One follow-up point from my previous post on ESPlanner: Prof. Kotlikoff also provided a brief and clear explanation about the value of waiting to begin Social Security.
To paraphrase, one should not think about Social Security from the perspective of a breakeven investment analysis for how long it will take for Social Security pay off. That missed the point of the insurance value which Social Security provides. Using the breakeven analysis, one would not buy any insurance. On average, insurance is never expected to pay off. Insurance companies need to make a profit and cover their expenses. But the reason insurance is valuable is that it pays off in the low probability states of the world when outcomes are bad.
People cannot rely on the average outcome for their personal situation: either things work out or they don't. With Social Security, you won't feel regret by delaying Social Security and then dying before collecting benefits, because you won't be around anyway. Regret comes when you live a long life and think about how your situation would have been improved through delay. By waiting from 62 to 70 to start benefits, your benefits will be 75% larger for the rest of your life. That is a valuable safe and real annuity based on an implicit real return of 2.9%. The premiums for that annuity are the 8 years of missed Social Security benefits between 62 and 70, but all in all it can be a pretty good deal and it protects your lifestyle in the event of living a particularly long life.