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Prices and Probability

Intotes uses an integer-based price system where prices represent probabilities. This page explains how prices work, how they map to probabilities, and how amounts are calculated.

The 0-10,000 price scale​

All prices in Intotes are integers in the range 0 to 10,000, representing probabilities from 0.00% to 100.00%.

PriceProbabilityMeaning
00.00%Impossible (never used in practice)
1001.00%Very unlikely
2,60026.00%
5,00050.00%Even odds
7,50075.00%
9,90099.00%Near certain
10,000100.00%Certain (never used in practice)

To convert a price to a probability percentage: probability = price / 100. To convert a probability to a price: price = probability * 100.

Complementary prices​

Every market has two sides: YES and NO. Their prices always sum to exactly 10,000:

YES_price + NO_price = 10,000

This means:

  • If YES is priced at 2,600 (26%), NO is priced at 7,400 (74%).
  • If YES is priced at 7,500 (75%), NO is priced at 2,500 (25%).

This relationship holds at all times, in both orderbook and LMSR markets. It ensures the probabilities of all outcomes in a binary market always sum to 100%.

Price sources by market type​

How prices are determined depends on the market type:

Orderbook markets​

In an orderbook market, prices are set by traders through limit orders:

  • Best bid — The highest price someone is willing to pay for YES shares.
  • Best ask — The lowest price someone is willing to sell YES shares at.
  • Mid-price — The midpoint between best bid and best ask:
mid_price = (best_bid + best_ask) / 2

The mid-price is used as the reference price for display and unrealized PnL calculations. The spread between bid and ask represents the cost of immediate execution.

LMSR markets​

In an LMSR market, the price is computed deterministically from the AMM state:

YES_price = e^(q_yes / b) / (e^(q_yes / b) + e^(q_no / b)) * 10000

Where:

  • q_yes — Current outstanding YES quantity (in cents).
  • q_no — Current outstanding NO quantity (in cents).
  • b — Liquidity parameter (in cents). Higher b means prices move less per trade.

There is no spread in LMSR — the buy and sell prices are the same (before fees). See LMSR AMM for full details.

Amounts and budgets​

All monetary amounts in the system are denominated in cents (1/100 of a ruble). There are two types of amounts depending on the order side:

BUY orders​

For a BUY order, amount is the budget — how much money you want to spend (in cents).

The number of shares you receive depends on the price:

shares_cents = (budget_cents * 10000) / price_cents

Example: You spend 10,000 cents (100 rubles) buying YES at a price of 2,500 (25%):

shares = (10000 * 10000) / 2500 = 40,000 shares (in cents)

If YES wins, each share pays out at 10,000, so your payout would be:

payout = 40000 * 10000 / 10000 = 40,000 cents (400 rubles)

Your profit: 40,000 - 10,000 = 30,000 cents (300 rubles).

SELL orders​

For a SELL order, amount is the number of shares you want to sell (in cents). The proceeds depend on the sell price:

proceeds_cents = (shares_cents * price_cents) / 10000

Price in trades​

Every executed trade records its price in the 0-10,000 scale. For orderbook trades, this is the matched price. For LMSR trades, this is the average execution price computed from the cost function.

Practical examples​

Low-probability event​

A market asks "Will Team X win the championship?" priced at 800 (8%).

  • Buying YES at 800 means you pay 8 cents per share and receive 125 cents of shares per 100 cents spent.
  • If YES wins: each share pays 100 cents. Your return is 12.5x your investment.
  • If NO wins: you lose your investment.

High-probability event​

A market asks "Will the sun rise tomorrow?" priced at 9,800 (98%).

  • Buying YES at 9,800 means you pay 98 cents per share.
  • If YES wins: each share pays 100 cents. Your profit is 2 cents per share (~2% return).
  • If NO wins: you lose 98 cents per share.

Even odds​

A coin flip market priced at 5,000 (50%).

  • Buying either side costs 50 cents per share.
  • If you win: each share pays 100 cents. Your return is 2x (100% profit).
  • If you lose: you lose your 50 cents.

Summary​

ConceptValueNotes
Price range0 - 10,000Integer, represents probability * 100
YES + NOAlways 10,000Complementary pricing
AmountsIn centsBudget for BUY, shares for SELL
Settlement payout10,000 per winning shareLosers receive 0
Share formula(budget * 10000) / priceHow many shares a budget buys