Fractional odds are generally expressed as Y to X (or sometimes as Y/X). It is the latter representation that has given this odds format its name.
Fractional odds are mostly associated with table games in casino gambling. They also have use in sports betting. Table games, apart from being played on tables at land casinos, have a specific characteristic. A table game may offer a number of bets each having distinct odds associated with it.
Some examples are given below:
Roulette: Single number bet – 35 to 1; Bet on red – 1 to 1
Craps: Pass bet – 1 to 1; Place bet on 4 – 9 to 5
Baccarat: Player hand – 1 to 1; Tie bet – 8 to 1
Blackjack: Blackjack is an exception of sorts. There are no separate bets. If you beat the dealer the odds are 1 to 1. If you win with a blackjack then the odds are 3 to 2.
How Fractional Odds Work
Let us start with the simple case where X is 1, in the Y to X fractional odds. The single number bet in roulette has the odds of 35 to 1. You bet $1 on the number 13, because you consider it lucky or for any other reason.
We evaluate the possible outcomes:
If the number called is other than 13 then you lose the bet. The croupier will take your $1 chip and move it to the bank. You will be down by $1.
If the number called is 13, since the odds are 35 to 1, you win $35. The croupier will pass on chips worth $35 to you and will also return your original bet of $1.
A Bet of $2 at Odds of 35 to 1
- If you lose the bet then you lose $2.
- If you win the bet this is how it works. For every $1 bet you win $35. Since you have bet $2 you will win $70. Your bet of $2 will also be returned to you.
A bet of $1 at Odds of 9 to 5
- If you lose the bet then you lose $1.
- If you win the bet this is how it works. Had you bet $5 then you would have won $9. Since you have bet $1 you will win (9/5) times your bet which works out to $1.80. Your bet of $1 will be returned to you as usual.
The General Case
You have bet $Z at odds of Y to X and have won.
- You will get $[Z x (Y/X)] as your winnings and will be returned your original bet of $Z
The House Edge
This is the most important issue associated with odds. The casino has administrative costs to meet and needs to make a profit for the investors. This is achieved by offering odds to players that are lower than fair odds. House edge arises from this. The exact definition of house edge is the percent of a wager that goes to the casino in the long run. In some games like roulette and craps the house edge is easy to calculate. In many casino games like blackjack and slot machines the house edge is determined through simulation.
We illustrate the calculation of house edge through the Any Seven bet in craps. The bet wins if the total on the two dice is 7 and loses otherwise.
A 7 can be rolled in six ways out of the total 36 combinations possible. Therefore the probability of rolling a 7 is 6/36 or 1/6. Most casinos offer a payout of 4 to 1 for this bet. Assuming a player bets $1 for six successive Any Seven bets. He will expect to win once and lose five times and will do so in the long run. At the end of the cycle he will win $4 and lose $5. From a total investment of $6 his net loss is $1. If the odds were fair (in this case 5 to 1) he would not have lost anything. Hence the house edge for this bet is 1/6 or 16.67%.
It is not possible to calculate the house edge for every bet.
The sample list below will help you in selecting casino games and bets. Bets with lower house edges are obviously better:
Blackjack: 0.5%. Will vary marginally based on variant.
Video Poker: 0.5%. Will vary marginally based on variant.
Baccarat Banker Hand: 1%
Craps Pass Bet: 1.4%
European Roulette (all bets): 2.7%
Slot Machines: 5%. This is an average figure. There can be considerable variation.
American Roulette (all bets): 5.3%
Craps Any Seven: 16.7%
Odds and Risk
Let us look at European Roulette. All bets have the same house edge, so we can set it aside in this section. The odds for a single number bet are 35 to 1 and a win with a $1 bet will pay $35. The odds for a bet on Red are 1 to 1 and a win with a $1 bet will pay $1. This does not automatically make the single number bet a better one. The probability of a single number bet winning is 1/37 or 2.7%. The probability of a bet on red winning is 18/37 or 48.6%
There is an important lesson here. Bets with higher odds will pay greater amounts but will win less frequently. Such bets are suited to players willing to take higher risks. Bets with lower odds will pay smaller amounts but will win more frequently. Such bets are suited to risk-averse players whose main objective is to preserve their bankroll. Middle paths exist as well to enable players to strike a balance. A bet on six numbers will pay 5 to 1 and win 16.2% of the times.
Other Formats for Odds
Odds can also be stated in Decimal and American formats. You can convert from one format to another. The resultant payout will be the same. Decimal and American format have widespread use in sports betting, but are rarely, if ever, used in casinos.