single-pot no-refund payoff; bet selling

functions/src/index.ts

@@ -2,7 +2,7 @@ import * as admin from 'firebase-admin'
 
 admin.initializeApp()
 
-export * from './keep-awake'
+// export * from './keep-awake'
 export * from './place-bet'
 export * from './resolve-market'
 export * from './sell-bet'

functions/src/place-bet.ts

@@ -43,7 +43,7 @@ export const placeBet = functions.runWith({ minInstances: 1 }).https.onCall(
         .collection(`contracts/${contractId}/bets`)
         .doc()
 
-      const { newBet, newPool, newDpmWeights, newBalance } = getNewBetInfo(
+      const { newBet, newPool, newTotalShares, newBalance } = getNewBetInfo(
         user,
         outcome,
         amount,
@@ -54,7 +54,7 @@ export const placeBet = functions.runWith({ minInstances: 1 }).https.onCall(
       transaction.create(newBetDoc, newBet)
       transaction.update(contractDoc, {
         pool: newPool,
-        dpmWeights: newDpmWeights,
+        totalShares: newTotalShares,
       })
       transaction.update(userDoc, { balance: newBalance })
 
@@ -79,29 +79,19 @@ const getNewBetInfo = (
       ? { YES: yesPool + amount, NO: noPool }
       : { YES: yesPool, NO: noPool + amount }
 
-  const dpmWeight =
+  const shares =
     outcome === 'YES'
-      ? (amount * noPool ** 2) / (yesPool ** 2 + amount * yesPool)
+      ? amount + (amount * noPool ** 2) / (yesPool ** 2 + amount * yesPool)
-      : (amount * yesPool ** 2) / (noPool ** 2 + amount * noPool)
+      : amount + (amount * yesPool ** 2) / (noPool ** 2 + amount * noPool)
 
-  const { YES: yesWeight, NO: noWeight } = contract.dpmWeights || {
+  const { YES: yesShares, NO: noShares } = contract.totalShares
-    YES: 0,
-    NO: 0,
-  } // only nesc for old contracts
 
-  const newDpmWeights =
+  const newTotalShares =
     outcome === 'YES'
-      ? { YES: yesWeight + dpmWeight, NO: noWeight }
+      ? { YES: yesShares + shares, NO: noShares }
-      : { YES: yesWeight, NO: noWeight + dpmWeight }
+      : { YES: yesShares, NO: noShares + shares }
 
   const probBefore = yesPool ** 2 / (yesPool ** 2 + noPool ** 2)
-
-  const probAverage =
-    (amount +
-      noPool * Math.atan(yesPool / noPool) -
-      noPool * Math.atan((amount + yesPool) / noPool)) /
-    amount
-
   const probAfter = newPool.YES ** 2 / (newPool.YES ** 2 + newPool.NO ** 2)
 
   const newBet: Bet = {
@@ -109,15 +99,14 @@ const getNewBetInfo = (
     userId: user.id,
     contractId: contract.id,
     amount,
-    dpmWeight,
+    shares,
     outcome,
     probBefore,
-    probAverage,
     probAfter,
     createdTime: Date.now(),
   }
 
   const newBalance = user.balance - amount
 
-  return { newBet, newPool, newDpmWeights, newBalance }
+  return { newBet, newPool, newTotalShares, newBalance }
 }

functions/src/resolve-market.ts

@@ -78,22 +78,27 @@ export const resolveMarket = functions
 const firestore = admin.firestore()
 
 const getPayouts = (outcome: string, contract: Contract, bets: Bet[]) => {
-  const [yesBets, noBets] = _.partition(bets, (bet) => bet.outcome === 'YES')
+  const openBets = bets.filter((b) => !b.isSold && !b.sale)
+  const [yesBets, noBets] = _.partition(
+    openBets,
+    (bet) => bet.outcome === 'YES'
+  )
 
-  const [pool, winningBets] =
+  const startPool = contract.startPool.YES + contract.startPool.NO
+  const truePool = contract.pool.YES + contract.pool.NO - startPool
+
+  const [totalShares, winningBets] =
     outcome === 'YES'
-      ? [contract.pool.NO - contract.startPool.NO, yesBets]
+      ? [contract.totalShares.YES, yesBets]
-      : [contract.pool.YES - contract.startPool.YES, noBets]
+      : [contract.totalShares.NO, noBets]
 
-  const finalPool = (1 - PLATFORM_FEE - CREATOR_FEE) * pool
+  const finalPool = (1 - PLATFORM_FEE - CREATOR_FEE) * truePool
-  const creatorPayout = CREATOR_FEE * pool
+  const creatorPayout = CREATOR_FEE * truePool
   console.log('final pool:', finalPool, 'creator fee:', creatorPayout)
 
-  const sumWeights = _.sumBy(winningBets, (bet) => bet.dpmWeight)
-
   const winnerPayouts = winningBets.map((bet) => ({
     userId: bet.userId,
-    payout: bet.amount + (bet.dpmWeight / sumWeights) * finalPool,
+    payout: (bet.shares / totalShares) * finalPool,
   }))
 
   return winnerPayouts.concat([

functions/src/sell-bet.ts

@@ -35,23 +35,17 @@ export const sellBet = functions.runWith({ minInstances: 1 }).https.onCall(
 
       const betDoc = firestore.doc(`contracts/${contractId}/bets/${betId}`)
       const betSnap = await transaction.get(betDoc)
-      if (!betSnap.exists)
+      if (!betSnap.exists) return { status: 'error', message: 'Invalid bet' }
-        return { status: 'error', message: 'Invalid bet' }
       const bet = betSnap.data() as Bet
 
-      if (bet.isSold)
+      if (bet.isSold) return { status: 'error', message: 'Bet already sold' }
-        return { status: 'error', message: 'Bet already sold' }
 
       const newBetDoc = firestore
         .collection(`contracts/${contractId}/bets`)
         .doc()
 
-      const { newBet, newPool, newDpmWeights, newBalance, creatorFee } = getSellBetInfo(
+      const { newBet, newPool, newTotalShares, newBalance, creatorFee } =
-        user,
+        getSellBetInfo(user, bet, contract, newBetDoc.id)
-        bet,
-        contract,
-        newBetDoc.id
-      )
 
       const creatorDoc = firestore.doc(`users/${contract.creatorId}`)
       const creatorSnap = await transaction.get(creatorDoc)
@@ -65,7 +59,7 @@ export const sellBet = functions.runWith({ minInstances: 1 }).https.onCall(
       transaction.create(newBetDoc, newBet)
       transaction.update(contractDoc, {
         pool: newPool,
-        dpmWeights: newDpmWeights,
+        totalShares: newTotalShares,
       })
       transaction.update(userDoc, { balance: newBalance })
 
@@ -82,69 +76,86 @@ const getSellBetInfo = (
   contract: Contract,
   newBetId: string
 ) => {
-  const { id: betId, amount, dpmWeight, outcome } = bet
+  const { id: betId, amount, shares, outcome } = bet
 
   const { YES: yesPool, NO: noPool } = contract.pool
-  const { YES: yesWeights, NO: noWeights } = contract.dpmWeights
+  const { YES: yesStart, NO: noStart } = contract.startPool
+  const { YES: yesShares, NO: noShares } = contract.totalShares
 
-  // average implied probability after selling bet position
+  const [y, n, s] = [yesPool, noPool, shares]
-  const p = outcome === 'YES'
-    ? (amount +
-      noPool * Math.atan((yesPool - amount) / noPool) -
-      noPool * Math.atan(yesPool / noPool)) /
-    amount
 
-    : yesPool * (Math.atan((amount - noPool) / yesPool) + Math.atan(noPool / yesPool)) /
+  const shareValue =
-    amount
-
-
-  const [sellYesAmount, sellNoAmount] = outcome === 'YES'
-    ? [
-      p * amount,
-      p * dpmWeight / yesWeights * noPool,
-    ]
-    : [
-      p * dpmWeight / noWeights * yesPool,
-      p * amount,
-    ]
-
-  const newPool = { YES: yesPool - sellYesAmount, NO: noPool - sellNoAmount }
-
-  const newDpmWeights =
     outcome === 'YES'
-      ? { YES: yesWeights - dpmWeight, NO: noWeights }
+      ? // https://www.wolframalpha.com/input/?i=b+%2B+%28b+n%5E2%29%2F%28y+%28-b+%2B+y%29%29+%3D+c+solve+b
-      : { YES: yesWeights, NO: noWeights - dpmWeight }
+        (n ** 2 +
+          s * y +
+          y ** 2 -
+          Math.sqrt(
+            n ** 4 + (s - y) ** 2 * y ** 2 + 2 * n ** 2 * y * (s + y)
+          )) /
+        (2 * y)
+      : (y ** 2 +
+          s * n +
+          n ** 2 -
+          Math.sqrt(
+            y ** 4 + (s - n) ** 2 * n ** 2 + 2 * y ** 2 * n * (s + n)
+          )) /
+        (2 * n)
+
+  const startPool = yesStart + noStart
+  const pool = yesPool + noPool - startPool
+
+  const f = outcome === 'YES' ? pool / yesShares : pool / noShares
+
+  const myPool = outcome === 'YES' ? yesPool - yesStart : noPool - noStart
+
+  const adjShareValue = Math.min(Math.min(1, f) * shareValue, myPool)
+
+  const newPool =
+    outcome === 'YES'
+      ? { YES: yesPool - adjShareValue, NO: noPool }
+      : { YES: yesPool, NO: noPool - adjShareValue }
+
+  const newTotalShares =
+    outcome === 'YES'
+      ? { YES: yesShares - shares, NO: noShares }
+      : { YES: yesShares, NO: noShares - shares }
 
   const probBefore = yesPool ** 2 / (yesPool ** 2 + noPool ** 2)
-  const probAverage = p
   const probAfter = newPool.YES ** 2 / (newPool.YES ** 2 + newPool.NO ** 2)
 
-  const keep = 1 - CREATOR_FEE - PLATFORM_FEE
+  const creatorFee = CREATOR_FEE * adjShareValue
+  const saleAmount = (1 - CREATOR_FEE - PLATFORM_FEE) * adjShareValue
 
-  const [saleAmount, creatorFee] = outcome === 'YES'
+  console.log(
-    ? [{ YES: sellYesAmount, NO: keep * sellNoAmount }, CREATOR_FEE * sellNoAmount]
+    'SELL M$',
-    : [{ YES: keep * sellYesAmount, NO: sellNoAmount }, CREATOR_FEE * sellYesAmount]
+    amount,
-
+    outcome,
-  console.log('SELL M$', amount, outcome, 'at', p, 'prob', 'for M$', saleAmount.YES + saleAmount.NO, 'creator fee: M$', creatorFee)
+    'for M$',
+    saleAmount,
+    'M$/share:',
+    f,
+    'creator fee: M$',
+    creatorFee
+  )
 
   const newBet: Bet = {
     id: newBetId,
     userId: user.id,
     contractId: contract.id,
-    amount: -amount,
+    amount: -adjShareValue,
-    dpmWeight: -dpmWeight,
+    shares: -shares,
     outcome,
     probBefore,
-    probAverage,
     probAfter,
     createdTime: Date.now(),
     sale: {
       amount: saleAmount,
-      betId
+      betId,
-    }
+    },
   }
 
-  const newBalance = user.balance + sellYesAmount + sellNoAmount
+  const newBalance = user.balance + saleAmount
 
-  return { newBet, newPool, newDpmWeights, newBalance, creatorFee }
+  return { newBet, newPool, newTotalShares, newBalance, creatorFee }
 }

functions/src/types/bet.ts

@@ -5,14 +5,13 @@ export type Bet = {
 
   amount: number // bet size; negative if SELL bet
   outcome: 'YES' | 'NO'
-  dpmWeight: number // dynamic parimutuel pool weight; negative if SELL bet
+  shares: number // dynamic parimutuel pool weight; negative if SELL bet
 
   probBefore: number
-  probAverage: number
   probAfter: number
 
   sale?: {
-    amount: { YES: number, NO: number } // amount user makes from YES and NO pools from sale
+    amount: number // amount user makes from sale
     betId: string // id of bet being sold
   }
 

functions/src/types/contract.ts

@@ -12,7 +12,7 @@ export type Contract = {
 
   startPool: { YES: number; NO: number }
   pool: { YES: number; NO: number }
-  dpmWeights: { YES: number; NO: number }
+  totalShares: { YES: number; NO: number }
 
   createdTime: number // Milliseconds since epoch
   lastUpdatedTime: number // If the question or description was changed

web/components/bet-panel.tsx

@@ -12,7 +12,7 @@ import { formatMoney, formatPercent } from '../lib/util/format'
 import { Title } from './title'
 import {
   getProbability,
-  getDpmWeight,
+  calculateShares,
   getProbabilityAfterBet,
 } from '../lib/calculation/contract'
 import { firebaseLogin } from '../lib/firebase/users'
@@ -84,9 +84,9 @@ export function BetPanel(props: { contract: Contract; className?: string }) {
     betChoice,
     betAmount ?? 0
   )
-  const dpmWeight = getDpmWeight(contract.pool, betAmount ?? 0, betChoice)
+  const shares = calculateShares(contract.pool, betAmount ?? 0, betChoice)
 
-  const estimatedWinnings = Math.floor((betAmount ?? 0) + dpmWeight)
+  const estimatedWinnings = Math.floor(shares)
   const estimatedReturn = betAmount
     ? (estimatedWinnings - betAmount) / betAmount
     : 0

web/components/bets-list.tsx

@@ -257,7 +257,16 @@ export function ContractBetsTable(props: {
 
 function BetRow(props: { bet: Bet; contract: Contract }) {
   const { bet, contract } = props
-  const { amount, outcome, createdTime, probBefore, probAfter, dpmWeight, sale, isSold } = bet
+  const {
+    amount,
+    outcome,
+    createdTime,
+    probBefore,
+    probAfter,
+    shares,
+    sale,
+    isSold,
+  } = bet
   const { isResolved } = contract
 
   return (
@@ -270,7 +279,7 @@ function BetRow(props: { bet: Bet; contract: Contract }) {
       <td>
         {formatPercent(probBefore)} → {formatPercent(probAfter)}
       </td>
-      {!isResolved && <td>{formatMoney(amount + dpmWeight)}</td>}
+      {!isResolved && <td>{formatMoney(shares)}</td>}
       <td>
         {formatMoney(
           isResolved
@@ -279,14 +288,19 @@ function BetRow(props: { bet: Bet; contract: Contract }) {
         )}
       </td>
 
-      {!isResolved && !sale && !isSold &&
+      {!isResolved && !sale && !isSold && (
         <td>
-          <button className='btn' onClick={async e => {
+          <button
-            e.preventDefault()
+            className="btn"
-            await sellBet({ contractId: contract.id, betId: bet.id })
+            onClick={async (e) => {
-          }}>Sell</button>
+              e.preventDefault()
+              await sellBet({ contractId: contract.id, betId: bet.id })
+            }}
+          >
+            Sell
+          </button>
         </td>
-      }
+      )}
     </tr>
   )
 }

web/components/contract-overview.tsx

@@ -90,7 +90,7 @@ export const ContractOverview = (props: {
 }) => {
   const { contract, className } = props
   const { resolution, creatorId } = contract
-  const { probPercent, volume } = compute(contract)
+  const { probPercent, truePool } = compute(contract)
 
   const user = useUser()
   const isCreator = user?.id === creatorId
@@ -140,7 +140,7 @@ export const ContractOverview = (props: {
       <ContractDescription contract={contract} isCreator={isCreator} />
 
       {/* Show a delete button for contracts without any trading */}
-      {isCreator && volume === 0 && (
+      {isCreator && truePool === 0 && (
         <>
           <Spacer h={8} />
           <button

web/components/contracts-list.tsx

@@ -17,7 +17,7 @@ import { Linkify } from './linkify'
 
 export function ContractDetails(props: { contract: Contract }) {
   const { contract } = props
-  const { volume, createdDate, resolvedDate } = compute(contract)
+  const { truePool, createdDate, resolvedDate } = compute(contract)
 
   return (
     <Row className="flex-wrap text-sm text-gray-500">
@@ -29,7 +29,7 @@ export function ContractDetails(props: { contract: Contract }) {
         {resolvedDate ? `${createdDate} - ${resolvedDate}` : createdDate}
       </div>
       <div className="mx-2">•</div>
-      <div className="whitespace-nowrap">{formatMoney(volume)} volume</div>
+      <div className="whitespace-nowrap">{formatMoney(truePool)} pool</div>
     </Row>
   )
 }
@@ -110,14 +110,14 @@ function ContractsGrid(props: { contracts: Contract[] }) {
   )
 }
 
-type Sort = 'createdTime' | 'volume' | 'resolved' | 'all'
+type Sort = 'createdTime' | 'pool' | 'resolved' | 'all'
 export function SearchableGrid(props: {
   contracts: Contract[]
   defaultSort?: Sort
 }) {
   const { contracts, defaultSort } = props
   const [query, setQuery] = useState('')
-  const [sort, setSort] = useState(defaultSort || 'volume')
+  const [sort, setSort] = useState(defaultSort || 'pool')
 
   function check(corpus: String) {
     return corpus.toLowerCase().includes(query.toLowerCase())
@@ -132,8 +132,8 @@ export function SearchableGrid(props: {
 
   if (sort === 'createdTime' || sort === 'resolved' || sort === 'all') {
     matches.sort((a, b) => b.createdTime - a.createdTime)
-  } else if (sort === 'volume') {
+  } else if (sort === 'pool') {
-    matches.sort((a, b) => compute(b).volume - compute(a).volume)
+    matches.sort((a, b) => compute(b).truePool - compute(a).truePool)
   }
 
   if (sort !== 'all') {
@@ -159,7 +159,7 @@ export function SearchableGrid(props: {
           value={sort}
           onChange={(e) => setSort(e.target.value as Sort)}
         >
-          <option value="volume">Most traded</option>
+          <option value="pool">Most traded</option>
           <option value="createdTime">Newest first</option>
           <option value="resolved">Resolved</option>
           <option value="all">All markets</option>

web/lib/calculation/contract.ts

@@ -22,7 +22,7 @@ export function getProbabilityAfterBet(
   return getProbability({ YES, NO })
 }
 
-export function getDpmWeight(
+export function calculateShares(
   pool: { YES: number; NO: number },
   bet: number,
   betChoice: 'YES' | 'NO'
@@ -30,8 +30,8 @@ export function getDpmWeight(
   const [yesPool, noPool] = [pool.YES, pool.NO]
 
   return betChoice === 'YES'
-    ? (bet * Math.pow(noPool, 2)) / (Math.pow(yesPool, 2) + bet * yesPool)
+    ? bet + (bet * noPool ** 2) / (yesPool ** 2 + bet * yesPool)
-    : (bet * Math.pow(yesPool, 2)) / (Math.pow(noPool, 2) + bet * noPool)
+    : bet + (bet * yesPool ** 2) / (noPool ** 2 + bet * noPool)
 }
 
 export function calculatePayout(
@@ -39,23 +39,20 @@ export function calculatePayout(
   bet: Bet,
   outcome: 'YES' | 'NO' | 'CANCEL'
 ) {
-  const { amount, outcome: betOutcome, dpmWeight } = bet
+  const { amount, outcome: betOutcome, shares } = bet
 
   if (outcome === 'CANCEL') return amount
   if (betOutcome !== outcome) return 0
 
-  let { dpmWeights, pool, startPool } = contract
+  let { totalShares } = contract
 
   // Fake data if not set.
-  if (!dpmWeights) dpmWeights = { YES: 100, NO: 100 }
+  // if (!totalShares) totalShares = { YES: 100, NO: 100 }
 
-  // Fake data if not set.
+  const startPool = contract.startPool.YES + contract.startPool.NO
-  if (!pool) pool = { YES: 100, NO: 100 }
+  const pool = contract.pool.YES + contract.pool.NO - startPool
 
-  const otherOutcome = outcome === 'YES' ? 'NO' : 'YES'
+  return (1 - fees) * (shares / totalShares[outcome]) * pool
-  const poolSize = pool[otherOutcome] - startPool[otherOutcome]
-
-  return (1 - fees) * (dpmWeight / dpmWeights[outcome]) * poolSize + amount
 }
 export function resolvedPayout(contract: Contract, bet: Bet) {
   if (contract.resolution)

web/lib/firebase/bets.ts

@@ -14,14 +14,13 @@ export type Bet = {
 
   amount: number // bet size; negative if SELL bet
   outcome: 'YES' | 'NO'
-  dpmWeight: number // dynamic parimutuel pool weight; negative if SELL bet
+  shares: number // dynamic parimutuel pool weight; negative if SELL bet
 
   probBefore: number
-  probAverage: number
   probAfter: number
 
   sale?: {
-    amount: { YES: number, NO: number } // amount user makes from YES and NO pools from sale
+    amount: number // amount user makes from sale
     betId: string // id of bet being sold
   }
 

web/lib/firebase/contracts.ts

@@ -30,7 +30,7 @@ export type Contract = {
 
   startPool: { YES: number; NO: number }
   pool: { YES: number; NO: number }
-  dpmWeights: { YES: number; NO: number }
+  totalShares: { YES: number; NO: number }
 
   createdTime: number // Milliseconds since epoch
   lastUpdatedTime: number // If the question or description was changed
@@ -48,14 +48,14 @@ export function path(contract: Contract) {
 
 export function compute(contract: Contract) {
   const { pool, startPool, createdTime, resolutionTime, isResolved } = contract
-  const volume = pool.YES + pool.NO - startPool.YES - startPool.NO
+  const truePool = pool.YES + pool.NO - startPool.YES - startPool.NO
   const prob = pool.YES ** 2 / (pool.YES ** 2 + pool.NO ** 2)
   const probPercent = Math.round(prob * 100) + '%'
   const createdDate = dayjs(createdTime).format('MMM D')
   const resolvedDate = isResolved
     ? dayjs(resolutionTime).format('MMM D')
     : undefined
-  return { volume, probPercent, createdDate, resolvedDate }
+  return { truePool, probPercent, createdDate, resolvedDate }
 }
 
 const db = getFirestore(app)

web/lib/service/create-contract.ts

@@ -2,7 +2,6 @@ import {
   Contract,
   getContractFromSlug,
   pushNewContract,
-  setContract,
 } from '../firebase/contracts'
 import { User } from '../firebase/users'
 import { randomString } from '../util/random-string'
@@ -38,7 +37,7 @@ export async function createContract(
 
     startPool: { YES: startYes, NO: startNo },
     pool: { YES: startYes, NO: startNo },
-    dpmWeights: { YES: 0, NO: 0 },
+    totalShares: { YES: 0, NO: 0 },
     isResolved: false,
 
     // TODO: Set create time to Firestore timestamp
@@ -49,8 +48,8 @@ export async function createContract(
   return await pushNewContract(contract)
 }
 
-export function calcStartPool(initialProb: number, initialCapital = 200) {
+export function calcStartPool(initialProbInt: number, initialCapital = 200) {
-  const p = initialProb / 100.0
+  const p = initialProbInt / 100.0
 
   const startYes =
     p === 0.5

web/pages/about.tsx

@@ -162,8 +162,8 @@ function Contents() {
       </p>
       <h3 id="how-are-markets-resolved-">How are markets resolved?</h3>
       <p>
-        The creator of the prediction market decides the outcome and earns 0.5%
+        The creator of the prediction market decides the outcome and earns 1% of
-        of the trade volume for their effort.
+        the betting pool for their effort.
       </p>
       <p>
         This simple resolution mechanism has surprising benefits in allowing a