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What do odds mean, and how to convert percentages or fractions into odds.
Odds
If this word conjures up nightmares about math exams, or if you believe odds are for math wizards teaching at the MIT, fret not: poker odds is really sixth grade material.
Definition
 When we toss a coin, we naturally know that getting heads is as likely as getting tails. In other words, there are 50% chances to get heads, and 50% to get tails. Even chances. Simple enough.
Odds are just another way to say the same thing. It consists in comparing the proportion of favorable cases againt unfavorable ones. In the coinflip example, chances are equal, so proportions are equal too. We say that the odds are one to one, noted 1:1 (there are other notation systems).
Here, we compared probabilities, but odds can be used every time two proportions are compared. If you bet on sports, the bookmaker will lay odds for the payout: you bet $100, the payout is $400, odds are 4:1 (again, in sports betting, other notations are used).
Now, let’s throw two coins. What are the chances to get exactly two heads? In case you forgot, in order to get the probability of two independent events occurring, we simply multiply their respective probabilities. Here, that would be 50% of 50% (or 0.5 times 0.5, if you prefer), that is, 25%. This means that if we repeat our experience (throwing two coins) four times, we will, on average, get two heads in the same toss only one time. Converting this into odds, we have one favorable occurrence, and three unfavorable ones. Consequently, the odds are three to one, noted 3:1.
Conversion
In order to convert percentages into odds, we take the percentage as a real number, compute the inverse, and substract one. For instance, for a 20% chance event: 20% = 0.2, 1/0.2 = 5, and 5-1 is 4. Therefore, a 20% event is 4:1.
Favorite or Underdog
By convention, odds are often noted as “x to 1”, or x:1. Most often, the context makes it clear what event is favorite: getting two heads in our last example is not the most likely scenario, so we know that 3:1 means it will happens one times in four, and not three times in four (which is what 3:1 would means if it were favorite). However, if there can be some ambiguity, or if you want to be crystal clear, add “favorite” or “underdog” after the odds eg. 3:1 favorite.
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