This app visually compares probability to odds.  User can adjust two probability values ("baseline" and "exposed") and compare their associated odds, along with relative risk and odds ratio.

The probability of something happening can be expressed as a number between 0 and 1.  The odds of  that thing  happening can be expressed as a  comparison of two probabilities: the probability it will happen vs. the probability it will not.  This is why odds are often expressed as  "___ to ___"; for instance "3 to 2 odds" says that the probability of this thing happening is 1.5 times as great as the probability of it not happening.  More simply,  an outcome with 3 to 2 odds should occur 3 times for every 2 times it does not occur, i.e. it should happen 3 times for every 5 attempts.  So, "3 to 2 odds" corresponds to a probability of 3/5 = 0.6.

This app does not display odds as "___ to ___", it simply calculates : Odds = (Prob)/(1 - Prob).   Here are the important properties of probabilities and odds that this app aims to convey:

•  The plot on the left gives probability on the horizontal axis and odds on the vertical axis.  The dashed straight line is y = x.  The curved line shows odds, given probability.  Notice that odds are always larger than probability (unless they are both zero).  Probability cannot exceed 1; odds are unbounded.  When probability is small, odds are similar to probability.  When probability is large, odds become much larger than probability.  

• It is often of interest to compare two probabilities or two odds to one another.  This app lets you set two.  I'm using the language of disease research, in which risk factors for disease are measured. One probability is a "baseline", and the other is "exposed", as in exposed to something that increases the probability of disease.

• The plot on the right shows two common statistics.  On the left is the "relative risk" ("RR", sometimes called "risk ratio"); this is the "exposed" probability divided by the "baseline" probability.  On the right is the "odds ratio" ("OR"); this is the "exposed" odds divided by the "baseline" odds.  

• Notice that RR cannot exceed OR.  When probabilities are small, OR is similar to RR.  When probabilities get larger, OR gets larger relative to RR.  This is especially pronounced when baseline and exposed probabilities differ substantially.

I have a different app that gives a more detailed look at relative risk vs. odds ratio here.