document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356899>Question 356899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When playing a game of cardwars with a friend, what are the odds that I play nine hands in a row without winning? \r<BR>\n" );
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document.write( "If you're not sure what cardwars are, it is a very simple game that involves 2 players drawing cards from a deck. If I draw a higher card I win, if I draw a lower card I lose. For this scenario, let's also assume that if 2 equal cards are drawn (ex: 2 Kings are drawn by him and me both) I lose as well. The only way I win is if I draw a higher card than my opponent. \r<BR>\n" );
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document.write( "So, what are the odds that I lose 9 hands in a row (I draw a lower or equal card nine straight times).\r<BR>\n" );
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document.write( "Thanks in advance for your help as I can not solve this problem on my own.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254930 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Out of 169 hands you will win 78 and lose 91<BR>\n" );
document.write( "probability of losing one hand 91/169 = 7/13<BR>\n" );
document.write( "Probability that you will lose nine hands in a row (7/13)^9=.0038...<BR>\n" );
document.write( "1-.0038=.9962<BR>\n" );
document.write( "Odds against losing 9 in a row: 9962 to 38 or 262 to 1<BR>\n" );
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document.write( "Ed </SPAN>\n" );
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