Poker Math That Matters

26
Let’s look at the probability and odds against rolling the 5. The
probability is 1
, and the odds against are 5:1. Notice if you add
6
together the two numbers in the ratio you get the bottom number
of the probability fraction. This is because the number of times
something doesn’t happen plus the number of times something
does happen equals all the times possible. And the bottom
number of the probability fraction represents to the total possible
outcomes. Now, the right number of the ratio is the number of
times it did happen. This is the same number represented by the
top of our probability fraction. So, we can then see how to
convert a ratio to a fraction.
Let’s take the ratio 6:1. What would the corresponding fraction
be? We know this ratio is telling us something doesn’t happen
six times and does happen one time. This means there are seven
total chances. So, that’s the bottom number of the probability
fraction. The right number of the ratio lets us know this thing
happens one time, which is what we’re after on the top of our
fraction. So, saying 6:1 is the same as saying 1
. Let’s just take
7
this one step further and convert a fraction to a ratio.
Let’s take the fraction 1
. What is the corresponding ratio? Let’s
3
do the easy part first and put the one on the right side of the ratio
(?:1). This tells us the thing will happen one time. Now, if
something will happen one time out of three, how many times
will it not happen? Here we take the three total chances and
subtract the one time is happened and we see that it did not
happen two times. So, two is the number of the left side of our
ratio. The probability 1
can be said as 2:1 against.
3
Let’s do one more of these. Let’s take the fraction 2
. Again, the
5
easy part first and put the two times it does happen on the right
of our ratio (?:2). Then we need to find out how many times it