{"id":383,"date":"2009-08-28T08:06:15","date_gmt":"2009-08-28T13:06:15","guid":{"rendered":"http:\/\/vgable.com\/blog\/?p=383"},"modified":"2009-08-29T19:51:21","modified_gmt":"2009-08-30T00:51:21","slug":"fair-coin-tosses","status":"publish","type":"post","link":"https:\/\/vgable.com\/blog\/2009\/08\/28\/fair-coin-tosses\/","title":{"rendered":"Fair Coin Tosses"},"content":{"rendered":"

Flipping a coin is, ever so slightly, unfair. As this article<\/a> (via<\/a>) points out, there is a bias for a coin to land on the same side it started on<\/strong>.<\/p>\n

Fortunately, all the biases coins have are systemic biases<\/em> — they effect all similar coins the same way.<\/p>\n

So, with a fair thrower, it’s possible to flip twice, and have the bias of the two throws cancel each other out.
\n<\/strong> <\/p>\n

Procedure<\/h3>\n
    \n
  1. Put a coin heads-up, and flip it, as you normally would.<\/li>\n
  2. Note the result, if certified this will be the decision.<\/li>\n
  3. Flip the coin again, exactly<\/em> as you did in step 1.<\/li>\n
  4. If the coin lands on the opposite<\/em> side as it did in step 2, the result from step 2 is certified. Otherwise, restart from step 1.<\/li>\n<\/ol>\n

    For maximum fairness and reproducibility, it’s best to let the coin land on the floor.<\/p>\n

    Why This Works<\/h3>\n

    To simplify discussion, let’s call the sides of the coin unlikely<\/em> (U) and likely<\/em> (L) instead of heads & tails.<\/p>\n

    There are only 4 possible results to a pair of coin tosses: UU, UL, LU, LL. Obviously LL is most likely, and UU is least likely, so we rethrow if we get either (steps 3-4). That means the only “certified” results are UL or LU, and the odds of getting UL are the same as getting LU<\/strong>.<\/p>\n

    Dexterous Cheating<\/h3>\n

    Unfortunately, this is not a self-enforcing protocol<\/a>, so if the thrower is skillful enough<\/a>, they can make the second throw go however they like, and keep re-throwing until they get the result they want.<\/p>\n

    Fortunately, most people aren’t able to manipulate a coin-toss. If you are worried that someone else is, then only let them flip once, and call the result in the air — that way they won’t know which side to pick. <\/p>\n

    If you<\/em> can throw the result, and can’t find someone else to call the result — it serves you right for driving away all your friends by cheating at coin tosses, you tosser. But I’m still impressed.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Flipping a coin is, ever so slightly, unfair. As this article (via) points out, there is a bias for a coin to land on the same side it started on. Fortunately, all the biases coins have are systemic biases — they effect all similar coins the same way. So, with a fair thrower, it’s possible […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,10],"tags":[480,481,482,455],"class_list":["post-383","post","type-post","status-publish","format-standard","hentry","category-security","category-tips","tag-coins","tag-decisions","tag-gambling","tag-games"],"_links":{"self":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts\/383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/comments?post=383"}],"version-history":[{"count":3,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts\/383\/revisions"}],"predecessor-version":[{"id":386,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts\/383\/revisions\/386"}],"wp:attachment":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/media?parent=383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/categories?post=383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/tags?post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}