[beambot]

Most of what you're describing is captured by the Kelly Criterion: it tells you the "optimal" fraction of your bankroll you should bet to maximize returns given the odds and EV. For a game with positive EV and 1 in 300M odds, you should be betting a very small fraction of your overall bankroll -- well below $2 for anyone not already in the 0.01% wealth bracket. So indeed, it would be irrational (suboptimal) to participate in the lottery unless you were already very wealthy.

Even beyond the Kelly Criteria, you could also tweak your EV based on the marginal utility of a dollar -- i.e. going from $0 in savings to $10M would have a massive impact on your quality of life, whereas 10x'ing from there ($100M) would provide marginal additional benefit comparatively. Thus, (ignoring Kelly) the "quality of life EV" for a $10M jackpot with 1 in 5M odds is vastly better than a $100M jackpot with 1 in 50M odds despite having the same EV.

https://en.wikipedia.org/wiki/Kelly_criterion

[jallen_dot_dev]

Nice, I had heard of the Kelly Criterion before but never thought to consider applying it to this situation. It's fantastic if the mathematically correct amount to wager (for any ordinary person) is less than $2 which rounds to 0 tickets which supports my intuition to not play.

Your second paragraph touches on another thought I had, which is why people think it's only worthwhile to play when the jackpot is $600M+. Any of us would be happy to win just $20M so why not play for every jackpot? Again it comes down to that misleading EV calculation, which I believe doesn't even matter if you are only going to buy 1 ticket only. Wagering based on the EV would only make sense if it was feasible to buy on the order of 100M tickets. Then you'd have a reasonable shot of winning each jackpot. And playing enough jackpots, you would come out ahead.