A mega sena (popular lottery ticket in Brazil) costs five reals if you fill it with six numbers. So I’d certainly pick the 5 reals bill, as the expected value per real is always smaller.
The picture changes if the ticket was filled with more numbers; if you hit any six then you get the jackpot, and it’s accordingly more expensive (seven numbers for R$35,00; eight for R$140,00). For those I’d need to do the maths, but there are complicating factors:
if multiple people hit the jackpot, the prize gets split
there’s a secondary prize if you hit five numbers, and a tertiary one if you hit four
the jackpot varies quite a bit from one draw to another, as it accumulates if nobody hit it in the previous draw
To simplify it: let’s say that only the primary prize counts, it’s around 30 million reals (typical value), and that your odds are one in 50 million. Then the expected value becomes:
with 6 numbers: R$30M/50M = R$0,60
with 7 numbers: 7*(R$0,60) = R$4,20
with 8 numbers: 8*(R$4,20) = R$33,60
The five reals bill is still more valuable than a mega sena ticket with seven numbers, even if it costs R$35. But if it was eight, I’d pick the ticket.
A mega sena (popular lottery ticket in Brazil) costs five reals if you fill it with six numbers. So I’d certainly pick the 5 reals bill, as the expected value per real is always smaller.
The picture changes if the ticket was filled with more numbers; if you hit any six then you get the jackpot, and it’s accordingly more expensive (seven numbers for R$35,00; eight for R$140,00). For those I’d need to do the maths, but there are complicating factors:
To simplify it: let’s say that only the primary prize counts, it’s around 30 million reals (typical value), and that your odds are one in 50 million. Then the expected value becomes:
The five reals bill is still more valuable than a mega sena ticket with seven numbers, even if it costs R$35. But if it was eight, I’d pick the ticket.