Suppose you just turned age 25. You look around at the state of the world and realize it's a dumpster fire : Soaring inflation, completely dysfunctional government, war in Europe, climate going haywire, financial markets tanking, flying anywhere is a nightmare, COVID might be making a comeback, you just had a bad relationship break-up, AND, last, but not least, the U.S. President is doing "air handshakes" (caught at least twice on camera)!. Is he seeing a ghost? .

You've decided on a retirement strategy. You'll grind it out in the corporate world to get there, but your goal is to win the Powerball on or before your 65th birthday and then retire in style! You resolve to keep playing until you win, then quit (retire), buying Powerball Quickpick tickets each time. What's the chance you'll meet your goal one or before 65? Your chances depends on how many tickets you purchase, of course. How many tickets do you need to buy to be 1%, 5%, 10%, 50%, 90%, 95% and 99% confident of meeting your goal?

It turns out there is an easy formula for this. Mathematically it's called the Geometric Distribution. The important take-away is the following formula.

**Legend**: "P" (capital letter) is the probability of reaching the goal (win the lottery on or before your 65th birthday), "p" (lower case) is the probability of a single lottery ticket matching the winning combination, and "N" is the number of tickets required to achieve "P" probability of success. "P" and "p" are both decimals or fractions in the formula.

N = ln(1-P) / ln(1-p)

You can use any base for the logarithm that you want as long as the numerator and denominator are the same. I chose to show Natural Logarithm.

Now for a reality jolt. Here's what the numbers look like for the Powerball, for which p = 1 / 292201338. Assume 104 drawings per year, and you play every drawing for up to 40 years (stopping if you win before that).

P |
N |
Tickets Purchased / Drawing |
Distributed Annual Cost (assuming $2/ticket for 40 years) |

1% |
2936722 |
706 |
$146,836 |

5% |
14987969 |
3603 |
$749,398 |

10% |
30786484 |
7401 |
$1,539,324 |

50% |
202538535 |
48687 |
$10,126,927 |

90% |
672818451 |
161735 |
$33,640,923 |

95% |
875356986 |
210422 |
$43,767,849 |

99% |
1345636901 |
323470 |
$67,281,845 |

Do you have a "Plan B"?!!!