## Poll

1 vote (12.5%) | |||

7 votes (87.5%) |

**8 members have voted**

So he says I will bet you straight up- $20 bucks that two or more people win. So basically I win $20 if no one or one person wins, he wins $20 if two or more people win. I tried to do a little statistical analysis to determine if this was a good bet. I offer the following and welcome any criticism because my probability skills are weak.

link to my google spreadsheet:

My Spreadsheet

I first looked at the last five mega million drawings to try to determine the avg. number of tickets bought in respect to the jackpot amount. I estimated the number of tickets won from the number of winning tickets per category - multiplied by the odds of winning. I then used a weighted average to aid in determining the actual number of tickets bought. The weighted average is the number of winning tickets divided by the sum of all winning tickets multiplied by the estimated number of winning tickets. I then sumed each of the weighted average to give me my final value.

I then took this number and divided by the jackpot prize for this week to give me a ratio.

I plotted all five ratios and used a polynomial trendline in the second order to generate the equation to estimate the amount of tickets that would be sold for the upcoming drawing.

I came up with 403,722,000, dividing that by the odds of winning the Mega Millions I come up with an estimated number of winners of 2.3. So no bet for me. Thoughts?

Thanks for all comments!

I addressed split jackpots in a recent Ask the Wizard, but it doesn't indicate how much jackpot size induces sales.

Quote:WizardI looked at the spreadsheet but couldn't follow how you got the 403,722,000 tickets will be sold. Can't we just do the jackpot growth divided by contribution per ticket? The odds of winning are 1 in 1 in 175,711,536. That would result in an expected 2.29764 winners. Using the Poisson distribution, the probability of 2 or more winners is 66.9%.

I addressed split jackpots in a recent Ask the Wizard, but it doesn't indicate how much jackpot size induces sales.

It is possible, (but unlikely) that less tickets will be sold (bad weather, system malfunction, player ruin, birds falling from the sky, zombie attack), reducing the chance of a split jackpot.

First lottoreport.com shows the jackpot grew from $242M to $355M, or by $113M.

According to Durango Bill you can roughly get the number of tickets sold by multiplying the jackpot growth by 3. So that would be 339M tickets sold.

The probability of winning is 1 in 175,711,536. So there should be 1.93 winners.

The probability of 0 is 14.53%.

The probability of 1 is 28.03%.

The probability of 2 or more is 57.44%.

Quote:WizardI have looked into this some more.

First lottoreport.com shows the jackpot grew from $242M to $355M, or by $113M.

According to Durango Bill you can roughly get the number of tickets sold by multiplying the jackpot growth by 3. So that would be 339M tickets sold.

The probability of winning is 1 in 175,711,536. So there should be 1.93 winners.

The probability of 0 is 14.53%.

The probability of 1 is 28.03%.

The probability of 2 or more is 57.44%.

Hmm, the Calfornia Mega Millions website states that 53.9 cents of every dollar goes to prizes. Here are some figures from the last 2 drawings:

Draw | 12/24 | 12/31 |
---|---|---|

Mega Prize | 200M | 242M |

Increase in Mega vs. prior draw | 32M | 42M |

Pct. Chng. | 19.05% | 21.00% |

Prizes Awarded | $2,445,053 | $3,763,734 |

Awards vs. Chg in Mega | 7.64% | 8.96% |

So assuming the trend holds, the expected payout for tonight's drawing is:

Draw | 12/24 | 12/31 | 1/4 |
---|---|---|---|

Mega Prize | 200M | 242M | 355M |

Increase in Mega vs. prior draw | 32M | 42M | 113M |

Pct. Chng. | 19.05% | 21.00% | 46.7% |

Prizes Awarded (assuming no Mega) | $2,445,053 | $3,763,734 | $10,170,000 |

Awards vs. Chg in Mega | 7.64% | 8.96% | 9% (assumption) |

$113M+$10.2M = $123.2M in prizes. If this is 53.9% of the new money, there were approximately 228.5M tickets sold since the last draw. Odds of hitting the Mega are 1 in 175,711,536, so it is possible that every combination has been sold.

Quote:pcket5sSo basically I win $20 if no one or one person wins, he wins $20 if two or more people win. I tried to do a little statistical analysis to determine if this was a good bet.

Looks like a bad bet. Just heard 2 people won. One in Idaho and the other in Washington. Sorry.