How does the Powerball Quick Pick mechanism assign ‘picks’? Does each terminal independently create a series of random picks? And if so, how random is it, truly?
(I seem to remember from Statistics 101 that ‘random’ can mean different things.)
Is there any attempt to prevent duplicate quick picks across the system? (obviously impossible if enough picks are made)
I would hope that the picks are completely random, but I noticed that out of the 6 quick pick tickets (5 picks each) I had for the big one last week, on three tickets the powerball number was repeated three times (i.e., 8 22 22 17 22; 14 11 14 14 6; 9 9 17 24 9), and on two tickets it was repeated twice. I can see it happening (hell, I’m playing a game with longer odds than that), but makes me wonder.
I’m curious if quick picks give you totally random numbers or combinations not yet chosen. Considering the volume involved I can’t see how they can absolutely choose unused combinations since some may still be processing as your number combinations are selected.
As I said in another thread, the chance of a Powerball repeating on a five-game ticket is about 33% and jumps to about 50% at the sixth game. Think of it as a variation on the birthday problem. Having three of the five powerballs match is a bit of a longer shot. I haven’t done the math for the odds of the rest of the ticket, but I would expect to see multiple repeated numbers. You have 25 non-powerball numbers on a ticket of 5, chosen from a pool of 69.
I have no reason to think it’s not randomized.
I am sure that each number is chosen randomly without knowing other ticket choices. To do otherwise is a complex problem that delivers no benefit to the powerball organization.
You should remember that true randomization has long been a bit of a bugaboo in computer science. There is more than one method and I don’t think the lottery people have advertised exactly what methods they use. I think it’s safe to say it’s as random as possible, thus they don’t worry about whether numbers are repeated at different machines. That would require massively larger amount of communication between terminals for no good reason.
It’s possible that there’s no one answer. The various states that participate in Powerball may have their own methods for selecting Quickpick numbers.
It doesn’t matter if the randomizer issued two tickets with the same number. If it did matter, sales would have to stop after all 292-million combinations are exhausted.
It took several hours after the drawing to determine how many winners (if any) there were. So that must imply it takes a long time to search the ticket data bases. It would be impossible to search whether a given combination of numbers has been used each time a quick pick ticket was sold.
This is speculation: But I assume the problem is that each state’s lottery commission sells tickets separately and there is some delay in getting the data downloaded to the Powerball headquarters from each state.
Not to mention it would be completely illegal as it would hardly fit any reasonable definition of ‘random’.
Why would that be illegal?
I don’t know about the US Powerball, but the UK Lotto “Lucky Dip” random numbers are generated as apseudo random number where the seed number is based on the terminal number and the time/date. http://lottery.merseyworld.com/Info/FAQ_tickets.html
Here is a document about the randomness of the EuroMillions lottery
If you want more details on exactly how random the numbers are and how they are generated, Elements of Simulation is a rather heavy going read.
Well, just whipping up a quick script, it seems, on average (on one million trials), a ticket with five games on them will have non-Powerball numbers repeat, on average, just over 3 times (3.16). That is to say, on average, just over 3 numbers will have at least duplicates on the ticket. (I haven’t bothered to check triplicates or more independently.)
As for the Powerball repeating, my Monte Carlo simulation appears to show that my math was correct in saying about a third of the time, showing me that having at least one duplicate on a 5-game Powerball ticket happens about 37% of the time (I originally said “33%”, but that was going by my memory of doing the math and it being somewhere around a third, so I actually slightly understated the probability), and it jumps to about 54% on the 6th game.
Here’s the distribution of ‘poker hands’ made by using five powerballs. (i.e. choosing five from 26 with replacement)
Five of a kind 0.00022%
Four of a kind 0.02735%
Full house 0.05471%
Three of a kind 1.31298%
Two pair 1.96947%
Pair 30.19852%
High Card 66.43675%
Here are the exact counts…
Five of a kind 26 out of 11,881,376
Four of a kind 3,250 out of 11,881,376
Full house 6,500 out of 11,881,376
Three of a kind 156,000 out of 11,881,376
Two pair 234,000 out of 11,881,376
Pair 3,588,000 out of 11,881,376
High Card 7,893,600 out of 11,881,376
Well of course IANAL, but in terms of lottery gambling there’s a specific definition of what constitutes ‘random numbers’. The winning numbers must be selected strictly this way and so must so-called machine-selected ‘Quick Pick’ tickets. Although the daily numbers and the bi-weekly big jackpot numbers are picked via physical, ping pong ball machines, the stuff like Quick Draw (keno) that’s played every four minutes everyday are selected electronically (as are all game’s ‘Quick Pick’ tickets). But they still cannot be ‘manipulated’ in even the slightest way or the game is essentially ‘fixed’.
I’ve had arguments with gamblers who insist that the keno game numbers are manipulated a little based on time of day, day of the week, numbers played etc. and I just laugh in their face. Unless this manipulation was explicitly declared on the game play tickets (which it is not) it would constitute deliberate fraud and be totally illegal.
Cool.
I ran my simulation again and got 33.5% for “at least one duplicate” instead of 37%, so I wonder if I transposed a number when reporting it before. So my result aligns with yours, but yours is more thorough, taking into account all the possible combinations, not just “duplicates or more” as mine. So “three of a kind” is about a 1 in 77 shot. Now we know. 
While these rules might apply to casinos in Nevada (and possibly other states), do you have any reason to believe that state-run lotteries are subject to the same laws?
According to my math, you need to buy 628 million random tickets to cover 90% of the numbers:
Logbase(x-1)/x where x = the exact count of Powerball possibilities.
So that’s almost 3 times the number of combinations just to get at least one of 90% of the numbers.
Not a massive amount of data ,
The algorithm for doing the check with little data is not too hard
generate random numbers
query how many tickets have been sold with that set of numbers
if > 0, query threshold for allowed duplication (the server runs its own count to bump this up to 2 , then 3, then 4…etc)
If the ticket is above the threshold for number of go back to start
(Could add the endless loop breaker test… eg if the 10th set of random number has been generated, just it … .)
Go ahead with these numbers… store ticket, print ticket, charger customer etc
So it would merely very often be one sql query, the count of number of tickets sold with that set of numbers. The worst case is the loop break number, eg 9 tickets, but that occurs one in a billion tickets sold.