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Friday, June 22, 2007

Your Lottery Odds May be Better than You Think

Introduction
The Mega Millions, Powerball, and other"Megaball" type Lotteries inform you your odds of winning the Jackpot and other prizes. However, we at Lottery Power Picks believe that your odds of winning the 3, 4, and 5 of five white ball prizes are better than what has been provided. This article explains your odds, and why we believe your chances of winning these prizes are better than what is printed.

Mega Millions Example
The Mega Millions lottery consists of a pool of a set of 56 numbered white balls and a set of 46 megaballs. The odds of selecting the 5 winning white balls is 1 in 3,819,816 (using the Excel function =combin( 56, 5) ). Multiplying this number by the 46 megaballs gives us 175,711,536. When we compare both of these numbers to those indicated on the Mega Millions Game Instructions page, we find that we match the 175M chances of picking all six numbers, but differ substantially in the winning 5 white ball combinations: 3,819,816 (from Excel) vs 3,904,701 (MegaMillions).

Why the Discrepancy?
This discrepancy led us to ask ourselves the question: If the total odds of selecting 6 numbers is correct, and knowing that there are 46 megaballs, then by working backwards, the odds of selecting the 5 white balls should be 3,819,816 as calculated in excel. So, Why do we have a difference of 84,885 chances?

Answer
The explanation is that there are only 45 combinations that have the correct 5 winning white balls, and 1 that has the winning megaball as well. This means that the odds of getting all 5 numbers correct, but not the megaball is 3,819,816 times 1/45, which equals 3,904,701 as MegaMillions states. For correctness, it is necessary for MegaMillions to state these odds because the do not payout the $250,000 prize to the holder of the complete 6 number winning combination. In this case, they only payout the Jackpot prize, which is a minimum or $12 million. Thus, there is only 45 payouts, not 46.

Should we care?
The answer to this question depends on your point of view. The mathematical enthusiast would argue that the Mega Millions odds are correct and cannot be misinterpreted. From this strict viewpoint, they are correct.

However, the Lottery enthusiast plays against the odds, always hoping to win the big prize. Most players would be thrilled and pleased to have one of the 5 winning white ball combinations, netting them the 2nd prize of $250,000. From this vantage point, it is better to consider the Mega Millions lottery as 2 separate games: One in which they win the 2nd prize with 5 white balls; and the second where they win the Jackpot prize because they did have the megaball. By aiming for the 5 white ball prize of $250,000, their odds have improved by 84,885 and have become 1 in 3,819,816. Additionally, they also have a 1 in 46 chance of winning the entire jackpot. Think of this: with this strategy and these odds, you will always win the 2nd prize of $250K, plus, you could receive the additional Jackpot less $250,000.

Your Improved Odds and Expectations
As a Lottery Player, you now have the improved odds of winning the 3, 4, and 5 white ball combinations, as well as having a 1 in 46 chance of receiving the megaball bonus.

The following table summarizes the quoted odds, the Lottery Power Picks straight odds, and your improvement in the odds for the: Mega Millions, Powerball, California Super Lotto, Hot Lotto, Euro Millions, and Thunderball lotteries.


Match...MegaMillions......LPP......Improve.....Win...+.Bonus
5 White...3,904,701...3,819,816.....84,855
...250,000.+.JP-250K
4 White
......15,313......14,980........333.......150.+.9,850
3 White
.........306.........300..........6.........7.+.143

Match.....Powerball.......LPP......Improve.....Win...+.Bonus
5 White...3,563,609...3,478,761.....84,848
...200,000.+.JP-200K
4 White
......14,254......13,915........339.......100.+.9,900
3 White
.........290.........284..........6.........7.+.93

Match....SuperLotto.......LPP......Improve.....Win...+.Bonus
5 White...1,592,937...
1,533,939.....58,998....10,000.+.JP-10K
4 White
.......7,585.......7,304........281........50.+.450
3 White
.........185.........178..........7........40.+.46

Match.....Hot Lotto.......LPP......Improve.....Win...+.Bonus
White..... .607,743.....575,757.....31,986
.......Percentage
4 White
.......3,575..... .3,387........188.......Percentage
3 White
.........108.........103..........5.......Percentage

Match...EuroMillions.......LPP.....Improve.....Win..+.Bonus
5 White...3,632,160...1,118,760..1,513,400
......Percentage
4 White
......16,143.......9,417......6,726......Percentage
3 White
..,......367.........214........153......Percentage

Match....Thunderball.......LPP.....Improve.....Win...+.Bonus
5 White.....299,661....278,256......21,405
.....5,000.+.245K
4 White
.......2,067......1,919.........148.......100.+.4,900
3 White
..........74.........69...........5.........5.+.15


Conclusion
As a dedicated Lottery Player, you now have the improved odds of winning the 3, 4, and 5 white ball combinations, as well as having a 1 in a XX chance of receiving the megaball bonus.

We believe these lower combinatorial odds are important for you to know because they represent the actual number of different combinations available in the multi-white ball pool. In future articles, we will be using these numbers to explain which combinations have a higher or lower probability of occurring, so this is important to understand this concept.

If you think of this as winning the lower prize PLUS a chance to win a Bonus amount, you will remain optimistic while controlling your expectations of winning at the same time. Remember, in the large jackpot games, every little bit helps.

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1 comment:

  1. I recently came accross your blog and have been reading along. I thought I would leave my first comment. I dont know what to say except that I have enjoyed reading. Nice blog. I will keep visiting this blog very often.


    Margaret

    http://lotterymegamillions.net

    ReplyDelete

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