Expect to See Repeated Pick 3 Numbers after 37 Drawings (Lottery Trivia Answer 2010-07)

Last Week's Trivia Question #2010-07 was: 

To win the Pick 3 State lottery games, a player must correctly predict the winning number in the range of 000 to 999. If this number correctly matches the one drawn, the player wins approximately $250 on a $0.50 bet. So, if you like to play this game, you have probably wondered:

• How often would you expect to see numbers repeat?
• Or, in other words, how big would given a subset of daily results need to be in order to see duplicate numbers?

To answer these questions, we must remember that there are 1000 different numbers.

• Based entirely on an even distribution, the probability of any number being drawn is 1 in 1000.
• This means that any one given number should repeat once every 1000 drawings on the average.
• But, we all know that numbers repeat at various intervals.
• Thus, we refer back to the "Birthday Question" to determine how large of a sample is required to observe duplicate numbers.
• After solving this problem, we find that: in a set of approximately 37 drawings, we can be 50% confident that one of the numbers in that group will be a duplicate.
• And, if we examine a results set of 118 drawings, we can be 99.9% confident that one of those numbers will be repeated!

JL.....

After How Many Pick 3 Drawings Do You Expect To See Repeats? (Lottery Trivia Question 2010-07)

This week's Lottery Trivia Question is about Pick 3 numbers.

Our Trivia Question #2010-07 is: 

In the Pick 3 games, players are required to select a number between 000 and 999. If their number correctly matches the one drawn, the player wins.

• How often would you expect to see numbers repeat?
• Or, in other words, how big would given a subset of daily results need to be in order to see duplicate numbers?

Enter your answer by leaving a Comment to this post below. Leave your name, and if you have a website or blog, provide it's URL and name.

We will provide the correct answer next Monday, April 19th, and will post your name and a URL link back to your site.

JL.........

As Expected, Powerball Draws All Even White Balls

In an earlier post written on Monday, March 8th, 2010, titled All Even White Powerball Numbers Are Overdue, we indicated that the likihood of all Even White Powerball numbers being drawn was overdue. This prediction was based on the mathematical probability that this type of combination should occur approximately 1.23 times every six months.

In slightly more than 4 weeks after we wrote this, the winning Powerball numbers on Wednesday April 07th were:  04 36 40 44 52 Powerball 33 and Powerplay 2x.

Yes indeed, all even white numbers were drawn. Slightly more remarkable, each of the numbers are also divisible by 4.

While we could not have known exactly when this event would occur, we were confident that the Powerball Lottery drawings truly do follow the laws of probability.

Had players followed this advice and limited their combinations, they would have increased their probability of winning a $150 million jackpot prize after only 9 subsequent drawings.


JL............

Why Lottery Winners Should NOT Take Cash Option? (Lottery Trivia Answer 2010-06)

Last Week's Trivia Question #2010-06 was: 

When the lottery jackpots grow, many more players are tempted to try their luck in hopes of winning the huge jackpots. And typically, they ask the retail clerk who sells the lottery tickets for the "Cash" payout option which is much lower than the advertised jackpot. As we stand in line waiting to purchase our tickets, we often wonder:

• Why do most players take the Cash Option?, And,
• Why do the States want you to take the Cash?

While there is no "wrong" choice, we believe players are encouraged to accept the lower amounts, because:

• Most players do not understand what an Annuity means. Simply stated, an annuity is a continuous stream of annual cash payments. For Mega Millions, a player would get 26 equal payments. In Powerball, the player receives 30 payments which gradually grow in size.
• Today, the Powerball Annuity Jackpot is $125 million. A player who wins the jackpot would receive the first payment of about $2.23 million, and the last payment of $6.95 million.
• Whereas, the Cash Option payout is only $60 million, which is 48% of the Annuity jackpot.
• But players are afraid that if they die, they will lose the money.
• That's not true. The money will continue to be paid to their heirs until all is paid out.
• Next, players always think they can invest the cash option money in the stock market and make much more. But, the State lotteries are guaranteeing a return of $4.80% for the next 30 years. With interest rates so low, this is a great rate of return.
• Again, recent history has shown that fortunes were lost when the Stock Market tanked. If you're lucky enough to win the lottery, do you really want to lose it all?
• And lastly, we read story after story about Lottery winners who spent or invested all their money, and ended up with nothing.
• So to us, we think that all players should take the Annuity Option.
• The member states, however, do not want you to take the Annuity for two reasons: First, they will have to manage that money and make sure that you get your payments; and, Second, the are offering you almost $1 million less in Cash than you deserve. That means that they keep the money and help booster their revenues. 
• We think that this is a lot of money to lose. We'd rather have that money in our pockets rather than the State.
• So next time you buy a lottery ticket, tell them you: "Want the Annuity", and you won't be sorry. 

JL.....

Why Do States Want Lottery Winners to Take Cash? (Lottery Trivia Question 2010-06)

This week's Lottery Trivia Question is about Investing Lottery Winnings.

Our Trivia Question #2010-06 is: 

The lure of huge jackpots draws folks to play the lottery. But, most players opt to collect the Cash Prize rather than the Annuity. So we ask:

• Why do most players take the Cash Option?
• Why do the States want you to take the Cash?

Enter your answer by leaving a Comment to this post below. Leave your name, and if you have a website or blog, provide it's URL and name.

We will provide the correct answer next Monday, April 5th, and will post your name and a URL link back to your site.

Happy Easter!

JL.........

Optimal Lottery Mix of 3 Even and 2 Odd Balls is Best (Lottery Trivia Answer 2010-05)

Last Week's Trivia Question #2010-05 was: 

In Mega Millions and Powerball, particular patterns of numbers tend to occur more frequently during certain periods of time.

• So, after a review the past 3 month results, is it possible to identify particular mix of odd and even numbers that outpaced the expected probabilities?

To this, the Correct Answer is: Absolutely YES! Here's why:

• In Mega Millions, there are an equal amount of 28 odd and even white balls. But, in the last 3 months, 3-even and 2-odd number combinations have been drawn 11 out of 26 times, although only 8 would be expected.
• Similarily in Powerball, the odd balls have a slight 30 to 29 even ball advantage.  But, in the last 3 months, the 3-even and 2-odd number combinations have been drawn 12 out of 26 times, although only 8 would be expected.
• From this, we can conclude that presently, the 3-even and 2-odd white ball combinations have a clear advantage.
• And, from this, we find that, presently, there is a short term bias toward the even numbers!

JL.........

What is the Optimal Mix of Odd & Even Numbers? (Lottery Trivia Question 2010-05)

This week's Lottery Trivia Question is about an Optimal Distribution of Numbers.

Our Trivia Question #2010-05 is: 

Given so many numbers to pick from, particular patterns of numbers tend to occur more frequently during certain periods of time.

• Reviewing the past 3 month, what is the best mix of odd and even numbers that outpaced the expected probabilities?

Enter your answer by leaving a Comment to this post below. Leave your name, and if you have a website or blog, provide it's URL and name.

We will provide the correct answer next Monday, March 29th, and will post your name and a URL link back to your site.

Have Fun,

JL.........