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Using Private Probability Information in a Three-Outcome Betting Game

Article Quant Q&A · Author: Lawrence
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Summary

The document poses a simple betting problem about how to profit from information that changes the estimated probabilities of three mutually exclusive outcomes. A bettor can stake money on any outcome, receiving twice the stake if correct and nothing otherwise. The stated baseline assigns equal probabilities, while the informed estimate makes wins and losses more likely than draws. The question invites strategies that could include selling claims on the bets to other participants.

No solution, pricing analysis, or evidence is provided. The setup can prompt analysis of expected value and how an informed trader might trade against participants who use the baseline probabilities, but the document does not specify the exact contracts, transaction costs, counterparties, or rules for selling claims. Those details would matter for evaluating whether any proposed revenue strategy is feasible or profitable.

Key ideas

  • The problem compares equal baseline probabilities with an informed probability estimate.
  • Each wager pays twice its stake when the selected outcome occurs and nothing otherwise.
  • The prompt suggests selling claims as one possible way to monetize information.
  • The document asks for a strategy but supplies no solution or profitability evidence.

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StatisticsRisk management
Full text
# Mechanism design for information priority


# Mechanism design for information priority












Assuming that there are 3 situation of a game: win, lose, and draw (no one wins). You can bet X on any situation, you'll get 2X if you win and 0 otherwise.

Originally, you know nothing about the player,and probability of each situation is 1/3. However, you accidently know some information and the probability of win, lose, draw if 0.4, 0.4, 0.2 for you.

How can you use this information to gain some extra revenue ? You can literally do anything including Selling your gamble bonds to others.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.