Let's consider an image which is either Cat or Dog.
<p>
If you report that the probability of Dog is q, 
there will be 1 − (1 − q)<sup>2</sup> chance of winning ${{ amount_paid }} if it is a Dog; 
and 1 − q<sup>2</sup> chance of winning the ${{ amount_paid }} if it is a Cat.
</p>

<p>
Why should you truthfully report?
</p>


<p>
Suppose you actually think the probability of a Dog is &pi;, which does not necessarily equal to q, then your overall probability of getting ${{ amount_paid }} is 
</p>

<p>
(1 − (1 − q)<sup>2</sup>)*&pi; + (1 − q<sup>2</sup>)*(1-&pi;)
</p>

After doing some math, you will see that it is maximized when q = &pi;.