An example household in the United States
A 66-year-old in Ohio with $940,000 saved, spending $70,000 a year to age 92, with investments earning 2% a year above inflation. The two results below differ only in which account each year's money comes out of, how much to convert to the Roth and when, and the age Social Security starts.
The usual order is the rule of thumb you have probably read: take the required minimum distribution, spend the brokerage account first, then the traditional IRA or 401(k), then cash, keep the Roth for last, and claim Social Security at 67. On this household it leaves $137,960 less than the plan RetOpt found. Your result will differ.
Why the tax part is hard
Most retirement calculators apply an average tax rate to a projection. An average misses the income levels where one more dollar costs far more than the rate suggests. Across one band of income, every extra dollar also makes up to 85 cents of your Social Security taxable, so the rate you pay on that dollar is far above your bracket. And one dollar over a Medicare threshold raises your premiums for a whole year, two years later.
So RetOpt works out the actual tax return, every year, for your household: the federal return, your state's and your city's or county's where they levy one, the deductions you qualify for, the thresholds you cross. Then it searches for the combination of choices that leaves the most after that tax, including when to claim Social Security, for every year of your plan: your working years as well as the years you spend. How it works has the longer version.