{"id":2629,"date":"2013-10-25T16:29:40","date_gmt":"2013-10-25T21:29:40","guid":{"rendered":"http:\/\/skullduggery.us\/wordpress\/?p=2629"},"modified":"2017-08-29T13:23:12","modified_gmt":"2017-08-29T18:23:12","slug":"the-monty-hall-problem","status":"publish","type":"post","link":"http:\/\/skullduggery.us\/rants\/the-monty-hall-problem\/","title":{"rendered":"The Monty Hall Problem"},"content":{"rendered":"

\"goat\"<\/a>“You are the contestant\u00a0on a game show that has 3 doors. One of them conceals\u00a0a big prize. After picking\u00a0a door (either A, B, or C), the show’s host reveals an unpicked losing door. He then asks if you’d\u00a0rather change to the remaining unopened door, or stick with the one you had\u00a0initially selected.”<\/p>\n

Do you switch, or do you stick with your original door?<\/strong><\/p>\n

Contrary to what\u00a0some may think, this classic\u00a0“Let’s Make a Deal” probability puzzle\u00a0proves that IF the contestant chooses a different door than the one picked first, they increase their probability of winning to two-thirds.\u00a0No tricks. I’m serious.<\/p>\n

(Let’s say that Door C is the winner.)<\/p>\n

Scenario 1:\u00a0Choose Door A. Door B is revealed. SWITCHING WINS<\/span>.
\nScenario 2:\u00a0Choose Door B. Door A is revealed. SWITCHING WINS<\/span>.
\nScenario 3:\u00a0Choose Door C. Door A\u00a0or B is revealed. SWITCHING LOSES<\/span>.<\/p>\n

Switching your initial choice has a higher chance of landing the ultimate prize!<\/strong><\/p>\n

It boils down to this: when the contestant makes the original choice, they have a\u00a01:3 chance of picking correctly. But then the game changes. After the\u00a0host removes an option, you’re down to one good answer of two total doors.\u00a0(It WOULD be simple probability if the contestant\u00a0was presented with only\u00a0two doors from the get-go.) If the player DOESN’T SWITCH, they’re assuming they’ve picked the prize accurately in round 1…. which isn’t likely. SWITCHING acknowledges\u00a0this and effectively reverses the player’s chances. In fact,\u00a0picking a dud door with this method isn’t likely.<\/p>\n

Don’t believe it?\u00a0Get a friend and 3 playing cards to see if you can’t statistically debunk the theory. If a “wrong” card is revealed and a contestant switches cards during phase two every time,\u00a0I predict\u00a0they’ll have a 66% success rate of getting the big prize…. as opposed to 33%\u00a0probability if\u00a0never switching answers. Strangely, the contestant\u00a0is likely to win if they choose wrong\u00a0in the first phase.\u00a0Your odds are initially slim, then\u00a0double in the player’s favor\u00a0upon flipping answers. Cool, huh?<\/p>\n

The big question is: how many would naturally switch choices without this knowledge?!<\/p>\n","protected":false},"excerpt":{"rendered":"

“You are the contestant\u00a0on a game show that has 3 doors. One of them conceals\u00a0a big prize. After picking\u00a0a door (either A, B, or C), the show’s host reveals an unpicked losing door. He then asks if you’d\u00a0rather change to … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[],"class_list":["post-2629","post","type-post","status-publish","format-standard","hentry","category-blurbs-and-links"],"_links":{"self":[{"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/posts\/2629","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/comments?post=2629"}],"version-history":[{"count":26,"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/posts\/2629\/revisions"}],"predecessor-version":[{"id":2658,"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/posts\/2629\/revisions\/2658"}],"wp:attachment":[{"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/media?parent=2629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/categories?post=2629"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/skullduggery.us\/rants\/wp-json\/wp\/v2\/tags?post=2629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}