Why take the median? For me personally all I need is one year where I make a couple million bucks. What I really care about for my personal financial position is either the sum or mean, because that's what hits my bank account.
Some lotteries that accumulate when there are no winners have weeks with better-than-even odds. By this logic, you should wait until the odds are sufficiently in your favor and then dump your entire savings account into lotto tickets, for an immediate gain.
Of course, even if you can pick up a 20% gain in EV, that small chance you end up a billionaire won't save you from the 99.99..% of cases when you're eating cat food in retirement.
