Also, some people might actually go with the annuity if they were given the option after actually winning. A lot of states (like Texas) make you pick an option at the time of purchasing the ticket and you can’t change it later. If you don’t specify the payment the default is the cash value option. How many people…

That’s incorrect. The annuity payments are guaranteed to go to the estate or transfer to a beneficiary. Of course 40% of that gets lost to estate taxes, but even so, it still get passed on.