 100.

C(0,0) = 100 * ln(e^0 + e^0) = 100 * ln(2) = 69.31
C(100,0) = 100 * ln(e^1 + 1) = 100 * ln(3.718) = 131.03
Cost = 131.03 - 69.31 = 61.72

Even though 100 shares were bought, the cost is only 61.72, because the price increases gradually (slippage).

4. Multi-Outcome Example (A, B, C)

Start: all equal → each 33%.

p_A = p_B = p_C = 0.333

Buying 100 shares on A:

p_A = e^(100/100) / ( e^(100/100) + 1 + 1 ) = 2.718 / 4.718 ≈ 0.576
p_B = p_C = 0.212

Result: A rises to ~58%, the others fall.

5. Cash-Out Logic (Position Value)

The mark-to-market value of your position before resolution:

Value = Shares  CurrentPrice  Payout

(Example: Payout = 1 token per winning share)

• You hold 100 YES shares

• Current market price: p_YES = 0.73

Value = 100 * 0.73 = 73

Position is worth 73 tokens.
You can sell anytime – LMSR guarantees liquidity.

The exact cash-out when selling is also computed via the cost function:

CashOut_exact = C(q_old) - C(q_new)

6. Final Settlement

At resolution, only the winning outcome pays out 1 token per share; all others are worth 0.

Example: 100 YES shares, bought for 61.72.

If YES wins → Payout = 100 → Profit = 100 - 61.72 = +38.28
If NO wins → Payout = 0 → Loss = 0 - 61.72 = -61.72

7. Advantages of LMSR

• Always liquid → You can buy/sell anytime

• Smooth & predictable → Prices change continuously, not in jumps

• Fair & transparent → No manual price-setters, no insider influence

• Supports multiple outcomes → Prices adjust automatically