One huge die payout versus a million tiny ones

You may choose between two games. In the first, a die is rolled once and you get $1 million for each pip showing. In the second, a die is rolled one million times and you get $1 per pip on every roll. Which should a risk-averse person choose?

The million small rolls. Both have expected value $3.5 million. The single roll has a standard deviation of about $1.71 million, while the sum of a million independent rolls has standard deviation $\sqrt{10^6\cdot35/12}\approx\text{\char36}1{,}700$, so it is almost a sure $3.5 million. Same mean, far less risk.