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    <h2>How Your Payment Works</h2>

    <p>This example aims to make clear how we will calculate your payment and highlight why it is crucial to share your true probability estimates. Note that the scenario described here is just for illustration and not real. If you understand that being honest with your estimates is the best approach, you may skip this example.</p>

    <div class="example-box">
        <p><strong>Scenario Context:</strong> During the experiment, you will be asked to estimate the probability of various events, like the chance of it raining tomorrow. During the experiment, you'll be asked to estimate the probability of various events, like the chance of it raining tomorrow. Suppose you believe there is a 60% chance.</p>

        <p>After you submit your estimate, a random number between 0 and 100 is generated. This number, combined with your probability estimate, determines your chance of earning the $5:</p>

        <ul>
           <li><strong>Scenario 1: Random number is higher than your estimate</strong>
                <ul>
                    <li>If the random number is 75, which is higher than your 60% estimate.</li>
                    <li>You then have a 75% chance to earn $5.</li>
                </ul>
            </li>
            <li><strong>Scenario 2: Random number is equal to or lower than your estimate</strong>
                <ul>
                    <li>If the random number is 50, equal to or lower than your 60% estimate.</li>
                    <li>You will earn $5 if it actually rains tomorrow.</li>
                </ul>
        </ul>

     <p><strong>Optimal Strategy:</strong> By reporting your true belief, you maximize your expected earnings. Let's explore this idea further. Let's dive deeper into this concept.</p>

<p>Consider you over-report the probability of raining tomorrow, stating a probability of 80% when, in fact, you believe it to be 60%. If a random number generated is 70, this falls between your true belief (60%) and your inflated report (80%). Due to over-reporting, you are now in a position where you rely on the event actually happening to earn the $5, since the generated number (70) is now treated as lower than your reported estimate (80%). However, had you reported your true belief of 60%, the generated number 70 would have given you a direct 70% chance to win the $5, without depending on the event's outcome. In this scenario, by over-reporting, you inadvertently reduce your earning potential from a straightforward 70% chance down to the actual occurrence of the event, which you estimated at only 60%.</p>

<p>On the opposite side, if you under-report, suggesting a chance of 40% when your true belief is 60%, and the event does occur, your lower estimate keeps you away from a better chance to earn more. By under-reporting, you might find yourself unnecessarily in the second scenario, where your earnings are entirely contingent on the event's occurrence, despite a higher random number potentially offering a better chance at winning the $5 based on your true estimate.</p>

<p>In short, neither over-reporting nor under-reporting benefits you. To maximize your potential earnings, it's crucial to report your genuine estimate.</p>


    </div>

    <p>If any part of this payment mechanism is unclear, or if you have any questions, please ask for assistance.</p>

    <form method="post">
        <button type="submit" class="btn btn-primary">I Understand</button>
    </form>
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