Originally Posted by
jordyn
The
birthday paradox means that the odds of a collision are a lot higher than you initially think. If PLTs were evenly distributed across say 5000 EQDs values, it would only take 84 of them on the same flight for there to be a 50/50 chance of two of them having the same EQD value. On the other hand, if there were only 20 PLTs on each upgrade list, you'd only have a 6% chance of a collision so you'd only expect to see one every 16 or 17 flights, but it would definitely still happen from time to time (but would be the exception rather than the rule.
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.