There is a crucial difference between the lottery and startup investments. Presumably the latter have positive expected payout, whereas the lottery has negative expected payout. If the $5 makes zero difference to your life then the expected payout of $3 makes even less than zero difference to you life, so it's still not rational to play the lottery. Certainly there are contrived circumstances when it's rational to play the lottery, such as you have $5 in your bank account but you need $500,000 for a medical operation otherwise you die, but for most people that does not apply.