Description
Calculate a single ticket payoff in a supplied event state; a Dutch book requires evaluating a portfolio over all states.
A logical calculation operates on a stated representation: truth values, token lists, counts, or an explicitly supplied relation. Checking one assignment, pair, trace, or witness is different from proving a formula or validating an entire argument. Empty domains, duplicate tokens, and scope conventions can change the result.
Calculate a single ticket payoff in a supplied event state; a Dutch book requires evaluating a portfolio over all states.
When to use this tool
Use Probability Dutch Book Single Payoff when you need this exact local truth, count, token, relation, or witness check within a larger logic workflow.
How to use the tool and how it works
- Enter price, payout, eventOccurs, stake. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read buyerNet, sellerNet. Use the output convention below.
Require nonnegative payout and price within zero through payout. Return buyerNet=stake*((eventOccurs?payout:0)-price) and sellerNet=-buyerNet.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| price | Price | Required. Finite number; minimum 0. |
| payout | Payout | Required. Finite number; minimum 0. |
| eventOccurs | Event Occurs | Required. Boolean. |
| stake | Signed quantity of the supplied payoff contract. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| buyerNet | Buyer Net | Required. Finite number. |
| sellerNet | Seller Net | Required. Finite number. |
{
"input": {
"price": 0.4,
"payout": 1,
"eventOccurs": true,
"stake": 10
},
"output": {
"buyerNet": 6,
"sellerNet": -6
}
}Limitations and assumptions
- Stake may be negative and all monetary terms need one currency basis. A single realized payoff does not detect a Dutch book across a portfolio or establish coherent probabilities.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a parser, scope-aware representation, model checker, or proof procedure when the supplied token or witness representation is insufficient. A local passing check should not be promoted to global validity.
References
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