On the other hand, if I don't buy a lottery ticket, I have no chance to waste my money on the lottery, but if I do buy a ticket, the odds of wasting money are infinitely higher.

Estimated monetary value might be a wiser metric to use :)

Going by the calculator, EMV of going from buying 0 tickets to 1 is -$1.85 for Mega Millions, same as going from n to n+1; n >= 0. The first ticket is the first one you lose with, statistically.

That's kind of how I look at it, in practice. I get the mathematical reality that buying lotto tickets is a financial waste. However, if I never buy a single ticket, there is a definite 0% chance I'll ever win the big prize. Whereas if I play at all, at least there's a chance, however remote, of a quite life-changing positive event happening. So, therefore, it makes sense to put a very small amount of totally throw-away income into big-prize lotto tickets, just so you're in the game at all.

Based on this kind of thinking, my personal rules are: never spend more than 0.1% of take-home pay per time-period buying tickets, and only buy big-prize lotto tickets that have potentially-life-changing payouts.

This is almost exactly how I think about it too - a good repeatable mental model is "infinite upside / near-zero downside".

These massively asymmetric choices occur elsewhere in life, e.g. "asking them out on a date"; "asking for a raise", and are good to look out for.

Dunno, seems wild to compare positive-but-still-unlikely ev things with straight up negative ev things like gambling.

There's a near-zero possibility that the next potato chip in the bag has been laced with cyanide. But if you never eat any potato chips, there's a definite 0% chance that you'll die of cyanide-laced potato chips.

This kind of thinking never holds up when it's a small chance of a horrible outcome.

How many potato chip killers have there been?

How many lottery winners?

More people have died from toxic food than won the jackpot.

> However, if I never buy a single ticket, there is a definite 0% chance I'll ever win the big prize.

I'm not sure about that. There is some chance of someone random buying a ticket and gifting it to you and then that ticket winning. Not a big chance. But it is not 0.

In the real world, there's a non-zero chance that someone purchased a ticket on your behalf without you knowing, so you're never quite at 0

Your chances were 0, you buy a ticket, and now your chances are x. Where x is not infinitely greater than 0, it's x greater than 0. Pretty sure your proposition implies that 2 tickets provide the same odds as one ticket (2 infinity vs 1 infinity).

I haven't gotten into the discrete math in many years. If you're right do you mind explaining please? I can intuit what you're getting at. 0 odds * inf < (odds with one ticket). Is that a decent description?

Odds for N tickets as odd(N):

odd(0) = 0

odd(1) = X, so odd(1) / odd(0) = +Inf increase in odds of winning vs 0

odd(2) = 2X, so odd(2) / odd(1) = 2x increase in odds of winning vs 1

This is nonsense if it's meant to be interpreted as anything but a joke, or as a way to maximize your own personal fun.

If you send me $20k of bitcoin and a UUID, I will run 'crypto.randomUUID()', and if I get the same UUID as you I'll send back $40k.

If you don't send me any money, you have 0% chance of winning, but if you do send me $20k, you have a mere 1 in 2^122 chance of winning, an infinite increase in your chance of winning, so surely it is rational to do so.

If you truly believe what you just wrote, I'll await my $20k.

I think the saying goes buying a lottery ticket only marginally increases your chance of winning.

I like that logic

But does that mean you only buy 1 lottery ever in life or one each lottery?

Just when the numbers get big :)