Converting Probability into Odds

In the last lesson we taught you how to take the number of outs and calculate the probability of winning a hand. Probability is a good tool and can be expressed as a decimal, fraction, or percentage. One nice thing about percentages; it is easy to calculate your opponent’s percentage to win if you already know your percentage, simply subtract from 100. If you are 35% to win or tie, your opponent is 65% to win or tie. However, percentages have some limitations, including the fact that they can not be compared to pot odds. Most of the examples in this lesson will deal with the converting percentages of winning into the odds of winning.

In this lesson we will teach you another way to express the likelihood that you will win the hand. Instead of using the percentage to win the hand, we want to use the odds of winning. Once we have calculated our odds of winning, we can compare it to the pot odds. Converting probability into odds is a very important skill to have and can be done using these steps:

Converting Probability into Odds For Limit Poker

Step 1: Convert the percentage into a fraction.
• Remove the percentage sign and divide by 100. Note for percentages under 1 percent, divide by a different number. (1,000, 10,000, 100,000, etc…)
• Reduce to the lowest common denominator.

Example 6a: If you have a 38% chance of winning the hand, what are your odds of winning?

38% = 38/100 =19/50. Note if you start with a fraction you can obviously skip this step.

Step 2: Calculate the total # of chances against. = (Denominator) – (Numerator)

So, if we express the fraction in terms of, y / z, then x = (z – y).

From this fraction we can deduct some very important information. The numerator is always the # of chances for, and the denominator is total # of chances. You can then subtract (the # of chances for) from (the # of total chances), to get (the # of chances against). For the purposes of this lesson we will use:

x = # of chances against
y = # of chances for
z = # of total chances

Example 6a continued: x = 31, y = 19, and z = 50.

For those of you who don’t remember here is an important excerpt from Lesson 2:

“If the odds in a situation are favorable, they are expressed as “Odds On” or IN FAVOR OF. If you express odds as “Odds On” (1 to 3 IN FAVOR OF), you put the chances for the event happening first and total chances second. If the event is more likely not to occur than occur; it is expressed as “Odds Against”. (i.e. 4 to 1 ODDS AGAINST) The first number is the number of chances against, and the second number is chances for.”

Step 3: If ODDS AGAINST, express it as:

x to y ODDS AGAINST

If IN FAVOR OF, express it as:

y to z IN FAVOR OF

Example 6a continued: In this case you are the underdog, so you express odds as ODDS AGAINST. So in this case you are 31 to 19 ODDS AGAINST.

Step 4: Reduce denominator to 1. If ODDS AGAINST, simply divide x by y, and replace x with the new number and y with the number 1. IF IN FAVOR OF, divide z by y, and replace y with the new number and z with the number 1.

Example 6a continued: Reduce to 1. 31/19 = ~1.632 / 1 or 38% is approximately 1.632 to 1 ODDS AGAINST.

Summary of Example 6a:
Step1: 38% = 38/100 =19/50
Step2: (50-19=31) x = 31, y = 19, and z = 50.
Step3: 31 to 19 ODDS AGAINST
Step 4: 31/19 = 1.632 to 1 ODDS AGAINST

This may seem difficult or overwhelming at first, but simply practicing a few of these problems will show you how easy it can be. In future lessons we will show you some tips for estimating this number for the most common situations, so you won’t have to do these long calculations for every hand. However, it is very difficult to become a great player, without mastering the information outlined in this lesson. The best way to become proficient in these conversions is to practice. Check back in the near future, for the test that will accompany this lesson.