Going back to the question: How many drawn raffle numbers on average does it take to win a prize?
Keep in mind, this is one person's ticket winning a prize in a raffle of 1,000,000 tickets numbered 000000 to 999999 and all tickets are sold.
Yes, there may be others playing and as in any raffle, all the prizes are guaranteed to have a winner.
However, only one prize can be awarded to one ticket and that's what the question relates to.
In the original method of a raffle, sequential numbered tickets are sold as pairs of the same number.
The ticket is torn in half and the person buying the ticket keeps the coupon and the ticket with the same number is placed in a mixing bin, tumbler or drum.
After all the tickets are sold, the drum is closed and turned to randomize the tickets, the drum is opened and a ticket is drawn to determine a prize won.
Next, a the drum is closed, the drum is turned, the drum is opened and a ticket is drawn to determine the next prize won.
This continues until all the prizes are won; usually a fixed number of prizes that is far less than the total number of tickets sold.
But, we made this interesting in that we keep drawing tickets until we find how many drawn tickets does it take until one person's ticket wins.
As we shown in the example before:
Draw
|
Raffle #
|
1
|
991946
|
2
|
349117
|
3
|
941078
|
·
|
·
|
N
|
478605
|
What's the average N draws for one person's ticket to win a prize?
Nowadays, raffles are conducted with computer generated numbers.
But, that does not matter, because each number was selected in the same way.
First, 991946 is generated; second, 349117 is generated; third, 941078 is generated and so on.
Regardless if the numbers are pick in 1 minute by hand or 1 microsecond by computer, the essence of the raffle is still the same.
So, back to the question.
How many drawn raffle numbers on average does it take to win a prize?
500,000 drawn raffle numbers
Yep, the average is Five Hundred Thousand drawn raffle numbers.
As we said before, sometimes sooner, sometimes later, but on average it is 500,000 drawn raffle numbers.
The average actually is related to the person's number of tickets bought by this formula:
In our own MN Lottery 2019 raffle where 700,000 tickets were sold and a person buys a ticket, the average is 350,000 drawn raffle numbers.
Getting back to actual raffles.
An actual raffle only draws a limited set of numbers; in the case of the MN Lottery it was 12,322 drawn numbers.
As we can see, a person buying one ticket with the expectation of winning something gets cut short of the average number of draws needed win something.
Stopping at 12,322 raffle draws is far from the 350,000 raffle draw average.
We can understand why some people are having a second thought about winning in a raffle.
We can carry this further in a 1,000,000 ticket raffle.
You might say, what if you bought more tickets?
Well, it does affect the drawn raffle numbers count, but not in the way you'd think.
Remember, we're looking at one person's ticket purchases.
Below is a table of increasing tickets bought.
Tickets Bought
|
Average Drawn Raffle #s
|
1
|
500000.00
|
2
|
333333.33
|
3
|
250000.00
|
4
|
200000.00
|
5
|
166666.67
|
6
|
142857.14
|
7
|
125000.00
|
8
|
111111.11
|
9
|
100000.00
|
10
|
90909.09
|
100
|
9900.99
|
1000
|
999.00
|
10000
|
99.99
|
We can see buying more tickets drops the average, but some of these raffles are $10.00 or more per ticket.
If you buy more tickets, you win more stuff... yes. But, when you win, you won and that's all we were looking for, the win.