Lottery/Powerball math question

[alfaniner]

All this talk of lottery reminded me that I have a ticket in my wallet that I haven't checked yet. Let's see.

(five numbers plus Powerball)
I had bought five sets of numbers. 5 times 6 numbers = 30 individual numbers. I think the field is 70 possible numbers. (1-70)

I did not match a single one in the entire batch.

I would think the chances of that (meaning my result) are really low, i.e. it should be easy to match at least one number in a 1-70 field by picking 30 numbers.

One of my early jobs was at a combination convenience store/ice cream parlor chain in Eastern upstate New York, and we sold an unusually large amount of lottery tickets. For the simple daily three number and four number drawings, the state limits the number of people who can bet on a particular number in a particular drawing. For numbers like 7-7-7, 1-2-3, or 1-2-3-4, people would usually have to bet a week in advance because large numbers of people would bet on those sorts of sequences and quickly hit the limit, then move on to playing them for the next day, and the day after that, and so on.

I don't see why there should be a limit. If the prize is equally distributed among all winners, the total payout would be the same. Or was that particular game a standard payout, say, $40 per win? Then I could see setting a limit.

 

[Armitage72]

I don't see why there should be a limit. If the prize is equally distributed among all winners, the total payout would be the same. Or was that particular game a standard payout, say, $40 per win? Then I could see setting a limit.

For the daily three and four number drawings, it was a flat payout. For the three number, $1 won $500.

 

[blutoski]

IMO this isn't a math question but a psychology question. The odds are random but human behavior is not necessarily random. Most people avoid sequences like that under the mistaken belief that it's somehow less likely than other combinations, however I don't find it surprising that there are at least some people attracted to it. Some may think "no one else would pick this" while others choose it because it's "easy" or "lucky".

Overall there are going to be combinations that people puck much more often than random chance would dictate and the winning numbers just hit one of them. 1, 2, 3, 4, 5 and Powerball 6 probabaly would have had even more winners.

And this is on topic for Skepticism and our JREF ancestry, in that magicians exploit our gravitation to specific numbers as a weak force technique.

Pick a 'random number' between 1 and 10.... most people pick 7. It's not 100% but it's something like 80%, and definitely more probable than 1 in 10, so the odds are in our favour if we go in ready for 7.

And there's some consistency within a culture. I seem to recall seeing published tables, showing most and least popular 'random' numbers in the West, and 47 kept coming up as the least popular in the 1..100 range, for example. Like, one in a million times.

 

[alfaniner]

For the daily three and four number drawings, it was a flat payout. For the three number, $1 won $500.

I remember the very first lottery draw in our state. It was a three-number setup. The digits, drawn in order, matched our area code. (Largest city in the state.) That certainly raised some eyebrows.

 

[Brainster]

All this talk of lottery reminded me that I have a ticket in my wallet that I haven't checked yet. Let's see.

(five numbers plus Powerball)
I had bought five sets of numbers. 5 times 6 numbers = 30 individual numbers. I think the field is 70 possible numbers. (1-70)

I did not match a single one in the entire batch.

I would think the chances of that (meaning my result) are really low, i.e. it should be easy to match at least one number in a 1-70 field by picking 30 numbers.

It's actually quite a bit higher than you might think. First there, are 69 regular ball #s and and 26 Powerball numbers, so it makes sense to consider the two events separately and the multiply the percentage chances together. First what are the odds that your 25 regular numbers won't match one of the 5 balls pulled? It's simply (44/69)*(43/68)*(42/67)*(41/66)*(40/65)=.097 or 9.7%. And the odds that the Powerball will not be match any of the ones one your tickets are just 21/26 or about 80.8%. So overall we would expect that you would come up blank on five Powerball tickets 7.8% of the time or about 1 in 13 times. Note that this assumes that your tickets all have discrete numbers on them--if you had any duplicate numbers (likely) the percentage chance would increase.