Welcome to Wikifunctions
What is everyone's favorite function / formula?<p>Mine is<p><pre><code>    n/(n+x)
</code></pre>
It has a bunch of interesting aspects:<p><pre><code>    As n gets bigger, it goes from 0 to 1.
    
    When n equals x, it is 0.5

    As n gets bigger, the difference between n and n+1 gets smaller

    For two sufficiently large n's, the results are equal.
</code></pre>
Say somebody told you about a new cafe in town and that it is completely awesome. The best cafe ever. What probability do you assign to it really being an exceptionally awesome cafe? If your x is 3, then the probability after one person praised it is 25%:<p><pre><code>    1/(1+3) = 0.25
</code></pre>
And if another person told you about that cafe being awesome, the probability becomes 40%:<p><pre><code>   2/(2+3) = 0.4
</code></pre>
And after 3 people told you the cafe is awesome, chances are 50% it really is:<p><pre><code>   3/(3+3) = 0.5
</code></pre>
The changes in probability are pretty strong at the beginning. But after 1000 people reported about the awesome cafe, the next report makes almost no difference anymore. It only ups the probability from 0.997008 to 0.997011.<p>By changing x from 3 to 4, your formula becomes more "suspicious", by changing it from 3 to 2, it becomes more "gullible".<p>I wonder if this formula has a name already. If not, "the trust formula" might be a candidate.