Wikipedia:Reference desk/Archives/Mathematics/2021 January 7

= January 7 =

limit of Likelihood of tie for most selected of others
(From this week's RuPaul's Drag Race)... If 7 queens vote at Random for one of the other queens (in this case they can't vote for themselves, Ben DeLaCreme isn't part of this), what is the probability of a tie in the queen with the most number of votes. Does this probability go up or down if they can vote for themselves? As the number of queens goes up, does the probability go up or down?
 * If self-votes are not allowed, the probability of a tie for 7 queens equals $129534/6^{7} =$ $0.46273$. If allowed, it goes down to $372540/7^{7} =$ $0.45236$. Increasing the number of queens increases the likelihood of a tie, except if that number was less than $3$. I suspect that the limit equals $1 − 1/e =$ $0.63212$. --Lambiam 09:56, 7 January 2021 (UTC)
 * Here's a computer calculation showing the same results as stated above, as well as the results for lower numbers. --116.86.4.41 (talk) 10:45, 7 January 2021 (UTC)