Expected Value and Break-even Probability: Costs Turn Beliefs into Math
Expected value in one sentence
Expected value is your average outcome if you could repeat the same trade many times. In prediction markets, EV depends on:
• your predicted probability
• the market's implied probability (what you pay)
• costs: fees, spread, and execution frictions
If you skip any of those, EV becomes fantasy.
Start with the payoff structure
Most binary prediction markets have a simple payoff: a YES contract settles to 1 if the event happens and 0 if it does not. That makes conversion intuitive, but you still must confirm the price scale.
If you pay price p to buy YES:
• if YES happens, you receive 1 and your gross profit is (1 minus p)
• if NO happens, you receive 0 and your gross profit is (0 minus p)
EV without costs
Let q be your predicted probability that YES happens. Let p be the price you pay (on a 0 to 1 scale).
Then gross EV is:
• EV = q times (1 minus p) minus (1 minus q) times p
This simplifies to:
• EV = q minus p
That simple identity is why people say price is probability. But remember: that is gross EV and assumes you can trade at p with no fees and no spread.
Why costs break the simple EV shortcut
Real trading has friction:
• trading fee (per contract, percent, maker taker, or other rules)
• spread cost from crossing the bid ask spread
• slippage and price impact when size is large relative to liquidity
Those costs reduce EV. That is why a small edge often becomes negative net EV.
Break-even probability is your real threshold
Break-even probability is the probability you must have so that net EV equals zero after costs. If your predicted probability is below break even, you should not take the trade.
In words:
• break even probability = what you need to believe for this price and these costs
A practical break-even method
You do not need perfect formulas to use break even correctly. Use this workflow:
• Step 1: use the execution price you will actually pay (usually the ask to buy, the bid to sell)
• Step 2: add expected fees for that order type (maker vs taker)
• Step 3: treat the total as your all in price
• Step 4: your break-even probability is approximately that all in price on the same scale
This is a clean approximation because gross EV is (q minus price). If your effective price increases due to costs, your required q increases too.
Worked example: small edge dies to costs
Suppose the market is on a 0 to 100 scale:
• bid 49, ask 51
You want to buy at ask 51 (implied probability 0.51).
You estimate:
• predicted probability q = 0.53
Gross edge is 0.02. Without costs, EV looks positive.
Now include costs:
• spread already costs you because you bought at ask instead of mid
• add fees and realistic slippage
Your all in price might be closer to 0.53. Your break-even probability becomes about 0.53. Your forecast is no longer above break even. Net EV is approximately zero or negative.
This is why serious traders require larger edge in thin markets.
Why this matters for market making and platform design
Platforms that hide costs create confused users. Responsible platforms surface:
• clear fee schedules (fees)
• bid and ask quotes, not just last trade
• warnings when spread and slippage are likely high
That transparency helps users estimate break even correctly and reduces churn from "I was right but I still lost".
Common mistakes
Using last traded price as p: use executable quotes.
Ignoring exit costs: if you plan to exit early, you may pay the spread twice.
Treating fees as small: in bounded price markets, fees can be a large fraction of edge.
Sizing too large: size increases slippage and price impact, which increases break even.
Takeaway
EV is simple in theory and brutal in practice. The clean mental model is: net EV depends on predicted probability minus your all in price. Break-even probability is the threshold that converts beliefs into a trade decision. If you want to trade responsibly, demand edge that clears fees, spread, and execution risk.
Related
• Fair Price and Edge: Turning Beliefs into Trade Thresholds
• Fees vs Spread: The Two Costs Most Traders Mix Up
• Slippage, Price Impact, Execution Risk: Why Good Forecasts Still Lose Money