It is infinitely easier for someone (poor, relatively uneducated), to buy a lottery ticket than it is to buy stock. Most poor people would not have the $2000 minimum to start an TDAmeritrade account, or the knowledge to manipulate their accounts successfully, but have the few spare bucks at the gas station to buy a few lotto tickets. That is why.
Well, they are only perpetuating their own cycle if that is the case... I would wager if they starting saving those "few spare bucks" they could come up with initial deposit amounts pretty easily...
In many cases, you don't need $2000.