75 lines
5.1 KiB
HTML
75 lines
5.1 KiB
HTML
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<h2>Billionaire</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 267</h3><span style="width:300px;color:#666;">Published on Friday, 4th December 2009, 01:00 pm; Solved by 1677</span></div>
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<p>You are given a unique investment opportunity.</p>
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<p>Starting with £1 of capital, you can choose a fixed proportion, <var>f</var>, of your capital to bet on a fair coin toss repeatedly for 1000 tosses.</p>
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<p>Your return is double your bet for heads and you lose your bet for tails.</p>
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<p>For example, if <var>f</var> = 1/4, for the first toss you bet £0.25, and if heads comes up you win £0.5 and so then have £1.5. You then bet £0.375 and if the second toss is tails, you have £1.125.</p>
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<p>Choosing <var>f</var> to maximize your chances of having at least £1,000,000,000 after 1,000 flips, what is the chance that you become a billionaire?</p>
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<p>All computations are assumed to be exact (no rounding), but give your answer rounded to 12 digits behind the decimal point in the form 0.abcdefghijkl.</p>
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