document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90905>Question 90905</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321458209/algebrahomeworkh>Using and Understanding Mathematics A Quantitative Reasoning Approach</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> House Edge in Blackjack: In a large casino, thehouse wins on its blackjack tables with a probablility of 50.7%. All bets at blackjack are 1 to 1: If you win, you gain the amount you bet; If you lose, you lose the amount you bet. <BR>\n" );
document.write( "a: What is the expected value to you of a single game? What is the house edge? If I am able to understand part a I should be able to understand the the rest of the problem. 3 days to go until the quarter is over. Thanks very much for your help this past year. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65958 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=65958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \"x\" be the gain on a bet:<BR>\n" );
document.write( "P(gain x) = 0.507<BR>\n" );
document.write( "P(lose or -x) = 1-0.507 = 0.493<BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "Expected Value calculation:<BR>\n" );
document.write( "Random variable is the gain:<BR>\n" );
document.write( "(gain x-dollars) * (0.493) = +0.493x dollars<BR>\n" );
document.write( "(lose x-dollars) * (0.507) = -0.507x dollars<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Take the sum to get the expected gain:<BR>\n" );
document.write( "0.493x-0.507x = -0.014x or a loss of 1.4% on each bet<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "I'm not sure I know what you mean by \"house edge\".\r<BR>\n" );
document.write( "\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );