X out of N Calculator

The X out of N calculator determines the fair odds for "X or more wins" bets. These are promotions where you need a certain number of outcomes to win from a larger set of events.

When to use it

Use this calculator when evaluating promotions like:

• "3+ home teams to win at 3.0 odds" across 5 AFL games
• "Bonus bet if 4+ of your 6 bets win"
• "Back all 8 races, get paid if 5+ win"

How it works

You enter the fair odds for each individual outcome. The calculator uses the Poisson Binomial distribution to determine the probability of X or more outcomes winning, then shows you the fair odds for that combined outcome.

Understanding the inputs

Click "Add event" to add events. For each event, enter the fair odds for the outcome you're interested in (e.g., the home team odds).

The calculator converts each odds to probability and computes the exact probability of any number of them winning.

Understanding the outputs

• Event #: Just a counter
• Odds: The odds you entered
• Minimum Wins: The minimum number of winning events for the result (e.g., 3 means "3 or more wins")
• Implied Probability (shown as Probability in the compact layout): The probability of at least the number of wins shown
• Implied Odds: Fair odds for at least the number of wins shown (1 ÷ probability)

Practical example

A bookmaker offers "3+ home teams to win at 3.0 odds" across 5 AFL games this weekend. The fair odds for the home teams are:

• Geelong (home) at 1.80
• Carlton (home) at 2.20
• Richmond (home) at 1.95
• Collingwood (home) at 2.50
• Essendon (home) at 1.70

Enter these five odds. The calculator shows:

• 3+ wins: 50.43% probability → Fair odds: 1.98

The bookmaker is offering 3.0, but the fair odds are 1.98. This is massive value. Take it.

Conversely, if the fair odds were 3.5, the bookmaker's 3.0 would be poor value. Skip it.

Evaluating "X wins = bonus bet" promotions

A bookmaker offers "$50 bonus bet if 4+ of your 6 bets win". You're planning $20 stakes on each, and you know you can expect 80% retention at this bookmaker.

Enter your six selections' odds. If the calculator shows 4+ wins has 18% probability:

• Expected value of bonus: $50 × 18% × 80% = $7.20 (you receive the bonus 18% of the time and expect to retain 80% of its value)
• Total turnover: $120
• EV boost: $7.20 ÷ $120 = 6%

The promotion adds 6% EV to your turnover. Combined with the underlying EV of your selections, this determines if the promotion is worthwhile.

Common issues

What odds should I enter?

Enter the fair odds for each outcome. If using bookmaker odds, use the best available odds with vig removed (devigged). If using exchange odds, those are typically close to fair.

The implied odds seem different from what bookmakers offer. Why?

If the implied odds are lower than bookmaker offers, it indicates value. If higher, it indicates poor value. This is normal - the calculator shows fair odds based on your inputs, not bookmaker prices.