Free · Probability models

Probability Weights, Decimal Odds and Independent Streaks

Convert positive success and failure weights into implied probability and decimal or moneyline odds, then estimate independent streak probabilities and payout arithmetic.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Weights2 and3 imply40% success and60% failure. Decimal odds2.5 give a250 total return on stake100, including150 net profit. Three independent successes have6.4% probability.

Success probability = success weight/(success+failure weights); decimal odds =1/p; independent streak probability=p^n; total return=decimal odds×stake.

Worked example

Enter these known values and leave the other values blank.

Chances for success
2
Chances against success
3
times in a row...
3
times in a row...
2
Stake
100 USD
Probability of winning
40 %
Success streak probability
6.4 %
Probability of losing
60 %
Failure streak probability
36 %
Decimal odds
2.5
American (moneyline odds)
150
Total returned
250 USD
Potential net profit
150 USD

Assumptions and limitations

  • The supplied weights define one hypothetical binary-outcome probability. Odds are mathematical implied odds without bookmaker margin, fees, taxes or a prediction model.
  • Streak formulas require independent identical trials. Changing odds, dependence or changing trial probabilities invalidate the simple p-to-the-n relationship. Counts must be positive whole numbers.
  • Both weights must be positive for finite decimal and moneyline outputs. Zero-probability and certainty endpoints make at least one reciprocal conversion singular and are rejected.
  • Return includes the original stake; net profit excludes it. These hypothetical values do not guarantee outcomes or recommend betting.

Common questions

Why are return and net profit different?

Return includes the original stake. With decimal odds2.5 and stake100, return250 consists of100 principal plus150 net profit.

When is a streak probability p raised to n?

Only when n trials are independent and have the same individual success probability p.

References

Exclude zero-weight singular odds and moneyline denominators while retaining all editable probability-weight inverses and independent-trial streak formulas.

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