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The math underlying odds and gambling can help determine whether a wager is worth pursuing. The first thing to understand is that there are three distinct types of odds: fractional, decimal and American. The various types are represent different formats to present probabilities, which are also used by bookmakers, and one type can be converted into another. Once the implied probability for an outcome is known, decisions can be made regarding whether or not to place a bet or wager.
KEY TAKEAWAYS
- The three types of odds are fractional, decimal, and American.
- One type of odd can be converted into another and can also be expressed as an implied probability percentage.
- A key to assessing an interesting opportunity is to determine if the probability is higher than the implied probability reflected in the odds.
- The house always wins because the bookmaker's profit margin is also factored into the odds.
Converting Odds to Implied Probabilities
Although odds require seemingly complicated calculations, the concept is easier to understand once you fully grasp the three types of odds and how to convert the numbers into implied probabilities.
- Fractional odds are sometimes called British odds or traditional odds and are sometimes written as a fraction, such as 6/1, or expressed as a ratio, like six-to-one.
- Decimal odds represent the amount that is won for every $1 that is wagered. For instance, if the odds are 3.00 that a certain horse wins, the payout is $300 for every $100 wagered.
- American odds are sometimes called moneyline odds and are accompanied by a plus (+) or minus (-) sign, with the plus sign assigned to the lower probability event with the higher payout.
There are tools available to make conversions between the three types of odds. Many online betting websites offer an option to display the odds in the preferred format. The table below can help convert odds with pen and paper, for those interested in doing the calculations by hand.
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Converting odds to their implied probabilities is perhaps the most interesting part. The general rule for the conversion of (any type of) odds into an implied probability can be expressed as a formula.
Why Does the House Always Win?
The odds on display never reflect the true probability or chance of an event occurring (or not occurring). There is always a profit marginadded by the bookmaker in these odds, which means that the payout to the successful punter is always less than what they should have received if the odds had reflected the true chances.
The bookmaker needs to estimate the true probability or chance of an outcome correctly in order to set the odds on display in such a way that it profits the bookmaker regardless of an event outcome. To support this statement, let’s look at the implied probabilities for each outcome of the 2015 ICC Cricket World Cup example.
- Australia: -250 (implied probability = 71.43%)
- New Zealand: +200 (implied probability = 33.33%)
If you notice, the total of these probabilities is 104.76% (71.43% + 33.33%). Doesn't that conflict with the fact that the sum of all probabilities must equal 100%? This is because the odds on display are not fair odds.
The amount above 100%, the extra 4.76%, represents the bookmaker’s "over-round," which is the bookmaker’s potential profit if the bookie accepts the bets in the right proportion. If you bet on both the teams, you are actually risking $104.76 to get $100 back. From the bookie’s perspective, they are taking in $104.76 and expect to pay out $100 (including the stake), giving them an expected profit of 4.5% (4.76/104.76), no matter which team wins. The bookie has an edge built into the odds.
According to a study published in the Journal of Gambling Studies, the more hands a player wins, the less money they are likely to collect, especially with respect to novice players. That is because multiple wins are likely to yield small stakes, for which you need to play more, and the more you play, the more likely you will eventually bear the brunt of occasional and substantial losses.
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