antes

common/antes.ts

@@ -10,5 +10,8 @@ export const calcStartPool = (initialProbInt: number, ante = 0) => {
   const poolYes = p * ante
   const poolNo = (1 - p) * ante
 
-  return { sharesYes, sharesNo, poolYes, poolNo }
+  const startYes = Math.sqrt(p) * PHANTOM_ANTE
+  const startNo = Math.sqrt(1 - p) * PHANTOM_ANTE
+
+  return { sharesYes, sharesNo, poolYes, poolNo, startYes, startNo }
 }

common/calculate.ts

@@ -104,7 +104,7 @@ export function calculateStandardPayout(
   const { amount, outcome: betOutcome, shares } = bet
   if (betOutcome !== outcome) return 0
 
-  const { totalShares, totalBets } = contract
+  const { totalShares, totalBets, startPool } = contract
   if (totalShares[outcome] === 0) return 0
 
   const truePool = contract.pool.YES + contract.pool.NO
@@ -112,7 +112,8 @@ export function calculateStandardPayout(
   if (totalBets[outcome] >= truePool)
     return (amount / totalBets[outcome]) * truePool
 
-  const total = totalShares[outcome] - totalBets[outcome]
+  const startShares = startPool.YES + startPool.NO
+  const total = totalShares[outcome] - startShares - totalBets[outcome]
   const winningsPool = truePool - totalBets[outcome]
 
   return (1 - FEES) * (amount + ((shares - amount) / total) * winningsPool)
@@ -139,8 +140,12 @@ function calculateMktPayout(contract: Contract, bet: Bet) {
   const winningsPool = truePool - weightedTotal
 
   const weightedShareTotal =
-    p * (contract.totalShares.YES - contract.totalBets.YES) +
+    p *
-    (1 - p) * (contract.totalShares.NO - contract.totalBets.NO)
+      (contract.totalShares.YES -
+        contract.startPool.YES -
+        contract.totalBets.YES) +
+    (1 - p) *
+      (contract.totalShares.NO - contract.startPool.NO - contract.totalBets.NO)
 
   return (
     (1 - FEES) *

common/contract.ts

@@ -11,6 +11,7 @@ export type Contract = {
   outcomeType: 'BINARY' // | 'MULTI' | 'interval' | 'date'
   // outcomes: ['YES', 'NO']
 
+  mechanism: 'dpm-2'
   startPool: { YES: number; NO: number }
   pool: { YES: number; NO: number }
   totalShares: { YES: number; NO: number }

common/new-contract.ts

@@ -12,10 +12,8 @@ export function getNewContract(
   ante?: number,
   closeTime?: number
 ) {
-  const { sharesYes, sharesNo, poolYes, poolNo } = calcStartPool(
+  const { sharesYes, sharesNo, poolYes, poolNo, startYes, startNo } =
-    initialProb,
+    calcStartPool(initialProb, ante)
-    ante
-  )
 
   const contract: Contract = {
     id,
@@ -29,7 +27,8 @@ export function getNewContract(
     question: question.trim(),
     description: description.trim(),
 
-    startPool: { YES: poolYes, NO: poolNo },
+    mechanism: 'dpm-2',
+    startPool: { YES: startYes, NO: startNo },
     pool: { YES: poolYes, NO: poolNo },
     totalShares: { YES: sharesYes, NO: sharesNo },
     totalBets: { YES: poolYes, NO: poolNo },

web/components/contract-prob-graph.tsx

@@ -1,6 +1,7 @@
 import { DatumValue } from '@nivo/core'
 import { ResponsiveLine } from '@nivo/line'
 import dayjs from 'dayjs'
+import { getProbability } from '../../common/calculate'
 import { useBets } from '../hooks/use-bets'
 import { useWindowSize } from '../hooks/use-window-size'
 import { Contract } from '../lib/firebase/contracts'
@@ -12,8 +13,7 @@ export function ContractProbGraph(props: { contract: Contract }) {
   let bets = useBets(id)
   if (bets === 'loading') bets = []
 
-  const startProb =
+  const startProb = getProbability(startPool)
-    startPool.YES ** 2 / (startPool.YES ** 2 + startPool.NO ** 2)
 
   const times = [
     contract.createdTime,