giaorl [Lexaloffle Blog Feed]https://www.lexaloffle.com/bbs/?uid=112915 Let's make a trade! (or: the Monty Hall Problem) <p><center> <table><tr><td> <a href="/bbs/?pid=158739#p"> <img src="/bbs/thumbs/pico8_monty_hall_problem-0.png" style="height:256px"></a> </td><td width=10></td><td valign=top> <a href="/bbs/?pid=158739#p"> monty_hall_problem</a><br><br> by <a href="/bbs/?uid=112915"> giaorl</a> <br><br><br> <a href="/bbs/?pid=158739#p"> [Click to Play]</a> </td></tr></table> </center></p> <h1>Aim</h1> <p>This cartridge can be used for educational purposes to make simulations for the <strong>Monty Hall problem</strong>, a well-known probability conundrum that puzzles many people. The statement of the problem is the following: </p> <p>-- <em>Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, &quot;Do you want to pick door No. 2?&quot; Is it to your advantage to switch your choice?</em> [cited from the Wikipedia page]</p> <p>For students attending a Probability course, this is an exercise about conditional probability. You can read more on the <a href="https://en.wikipedia.org/wiki/Monty_Hall_problem">dedicated Wikipedia page</a>. </p> <h1>Name</h1> <p>The name <em>Let's make a trade</em> is reminiscent of the name of the TV show that inspires the setting of the problem.</p> <table> <thead> <tr> <th style="text-align: center;"></th> <th style="text-align: center;"></th> </tr> </thead> <tbody> <tr> <td style="text-align: center;"><img loading="lazy" style="margin-bottom:16px" border=0 src="/media/112915/monty_hall_1.gif" alt="" /></td> <td style="text-align: center;"><img loading="lazy" style="margin-bottom:16px" border=0 src="/media/112915/monty_hall_0.png" alt="" /></td> </tr> <tr> <td style="text-align: center;"><em>Title screen.</em></td> <td style="text-align: center;"><em>The host of the show presenting the game.</em></td> </tr> </tbody> </table> <h1>How to use this game</h1> <p>The first time you play, the game is presented in all details. You choose a door, the host opens another door, which has a goat, and you are free to choose the other closed door, if you wish. </p> <table> <thead> <tr> <th style="text-align: center;"></th> <th style="text-align: center;"></th> </tr> </thead> <tbody> <tr> <td style="text-align: center;"><img loading="lazy" style="margin-bottom:16px" border=0 src="/media/112915/monty_hall_2.gif" alt="" /></td> <td style="text-align: center;"><img loading="lazy" style="margin-bottom:16px" border=0 src="/media/112915/monty_hall_3.gif" alt="" /></td> </tr> <tr> <td style="text-align: center;"><em>An unlucky guest.</em></td> <td style="text-align: center;"><em>A lucky guest.</em></td> </tr> </tbody> </table> <p>After the first round, the game resets and you can observe many instances of the game. You can try the following experiment: pick a strategy (e.g., always switch/never switch) and apply it consistently in all instances to see which one is more favourable!</p> <table> <thead> <tr> <th style="text-align: center;"></th> <th style="text-align: center;"></th> </tr> </thead> <tbody> <tr> <td style="text-align: center;"><img loading="lazy" style="margin-bottom:16px" border=0 src="/media/112915/7_monty_hall_1.png" alt="" /></td> <td style="text-align: center;"><img loading="lazy" style="margin-bottom:16px" border=0 src="/media/112915/monty_hall_0 copy.png" alt="" /></td> </tr> <tr> <td style="text-align: center;"><em>Observing the strategy &quot;never switch&quot;.</em></td> <td style="text-align: center;"><em>Observing the strategy &quot;always switch&quot;.</em></td> </tr> </tbody> </table> <p>Have fun experimenting!</p> https://www.lexaloffle.com/bbs/?tid=145926 https://www.lexaloffle.com/bbs/?tid=145926 Thu, 05 Dec 2024 07:42:20 UTC