CareerCup

don't know what he is asking.........
if he is talking about zoccihedron (100 sided die - a sphere), the probability distribution is uneven because extreme numbers (93 and above, 8 and above) are placed near the poles where they are closer together (so probability is less) whereas numbers near the equator are more widely spaced (higher probability). The expected value at poles is 66.25(average of 1-8 & 93-100) and for the rest it's 50.5(av of rest).
But to calculate the expected pay off, we need the spacing. from spacing we can calculate p(near the equator or near the poles).... Suppose probability at the poles be 'x' and at equator its 'y'. Then expected value of a single roll is: (66.25x+50.5y)/(x+y).....

Please correct the question, incomplete questions lead to meaningless discussions.....

can't understand the question

I believe he is saying, with a 100 sided dice you roll once and then have the option (second chance) to roll again if you want to try and increase your number. what is you rstrategy i.e. what numbers would you roll again for and what numbers would you simply take. I think the probability distribution between the 100 numbers is assumed equal

The bet is 63
The expected value for the first time the dice is rolled is 50.50 ie n*(n+1)/2,in this case it is 100*101/2 viz 50.50.
However,as i have a 2nd chance ie i choose this only if the actual value that turns up on the dice during first throw is less than 50.50 which has 50% probability.Therefore, I have 50% chance to get an expected value between 51 to 100 ie 75.50 and 50% chance to retry if the value is between 1 to 50.
In the 2nd try the expected value will be again 50.50
Therefore,the final summary is

Probability Expected Value Calculation
50% 51 to 100(75.50) 50%*75.50
50% Retry 1 to 100(50.50) 50%*50.50
---------------------------------------------------------------------------------------
Sum= 50%*(75.50+50.50)=63

- canmpuppala on January 28, 2012 Edit