<p>With the previous mountain entry on Expected Value in mind, we <strong><u>Should</u></strong> <strong><span style="color:#8e44ad;">Play the Lottery Sometimes</span></strong>.</p>
<p><strong><span style="color:#2980b9;">Really?</span></strong></p>
<p>Yeah, think about it. If the "expected value" of one lottery ticket is greater than the price we paid for it, it actually makes mathematical sense to purchase one, several, or many. You're "earning" money by doing so. </p>
<p><strong><span style="color:#e74c3c;">Let's Illustrate with an Example</span></strong></p>
<p>As shown in the previous mountain entry on Don't Play the Lottery, the odds of winning the PowerBall lottery are as follows:</p>
<p style="text-align: center;">$1$ in approximately $292$ million</p>
<p>To calculate the expected value of one ticket, we multiply the above odds by the award -- in this case, a dumpload of money. Let's imagine the cash prize is $\$100$ million. What would be the "value" of each ticket?</p>
<p style="text-align: center;">$(1$ in approximately $292$ million$)$ $\times \$100$ million</p>
<p style="text-align: center;">$$\$0.34$$</p>
<p>lol. Each ticket is worth about $34$ cents. Given that each ticket costs $\$2$, you're actually <span style="color:#e74c3c;">losing $\$1.66$</span> every time you buy a lottery ticket in these conditions. </p>
<p><strong><span style="color:#27ae60;">But Not Always</span></strong></p>
<p>Imagine the cash prize was not $\$100$ million but rather $\$1$ billion. Does that change things?</p>
<p style="text-align: center;">$(1$ in approximately $292$ million$)$ $\times \$1$ <strong><u>billion</u></strong></p>
<p style="text-align: center;">$$\$3.42$$</p>
<p>Dang! With each ticket costing us $2$ bucks, we're <span style="color:#27ae60;">earning approximately $\$1.42$</span> on every ticket we buy. Score.</p>