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Q: Drawing sixteen ping-pong balls from a bag for a fantasy football draft ( No Answer,   3 Comments )
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 Subject: Drawing sixteen ping-pong balls from a bag for a fantasy football draft Category: Science > Math Asked by: justaguy1969-ga List Price: \$10.00 Posted: 26 Aug 2006 06:52 PDT Expires: 29 Aug 2006 17:49 PDT Question ID: 759701
 ```My office is doing a fantasy football draft. Everyone in the league is going to pull one of sixteen numbered ping-pong balls out of a bag. Another person and I randomly selected the order in which people will draw their ball from the bag, using these same ping-pong balls. However, there are people in this group who believe there is an advantage to drawing a ball first or early, rather than late or last. Does everyone have the same odds of getting the #1 ball, or is there an advantage to drawing first?``` Clarification of Question by justaguy1969-ga on 29 Aug 2006 12:13 PDT `We are determining the order in which we will draft.`
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 ```Might I suggest that each draw cancels the other out? 1:16, 1:15, etc. Regardless, the numbered ball is allocated to the team, not to the person drawing the ball. Others learned in combinations and permutations may beg to differ and provide a better answer. e.g. Take the game show example. The host asks the contestant to choose one of three doors from which the prize is concealed. The contestant chooses door number 2. The host opens door number 1, with no prize revealed. The host then offers a second chance. 2 questions remain .. has the ratio of chance changed from 1:3 to 1:2 AND should the contestant change their selection to door 3? Arguments exist that the ratio is unchanged given the selection, yet logic suggests that the contestant should select door 3. Psychology however hinders the thought process and fear of the failure of loss through changing one's mind. Any thoughts to differ?```
 ```I am no statistician but think that each participant has the same odds. The trouble is that if they are drawing in turn, once someone has drawn #1, all the subsquent participants will know that they cannot draw that number and feel that they are at a disadvantage. I would too, despite my thinking the system is fair. IF you mark the balls with a code, maybe using four colors and four symbols (red, green, blue, black; square, circle, triangle, star), no one will know what his/her ball represents, until you uncover the chart that gives a number to each thusly coded ball. The chart, covered on an easel, but present from the beginning, will assure that there can have been no manipulation. This will keep the result a surprise till the last person has drawn. Actually, your attempt to select a random order for the persons to draw is superfluous, indeed, may by itself cause distrust. Again, I am no expert, but I would accept the system. (I once lost out on a drawing for a round-the-world flight that was chosen by ticket number and color (red or blue). I had the right number, but then the wrong color was drawn. Arghh! We already had plans to fly to Australia the next year!)```
 ```I concur with Myoarin. The order of persons is superfluous .. at first. However, having spent a sleepless night upon your question, I would consider taking the last choice, given the opportunity. Opposed to my first view, I feel that the odds increase in favour of the person, further down the ladder of ball plucker. I should have realised this earlier. First choice odds are 1:16 in drawing the winning ball. Upon drawing, the selection has now reduced to 15 possibilities. The human nature bit comes in, given that the second drawer has "more chances" of selection as opposed to more odds stacked against him as compared to the last, who has a chance of 1:1 .. a given. Again, given the choice, I would opt for last. An interesting question.```