[dba-Tech] The Three Doors Problem

On 26 Aug 2005 at 19:20, Billy Pang wrote:

> first ping pong ball selected gets first pick in the entry draft, the teams 
> with three ping pong balls have a greater chance of getting the coveted 
> first pick than the other teams with only two or one ping pong ball.  I 
> watched the draft live as it took place.  To increase drama, they select the 
> ping pong balls behind closed doors to determine the order of the thiry 
> teams; then they come out and reveal the order in reverse (starting with 30, 
> 29, 28, etc...); however, i realized that if they pick the ping pong balls 
> in reverse order (ie. first ball they picked is 30th pick), the teams with 
> three ping pong balls would no longer be favorites because they have a 
> greater chance of being selected.  

 They are still favourites.  A team with three balls still has two balls in 
the running for 1st even if one of their balls comes up as 30th. They are 
still better off than a team with only one ball.

Take it to it's logical conclusion.  Imagine you get down to the "last" 
three picks  (3rd,2nd,1st)  and have two teams left - one with two balls 
and one with one ball.  How often will the team with one ball end up with 
the 1st draft and how ofter will the team with two balls get him?

-- 
Stuart