<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/86dfac26-2c34-497b-a8ed-a63b11c24044/271DEE17-0373-4A31-9C2F-892B5F1EBE04/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://en.wikipedia.org/w/index.php?title=Inverse_gambler%27s_fallacy&oldid=294159502" href="http://en.wikipedia.org/w/index.php?title=Inverse_gambler%27s_fallacy&oldid=294159502" style="font-size: 11px;">en.wikipedia.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Inverse_gambler%27s_fallacy&oldid=294159502"><P>The <B>inverse gambler's fallacy</B> is a term coined by philosopher <A title="Ian Hacking" href="http://en.wikipedia.org/wiki/Ian_Hacking" linkindex="3">Ian Hacking</A> to refer to a <A title="Formal fallacy" href="http://en.wikipedia.org/wiki/Formal_fallacy" linkindex="4">formal fallacy</A> of <A title="Bayesian inference" href="http://en.wikipedia.org/wiki/Bayesian_inference" linkindex="5">Bayesian inference</A> which is similar to the better known <A title="Gambler's fallacy" href="http://en.wikipedia.org/wiki/Gambler%27s_fallacy" linkindex="6">gambler's fallacy</A>. It is the fallacy of concluding, on the basis of an unlikely outcome of a <A class="mw-redirect" title="Random" href="http://en.wikipedia.org/wiki/Random" linkindex="7">random</A> process, that the process is likely to have occurred many times before. For example, if one observes a pair of fair <A title="Dice" href="http://en.wikipedia.org/wiki/Dice" linkindex="8">dice</A> being rolled and turning up double sixes, it is wrong to suppose that this lends any support to the hypothesis that the dice have been rolled before. We can see this from the Bayesian update rule: letting <I>U</I> denote the unlikely outcome of the random process and <I>M</I> the proposition that the process has occurred before, we have</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Inverse_gambler%27s_fallacy&oldid=294159502"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/en.wikipedia.org/img/5E8D1563-6CE4-4AB4-8013-EE0C8D96921B" alt="P(M|U) = P(M) \frac{P(U|M)}{P(U)}" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Inverse_gambler%27s_fallacy&oldid=294159502"><P>and since <I>P</I>(<I>U</I>|<I>M</I>) = <I>P</I>(<I>U</I>) (the outcome of the process is unaffected by previous occurrences), it follows that <I>P</I>(<I>M</I>|<I>U</I>) = <I>P</I>(<I>M</I>); that is, our confidence in <I>M</I> should be unchanged when we learn <I>U</I>.</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Inverse_gambler%27s_fallacy&oldid=294159502"><I>No Inverse Gambler's Fallacy in Cosmology.</I></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/271DEE17-0373-4A31-9C2F-892B5F1EBE04/blog/" title="blog or email this clip"><img src="http://content8.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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