If the number of players = more than 2x the number of prizes available, then it is completely, totally, and absolutely impossible for most(51%) of players to win, no?
Maybe there will be a contest where there are hundreds of thousands of prizes though, in which case most players could win.
It is "unlikely" (very, very) for all players, but not impossible for any of them.
The word "impossible" requires a future event unless you deliberately add a past verb (it is, indeed, impossible for all of the entrants to have won). Until the contest is closed, it is "possible" for any given entrant to win.
Yeah ok, "It is impossible for most players to win"
"It is impossible that most players will win"
or
"It is guaranteed that most players will not win"*
*based on the assumption that fewer than (tens of?) thousands of prizes will be won.
BTW what's our estimate of "active" players? 20 regions, 4 worlds per region, 3k players per world = 240K players?