|Posted: May 20, 2013, 1:16 am - IP Logged|
What are the chances that the winning set will be contained in the remainder of unsold
Billion dollar territory would be insane!
Someone once provided a breakdown I believe even Todd remarked on....it described
just how the quick pick pool might be handled.
Does anyone remember that thread comment, poster or have a link?
Any chance you might be referring to a post I made about how probability results in duplicate combinations? I'm not going to dig up the one Todd commented on, but here's the short and simple version. After they've sold 1% of the combinations you should expect that 1 out of every 100 tickets with random combinations will be duplicates from the first 1%. When 2% of combinations have been sold 2 out of every 100 tickets with random combinations should be duplicates from the first 2%. And so on.
For modest jackpots the number of duplicates from random selections is small, but for really big jackpots with very large numbers of tickets sold the effect becomes significant. When 50% of combinations have already been played selling another 10 million tickets will only use about 5 million of the unused combinations. If 75% have already been used selling another 10 million tickets will only use about 2.5 million. That makes it virtually impossible to sell all combinations and literally have 0% chance of a rollover. FWIW, a rollover with an increase of $400 million to give us the first billion dollar jackpot would still have had about a 10% chance of rolling to an even crazier amount.
Lottoreport says that just over 232 million tickets were sold. For an increase from 350 to 590.5 million I'd figure it was a bit over 235 million, but the last drawing may have topped out a bit over 350. Either way, if all combinations had been selected randomly slightly less than 75% of combinations should have been in play. Of course the actual results won't perfectly match what probability suggests, but with 175 million combinations a significant departure is very unlikely.
Players making non-random selections increases the number of duplicates, and lowers the percentage of combinations in play, because they pick from subsets of all possible combinations.