Payout and profit
Profit odds describe the amount won in addition to the returned stake. At 3 to 1, a winning $20 bet earns $60 profit and returns $80 in total. The total-return multiplier is 4.
A 3× total-return multiplier gives a different result: $60 returned from a $20 stake, including the original $20, for $40 profit. Choose the convention that matches the game's pay table.
A push returns the original stake and has zero net profit. Its probability must be entered separately so those outcomes are not treated as losses.
| A $20 winning stake | Winning profit | Total return |
|---|---|---|
| 3 to 1 profit odds | $60 | $80 |
| 3× total-return multiplier | $40 | $60 |
Expected value
Expected net result = win probability × winning profit − loss probability × stake. Probabilities use decimal form in the equation. In this model, loss probability is 100% minus the entered win and push probabilities.
For a $10 bet that wins 48% of the time at even money, pushes 0%, and loses 52%, expected net result is 0.48 × $10 − 0.52 × $10 = −$0.40 per bet.
Expected value is a probability-weighted average. A single bet settles at one of its actual outcomes. The average does not describe a guaranteed payment or the most likely session result.
Break-even probability
With no pushes, the break-even win probability is 1 ÷ the total-return multiplier. A 3 to 1 profit payout has a multiplier of 4, so it breaks even at a 25% win probability.
If push probability is fixed, the required win probability is (1 − push probability) ÷ the total-return multiplier. At even money with a 10% push probability, a 45% win probability and 45% loss probability break even.
Payout terms do not supply the true probability of winning. Use a probability supported by the game's rules or a verified mathematical model. Counting favorable outcomes works only when every counted outcome is equally likely.
Common questions
What if different wins pay different amounts?
A single winning multiplier cannot represent several payouts unless it is the correct conditional average. The general method is to multiply every possible net outcome by its probability, then add the results.
How should commission be handled?
Deduct commission from the winning profit it affects before calculating expected value. An unadjusted payout can overstate the return.