Originally Posted by
SeattleDavid
Given that there are only (say) 5 upgrades available for any flight it doesn't matter if there are 84 PLTs on the upgrade list or 10. The tiebreaker only matters if two of the first 5 on the list have a matching EQD value. Or rather the tie breaker only matters between the 5th and 6th on the list. So the probability of EQD failing to resolve the upgrades is really really small. Thus, the probability of any two PLTs on a flight having the same EQD is maybe surprisingly high, but the probability of it being relevant to upgrades is surprisingly small.
The birthday paradox is about two random people sharing a birthday - if I'm interested in the number sharing my birthday the probabilities are much smaller. But in the upgrade scenario we are talking of the person next to me sharing my birthday, which is very very small.
In fact, the only comparison that really matters is whether two people at the border between "upgraded" and "not upgraded" have the same number of EQDs, because it doesn't really matter if
#1 and
#2 on the list have the same EQDs if there's five upgrades available--the key would be breaking a tie between
#5 and
#6 . If we go back to the (almost certainly incorrect) assumption that PLTs are distributed evenly across 5000 EQD values, then the odds that the two people right at the boundary line have the same EQDs are only 1 in 5000. That's obviously quite uncommon, but still means that it would happen on average every day somewhere across the system.