maybe pennies become more valuable the less you have, which would interrupt the cycle?
Under the conditions of this scenario and some simplifying assumptions (such as your marginal utility function depending only on how much money you have in each outcome), then they mathematically must become more valuable somewhere between spending $0.01 and spending $1.
Without the simplifying assumptions, you can get counterexamples like someone who gets a bit of a thrill from buying lottery tickets, and who legitimately does attain higher utility from buying 100 tickets for $1 than one big ticket.
I just thought I’d also comment on this:
Under the conditions of this scenario and some simplifying assumptions (such as your marginal utility function depending only on how much money you have in each outcome), then they mathematically must become more valuable somewhere between spending $0.01 and spending $1.
Without the simplifying assumptions, you can get counterexamples like someone who gets a bit of a thrill from buying lottery tickets, and who legitimately does attain higher utility from buying 100 tickets for $1 than one big ticket.