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Play until you win (Posted on 2018-06-15) Difficulty: 4 of 5
Consider this game:

You have a 1% chance of winning on the first try. If you win, great!

If you don't, win on the first try, you have a 2% chance of winning on the second try.

If needed you have a 3% chance on the third try and so on until you eventually win.

What is the expected number of tries to win this game?

No Solution Yet Submitted by Jer    
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Solution Unsatisfying computer solution (spoiler) Comment 1 of 1
129277986730885202106151856642773382549665465071825090615034369359178917814747670780594211447306244001059786961886915926297133393516168977984471526892507817
------------------------------------------------------------------------------------------------------------------------------------------------------------
 10587911840678754238354031258495524525642395019531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 

 ~= 12.2099606302159803002 
 
from
 
    5   kill "play2win.txt":open "play2win.txt" for output as #2
   10   PWon=0
   20   for Round=1 to 100
   30      PWin=(1-PWon)*Round//100
   35      PWon=PWon+PWin
   40      ExpVal=ExpVal+Round*PWin
   50   next
   60   print ExpVal
   65   print #2,ExpVal
   70   print:print ExpVal/1
   75   print #2,:print #2,ExpVal/1
   80   close #2


  Posted by Charlie on 2018-06-15 12:08:54
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