So you want a lot of money right? Let’s try to mathematize that by saying you want to maximize how much money you make. This is not a statement that can be used to compute decisions.

What if something gives you a one percent chance of getting a million dollars and someone else gives you a fifty percent chance of making a hundred thousand dollars? Should you always take the million dollar bet? If you want to maximize your money, do you mean that you want a slim chance of making as much money as possible? Or the highest expected value?

So what you have to do is you have to decide on specific goals and then you can make decisions based on those goals.

So here’s a normal goal: let’s say I want to be a millionaire in today’s dollars by the time I retire. Or let’s say I want $1.5 million by the time I retire. Okay, well, I can backwards calculate that considering I am 25 years old and I hope to retire at 65.

I can calculate an annuity based on conservative estimates of market or bond gains, take off some for inflation, and do the math:

Assume returns of 8%, and inflation of %3, which gives net gains of %5.

$\text{Future Value} = x * s_{\overline{40|.05}} = x*\frac{(1+.05)^{40} - 1}{.05} = x*\frac{6.03998871212}{.05} = 120.8x$

Set this equal to our desired amount

$\$1,500,000 = 120.8x => x = \$12,417$

So as long as I put $12,417 amount into my taxed advantage accounts every year, (a bit more math needed to split this up between Roth vs Trad 401k and IRA), then I should be able to be a millionaire by the time I retire.

Okay. What about if I want to be a ten millionaire by the time I retire? Well, based on my income level, I don’t really have a sure-fire way to get there. So now I have to give up some certainty in order to get to higher returns, or play the game of increasing my income. Some off the cuff ways of increasing returns might be to buy some property or whatever, or I can bet on crypto or on something else like a startup. Or I can work harder of course. The point is my chances of reaching this goal go down and/or my effort level goes up, but I can put together a strategy that might give me the best chance of getting to be a ten millionaire, even if that percentage chance is only like 20% or something.

But what about if I want to be a hundred millionaire? Well, at this point, you pretty much have to start a large company and you have to start putting a lot of time and resources into it and working very hard. Even that only gives you a slim chance because, you know, startups only win at two percent rate, and even smaller rate become 100M+ companies. So, your chances are going to be pretty low and it requires a lot of upfront work.

So you’re walking down the street and say you have a pretty certain chance of retiring comfortably and a 0% chance of retiring uber wealthy…for two to five dollars, you can now have a non-zero chance of being a hundred millionaire by the time when you retire, enabled by the lottery.

It’s not just about purchasing the hope of winning, its about purchasing the chance of winning.

It’s a bit of a funny thing because people say it doesn’t make sense to play the lottery because you know, the expected value is negative, right? Yes, there is a premium for that chance of having a dramatically different life. But compared to the costs of time and money for an alternative means to such wealth, its not bad.

The slogan from the Arizona lottery is “You can’t win if you don’t play”, and that’s a real mathematical statement that deserves some respect.

Thanks for reading.