The thesis - you do better in the market than holding cash - is a strong one. But the premise - that the only source of information you have available is the current real time... I'm guessing DOW Jones Index? it's deeply flawed.
Also, that you only have two years of investment time. And you start with $10k but never have more income to invest.
Where's p/e or p/b values? Where's dividend yields or debt to equity? Is there any other useful information to trade on - like Fed Interest Rate changes or technological breakthroughs or government spending policy?
You don't have to simply throw your money at the market blindly and you aren't forced to invest exclusively against a small basket of blue chip industrial firms.
You might also consider time periods prior to the bottom of the market in '29. Adjust your boundaries back a century - 1829 to 1929 - and the long string of depressions plus a civil war give you much better odds against the couch.