Gaming rules and answers

Betting maths and calculators

Fractional and decimal odds, expected values and probabilities. These answers focus on the actual question, with source references and conditions where applicable.

1. How do I convert 7/4 betting odds to decimal odds?
2. What is the implied probability of decimal odds of 1.80?
3. What's the best way to find the bookmaker margin in a two-outcome market?
4. Can two bookmakers offer opposite sides with a combined implied probability under 100%?
5. What is the difference between expected value and the probability of winning?
6. Why can a 90% chance bet still be bad value?
7. How can a four-leg accumulator lose if three selections win?
8. What is the best way to calculate an accumulator when one leg is void?
9. Why is my 10-to-1 win returning only $55 on a $10 each-way bet?
10. What's the best way to compare odds boosts?
11. What is the difference between a free bet and free cash?
12. Can a 3% cashback offer compensate for a 5% average house edge?
13. How do I calculate a 4/1 each-way place return at one-fifth odds?
14. Does a bookmaker's 'best price' always mean highest expected value?
15. What is the best way to visualise a bookmaker's overround?
16. Can a bookmaker lose money despite offering negative-EV odds?
17. What is the difference between 'risk-free' and 'money back' betting promotions?
18. How do I explain why the favourite does not always win?
19. What is the best way to compare the real price of lottery tickets and sportsbook bets?
20. Can an odds converter tell me whether a bet is profitable?
21. What does a 25% bookmaker margin mean in a three-way football market?
22. Why does my probability calculation change after I include a push outcome?
23. Can I use an online betting calculator without placing a wager?
24. What's the best way to compare the payout of a dead heat at 3/1?