Paucle wrote:Someone here can probably explain the math involved much more clearly than I can. (Or, alternatively, can explain to me why my math is wrong.)
From the perspective of third place, we don't care about first's lock over second (i.e. having twice as much), what we care about is whether first has a lock over third. The condition for that is, that third place's score is less than the difference between first and second.
So let's say there's just one clue remaining on the board, worth 2000 (not a DD), and the scores are 13000, 7000, 4100. The current difference between the scores of first and second is 6000. We will be in contention (from third place) if either
we get the clue, bringing our score above 6000 or
if second place gets the clue, bringing the difference between first and second down below 4100. If the daily doubles are gone in the endgame, then there is never any situation where we in third place would prefer
that a given clue be gotten by second place, rather than by us. (Certainly from third we would prefer that a given clue be gotten by second place rather than by first, but that's something we have no control over.)
If there is still a daily double remaining, then
it is conceivable to have a situation where our best strategy in third place is not to ring in even when we know the correct response. For example, suppose we're in third with 1300, the other players have 15000 and 7000, and there are two clues remaining on the board of which one is the daily double. It would be a huge strategic error for us to ring in, because if we give a correct response we might be forced to take the DD, when our only possibilities of being in contention are if second place is correct on the DD and gets close to first's score, or if first place is wrong on the DD and (foolishly) wagered enough to fall close to second's score.