Split & Merge

Split and Merge allow users to convert between KP and paired YES+NO shares without affecting the market price. These operations bypass the AMM entirely.

Split

Convert KP into equal amounts of YES and NO shares.

N KP  →  N YES shares + N NO shares

Property	Value
Price impact	None (bypasses AMM)
Fee	None
Use case	Acquire both sides to sell one later

How it works:

1. User deposits N KP
2. System creates N YES shares and N NO shares in user’s positions
3. Market quantities q_yes and q_no both increase by N
4. Because LS-LMSR uses b = α × (q_yes + q_no), the ratio q/b stays nearly constant, so prices remain approximately unchanged

Merge

Convert paired YES+NO shares back into KP.

N YES shares + N NO shares  →  N KP

Property	Value
Price impact	None (bypasses AMM)
Fee	None
Limit	Cannot merge more than min(YES held, NO held)
Use case	Exit both sides simultaneously; redeem guaranteed value

How it works:

1. User specifies N shares to merge
2. System burns N YES shares and N NO shares
3. User receives N KP
4. Market quantities decrease by N on both sides, preserving price ratio

Why Split & Merge?

In a binary market, holding 1 YES share + 1 NO share guarantees a 1 KP payout regardless of outcome. Split and Merge formalize this equivalence:

• Split lets users acquire “raw” exposure that they can then selectively sell
• Merge lets users cash out paired positions without incurring AMM slippage

Technical Note

Because LS-LMSR uses b = α × Σqᵢ, adding or removing equal amounts on both sides changes the absolute value of b. For small operations this is negligible, but very large splits/merges can cause slight price shifts. This is an inherent property of the liquidity-sensitive model.