new cfmm: k = y^(1-p) * n^p

common/antes.ts

@@ -1,6 +1,6 @@
 import { Bet } from './bet'
 import { getDpmProbability } from './calculate-dpm'
-import { getCpmmLiquidity, getCpmmProbability } from './calculate-cpmm'
+import { getCpmmProbability } from './calculate-cpmm'
 import { Binary, CPMM, DPM, FreeResponse, FullContract } from './contract'
 import { User } from './user'
 import { LiquidityProvision } from './liquidity-provision'
@@ -9,42 +9,13 @@ import { noFees } from './fees'
 export const PHANTOM_ANTE = 0.001
 export const MINIMUM_ANTE = 10
 
-export function getCpmmAnteBet(
-  creator: User,
-  contract: FullContract<CPMM, Binary>,
-  anteId: string,
-  amount: number,
-  outcome: 'YES' | 'NO'
-) {
-  const p = getCpmmProbability(contract.pool)
-
-  const { createdTime } = contract
-
-  const bet: Bet = {
-    id: anteId,
-    userId: creator.id,
-    contractId: contract.id,
-    amount: amount,
-    shares: amount,
-    outcome,
-    probBefore: p,
-    probAfter: p,
-    createdTime,
-    isAnte: true,
-    fees: noFees,
-  }
-
-  return bet
-}
-
 export function getCpmmInitialLiquidity(
   creator: User,
   contract: FullContract<CPMM, Binary>,
   anteId: string,
   amount: number
 ) {
-  const { createdTime, pool } = contract
-  const liquidity = getCpmmLiquidity(pool)
+  const { createdTime, pool, p } = contract
 
   const lp: LiquidityProvision = {
     id: anteId,
@@ -54,7 +25,8 @@ export function getCpmmInitialLiquidity(
     isAnte: true,
 
     amount: amount,
-    liquidity,
+    liquidity: amount,
+    probability: getCpmmProbability(pool, p),
   }
 
   return lp

common/calculate-cpmm.ts

@@ -2,12 +2,14 @@ import * as _ from 'lodash'
 
 import { Bet } from './bet'
 import { Binary, CPMM, FullContract } from './contract'
-import { CREATOR_FEE, Fees, LIQUIDITY_FEE, PLATFORM_FEE } from './fees'
+import { CREATOR_FEE, Fees, LIQUIDITY_FEE, noFees, PLATFORM_FEE } from './fees'
 
-export function getCpmmProbability(pool: { [outcome: string]: number }) {
-  // For binary contracts only.
+export function getCpmmProbability(
+  pool: { [outcome: string]: number },
+  p: number
+) {
   const { YES, NO } = pool
-  return NO / (YES + NO)
+  return (p * NO) / ((1 - p) * YES + p * NO)
 }
 
 export function getCpmmOutcomeProbabilityAfterBet(
@@ -16,7 +18,7 @@ export function getCpmmOutcomeProbabilityAfterBet(
   bet: number
 ) {
   const { newPool } = calculateCpmmPurchase(contract, bet, outcome)
-  const p = getCpmmProbability(newPool)
+  const p = getCpmmProbability(newPool, contract.p)
   return outcome === 'NO' ? 1 - p : p
 }
 
@@ -25,14 +27,17 @@ function calculateCpmmShares(
   pool: {
     [outcome: string]: number
   },
+  p: number,
   bet: number,
   betChoice: string
 ) {
   const { YES: y, NO: n } = pool
-  const numerator = bet ** 2 + bet * (y + n)
-  const denominator = betChoice === 'YES' ? bet + n : bet + y
-  const shares = numerator / denominator
-  return shares
+  const k = y ** (1 - p) * n ** p
+
+  return betChoice === 'YES'
+    ? // https://www.wolframalpha.com/input?i=%28y%2Bb-s%29%5E%281-p%29*%28n%2Bb%29%5Ep+%3D+k%2C+solve+s
+      y + bet - (k * (bet + n) ** -p) ** (1 / (1 - p))
+    : n + bet - (k * (bet + y) ** (p - 1)) ** (1 / p)
 }
 
 export function getCpmmLiquidityFee(
@@ -40,7 +45,7 @@ export function getCpmmLiquidityFee(
   bet: number,
   outcome: string
 ) {
-  const p = getCpmmProbability(contract.pool)
+  const p = getCpmmProbability(contract.pool, contract.p)
   const betP = outcome === 'YES' ? 1 - p : p
 
   const liquidityFee = LIQUIDITY_FEE * betP * bet
@@ -59,10 +64,10 @@ export function calculateCpmmSharesAfterFee(
   bet: number,
   outcome: string
 ) {
-  const { pool } = contract
-  const { remainingBet } = getCpmmLiquidityFee(contract, bet, outcome)
+  const { pool, p } = contract
+  // const { remainingBet } = getCpmmLiquidityFee(contract, bet, outcome)
 
-  return calculateCpmmShares(pool, remainingBet, outcome)
+  return calculateCpmmShares(pool, p, bet, outcome)
 }
 
 export function calculateCpmmPurchase(
@@ -70,10 +75,12 @@ export function calculateCpmmPurchase(
   bet: number,
   outcome: string
 ) {
-  const { pool } = contract
-  const { remainingBet, fees } = getCpmmLiquidityFee(contract, bet, outcome)
+  const { pool, p } = contract
+  // const { remainingBet, fees } = getCpmmLiquidityFee(contract, bet, outcome)
+  const remainingBet = bet
+  const fees = noFees
 
-  const shares = calculateCpmmShares(pool, remainingBet, outcome)
+  const shares = calculateCpmmShares(pool, p, remainingBet, outcome)
   const { YES: y, NO: n } = pool
 
   const { liquidityFee: fee } = fees
@@ -84,6 +91,7 @@ export function calculateCpmmPurchase(
       : [y + remainingBet + fee, n - shares + remainingBet + fee]
 
   const newPool = { YES: newY, NO: newN }
+  // console.log(getCpmmLiquidity(pool, p), getCpmmLiquidity(newPool, p))
 
   return { shares, newPool, fees }
 }
@@ -96,6 +104,7 @@ export function calculateCpmmShareValue(
   const { pool } = contract
   const { YES: y, NO: n } = pool
 
+  // TODO: calculate using new function
   const poolChange = outcome === 'YES' ? shares + y - n : shares + n - y
   const k = y * n
   const shareValue = 0.5 * (shares + y + n - Math.sqrt(4 * k + poolChange ** 2))
@@ -136,63 +145,57 @@ export function getCpmmProbabilityAfterSale(
   bet: Bet
 ) {
   const { newPool } = calculateCpmmSale(contract, bet)
-  return getCpmmProbability(newPool)
+  return getCpmmProbability(newPool, contract.p)
 }
 
-export const calcCpmmInitialPool = (initialProbInt: number, ante: number) => {
-  const p = initialProbInt / 100.0
-
-  const [poolYes, poolNo] =
-    p >= 0.5 ? [ante * (1 / p - 1), ante] : [ante, ante * (1 / (1 - p) - 1)]
-
-  return { poolYes, poolNo }
-}
-
-export function getCpmmLiquidity(pool: { [outcome: string]: number }) {
-  // For binary contracts only.
+export function getCpmmLiquidity(
+  pool: { [outcome: string]: number },
+  p: number
+) {
   const { YES, NO } = pool
-  return Math.sqrt(YES * NO)
+  return YES ** (1 - p) * NO ** p
 }
 
-export function addCpmmLiquidity(
-  contract: FullContract<CPMM, Binary>,
-  amount: number
-) {
-  const { YES, NO } = contract.pool
-  const p = getCpmmProbability({ YES, NO })
+// TODO: use new pricing equation
+// export function addCpmmLiquidity(
+//   contract: FullContract<CPMM, Binary>,
+//   amount: number
+// ) {
+//   const { YES, NO } = contract.pool
+//   const p = getCpmmProbability({ YES, NO }, contract.p)
 
-  const [newYes, newNo] =
-    p >= 0.5
-      ? [amount * (1 / p - 1), amount]
-      : [amount, amount * (1 / (1 - p) - 1)]
+//   const [newYes, newNo] =
+//     p >= 0.5
+//       ? [amount * (1 / p - 1), amount]
+//       : [amount, amount * (1 / (1 - p) - 1)]
 
-  const betAmount = Math.abs(newYes - newNo)
-  const betOutcome = p >= 0.5 ? 'YES' : 'NO'
+//   const betAmount = Math.abs(newYes - newNo)
+//   const betOutcome = p >= 0.5 ? 'YES' : 'NO'
 
-  const poolLiquidity = getCpmmLiquidity({ YES, NO })
-  const newPool = { YES: YES + newYes, NO: NO + newNo }
-  const resultingLiquidity = getCpmmLiquidity(newPool)
-  const liquidity = resultingLiquidity - poolLiquidity
+//   const poolLiquidity = getCpmmLiquidity({ YES, NO })
+//   const newPool = { YES: YES + newYes, NO: NO + newNo }
+//   const resultingLiquidity = getCpmmLiquidity(newPool)
+//   const liquidity = resultingLiquidity - poolLiquidity
 
-  return { newPool, liquidity, betAmount, betOutcome }
-}
+//   return { newPool, liquidity, betAmount, betOutcome }
+// }
 
-export function removeCpmmLiquidity(
-  contract: FullContract<CPMM, Binary>,
-  liquidity: number
-) {
-  const { YES, NO } = contract.pool
-  const poolLiquidity = getCpmmLiquidity({ YES, NO })
-  const p = getCpmmProbability({ YES, NO })
+// export function removeCpmmLiquidity(
+//   contract: FullContract<CPMM, Binary>,
+//   liquidity: number
+// ) {
+//   const { YES, NO } = contract.pool
+//   const poolLiquidity = getCpmmLiquidity({ YES, NO })
+//   const p = getCpmmProbability({ YES, NO }, contract.p)
 
-  const f = liquidity / poolLiquidity
-  const [payoutYes, payoutNo] = [f * YES, f * NO]
+//   const f = liquidity / poolLiquidity
+//   const [payoutYes, payoutNo] = [f * YES, f * NO]
 
-  const betAmount = Math.abs(payoutYes - payoutNo)
-  const betOutcome = p >= 0.5 ? 'NO' : 'YES' // opposite side as adding liquidity
-  const payout = Math.min(payoutYes, payoutNo)
+//   const betAmount = Math.abs(payoutYes - payoutNo)
+//   const betOutcome = p >= 0.5 ? 'NO' : 'YES' // opposite side as adding liquidity
+//   const payout = Math.min(payoutYes, payoutNo)
 
-  const newPool = { YES: YES - payoutYes, NO: NO - payoutNo }
+//   const newPool = { YES: YES - payoutYes, NO: NO - payoutNo }
 
-  return { newPool, payout, betAmount, betOutcome }
-}
+//   return { newPool, payout, betAmount, betOutcome }
+// }

common/calculate.ts

@@ -21,7 +21,7 @@ import { Binary, Contract, CPMM, DPM, FullContract } from './contract'
 
 export function getProbability(contract: FullContract<DPM | CPMM, Binary>) {
   return contract.mechanism === 'cpmm-1'
-    ? getCpmmProbability(contract.pool)
+    ? getCpmmProbability(contract.pool, contract.p)
     : getDpmProbability(contract.totalShares)
 }
 
@@ -31,14 +31,14 @@ export function getInitialProbability(
   return (
     contract.initialProbability ??
     (contract.mechanism === 'cpmm-1'
-      ? getCpmmProbability(contract.pool)
+      ? getCpmmProbability(contract.pool, contract.p)
       : getDpmProbability(contract.phantomShares ?? contract.totalShares))
   )
 }
 
 export function getOutcomeProbability(contract: Contract, outcome: string) {
   return contract.mechanism === 'cpmm-1'
-    ? getCpmmProbability(contract.pool)
+    ? getCpmmProbability(contract.pool, contract.p)
     : getDpmOutcomeProbability(contract.totalShares, outcome)
 }
 

common/contract.ts

@@ -49,6 +49,7 @@ export type DPM = {
 
 export type CPMM = {
   mechanism: 'cpmm-1'
+  p: number // probability constant in y^(1-p) * n^p = k
   pool: { [outcome: string]: number }
 }
 

common/liquidity-provision.ts

@@ -8,4 +8,5 @@ export type LiquidityProvision = {
 
   amount: number // M$ quantity
   liquidity: number // sqrt(k)
+  probability: number
 }

common/new-bet.ts

@@ -34,8 +34,9 @@ export const getNewBinaryCpmmBetInfo = (
 
   const newBalance = user.balance - (amount - loanAmount)
 
-  const probBefore = getCpmmProbability(contract.pool)
-  const probAfter = getCpmmProbability(newPool)
+  const { pool, p } = contract
+  const probBefore = getCpmmProbability(pool, p)
+  const probAfter = getCpmmProbability(newPool, p)
 
   const newBet: Bet = {
     id: newBetId,

common/new-contract.ts

@@ -10,7 +10,6 @@ import {
 import { User } from './user'
 import { parseTags } from './util/parse'
 import { removeUndefinedProps } from './util/object'
-import { calcCpmmInitialPool } from './calculate-cpmm'
 import { calcDpmInitialPool } from './calculate-dpm'
 
 export function getNewContract(
@@ -86,13 +85,14 @@ const getBinaryDpmProps = (initialProb: number, ante: number) => {
 }
 
 const getBinaryCpmmProps = (initialProb: number, ante: number) => {
-  const { poolYes, poolNo } = calcCpmmInitialPool(initialProb, ante)
-  const pool = { YES: poolYes, NO: poolNo }
+  const pool = { YES: ante, NO: ante }
+  const p = initialProb / 100
 
   const system: CPMM & Binary = {
     mechanism: 'cpmm-1',
     outcomeType: 'BINARY',
-    initialProbability: initialProb / 100,
+    initialProbability: p,
+    p,
     pool: pool,
   }
 

common/sell-bet.ts

@@ -89,13 +89,13 @@ export const getCpmmSellBetInfo = (
   contract: FullContract<CPMM, Binary>,
   newBetId: string
 ) => {
-  const { pool } = contract
+  const { pool, p } = contract
   const { id: betId, amount, shares, outcome } = bet
 
   const { saleValue, newPool, fees } = calculateCpmmSale(contract, bet)
 
-  const probBefore = getCpmmProbability(pool)
-  const probAfter = getCpmmProbability(newPool)
+  const probBefore = getCpmmProbability(pool, p)
+  const probAfter = getCpmmProbability(newPool, p)
 
   console.log(
     'SELL M$',

functions/src/create-contract.ts

@@ -20,7 +20,6 @@ import { randomString } from '../../common/util/random'
 import { getNewContract } from '../../common/new-contract'
 import {
   getAnteBets,
-  getCpmmAnteBet,
   getCpmmInitialLiquidity,
   getFreeAnswerAnte,
   MINIMUM_ANTE,
@@ -131,27 +130,6 @@ export const createContract = functions
           await yesBetDoc.set(yesBet)
           await noBetDoc.set(noBet)
         } else if (outcomeType === 'BINARY') {
-          const { YES: y, NO: n } = contract.pool
-          const anteBet = Math.abs(y - n)
-
-          if (anteBet) {
-            const betDoc = firestore
-              .collection(`contracts/${contract.id}/bets`)
-              .doc()
-
-            const outcome = y > n ? 'NO' : 'YES' // more in YES pool if prob leans NO
-
-            const bet = getCpmmAnteBet(
-              creator,
-              contract as FullContract<CPMM, Binary>,
-              betDoc.id,
-              anteBet,
-              outcome
-            )
-
-            await betDoc.set(bet)
-          }
-
           const liquidityDoc = firestore
             .collection(`contracts/${contract.id}/liquidity`)
             .doc()

web/components/contract-card.tsx

@@ -20,7 +20,6 @@ import { Avatar } from './avatar'
 import { Spacer } from './layout/spacer'
 import { useState } from 'react'
 import { TweetButton } from './tweet-button'
-import { getCpmmLiquidity } from '../../common/calculate-cpmm'
 
 export function ContractCard(props: {
   contract: Contract

web/lib/firebase/contracts.ts

@@ -43,17 +43,17 @@ export function contractMetrics(contract: Contract) {
   const liquidityLabel =
     contract.mechanism === 'dpm-2'
       ? `${formatMoney(truePool)} pool`
-      : `${formatMoney(getCpmmLiquidity(contract.pool))} liquidity`
+      : `${formatMoney(getCpmmLiquidity(pool, contract.p))} liquidity`
 
   return { truePool, liquidityLabel, createdDate, resolvedDate }
 }
 
 export function getBinaryProbPercent(contract: FullContract<any, Binary>) {
-  const { totalShares, pool, resolutionProbability, mechanism } = contract
+  const { totalShares, pool, p, resolutionProbability, mechanism } = contract
 
   const prob =
     resolutionProbability ?? mechanism === 'cpmm-1'
-      ? getCpmmProbability(pool)
+      ? getCpmmProbability(pool, p)
       : getDpmProbability(totalShares)
 
   const probPercent = Math.round(prob * 100) + '%'