Odds and prices
How to calculate odds in gambling
For a game with countable outcomes, divide the ways you win by the total number of outcomes. For a price, divide one by the decimal and you get the implied chance.
Everything else is those two sums pointed at a different question.
Sum one: counting a game
Roulette, dice and cards can be counted. A six-sided die rolling a four is one outcome out of six, so 16.7%. Two dice totalling seven is six combinations out of thirty six, so 16.7% again, which surprises people who have not laid the grid out.
Slots cannot be counted this way. The reel strips are weighted and the studio does not publish the weights, so the only number you get is the return rate on the info panel.
Sum two: a price into a percentage
Decimal price: 1 ÷ price. So 4.00 is 25%, 1.50 is 66.7%.
American minus: n ÷ (n + 100). So −220 is 220 ÷ 320, or 68.8%.
American plus: 100 ÷ (n + 100). So +260 is 100 ÷ 360, or 27.8%.
Sum three: how much the book is holding
Convert every outcome in a market to a percentage and add them up. A two-way market at 1.91 each side gives 52.4% plus 52.4%, which is 104.8%. The 4.8% over is the hold.
Divide the hold across the number of outcomes and you have the cost per bet. Do this once on your regular market and you will know instantly whether a price is normal or bad.
Sum four: what a bonus is worth
A C$100 bonus at 35x asks for C$3,500 of turnover. At an average 96% return, pushing C$3,500 through the games costs about C$140 in expectation.
So the offer hands you a hundred and asks for a hundred and forty back on the way out. Every offer page on this site runs that same sum, and you can run it yourself in ten seconds on any promo you are shown.