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A few of topics to cover here to explain it all: 1. Lottery Annuities, 2. Taxation 3. Wealth based Tax Avoidance.

For a lottery grand prize, the actual payout of the total is done via a multiple (30 in this case) payment yearly annuity, usually one that increases in size by a fixed amount (5% for this), where the total face value of the payments equals the winnings. If the winner took the annuity payout, they'd get like $25M today and more every year for 29 more years until they got about $100M, which would equal the jackpot. Alternatively, the lottery offers a "lump sum" payment, based on the value of the annuity (basically what it would cost today for someone to buy that stream of payments), which will be like half of the jackpot face value due to how compound interest works.

For taxes, any lottery payment is income and will be taxed accordingly by relevant entities, this will further reduce the take home amount by another 40%-60%.

For billionaires, they have wealth in the form of investment in the billions, not typically income. There are lots of loopholes here due to tax code complexity, but the 2 common examples are: long term investment tax and loans. If you've held any stock for at least a year, you only need to pay a reduced tax amount (this exists to incentivize stable participation in the stock market). Money you received from a loan is not income and is not taxed, lenders will allow you to secure your loan with investment holdings. There might be some additional trickery related to the cost basis used for payments of stock as compensation, I'm not looking into it. Basically, you can combine these into a process where you make large purchases or even day to day based on money from loans, and only pay those off using long-term investments, paying less income tax on your profit from them, which effectively reduces your tax burden. With massive holdings, you can turbo charge this, into what is essentially a ponzi scheme of loans, assuming interest on your investments is better than your loans (which will be lower because of your low risk to default).

Say you have $1B in mixed assets ($700M in long-term assets, $150M in each of short-term assets and cash), you want to buy a $100M house. You basically have 4 choices. Choice 1, pay with cash, you already paid taxes on it at whatever rate you did, but now it can't earn you money by being invested. Choice 2, sell short-term holdings, you'll pay taxes on your profits for this year as ordinary income, it also cannot earn more interest. Choice 3, sell long-term holdings, you pay reduced taxes on your profits for this year, it cannot earn more interest. Choice 4, purchase using a loan secured by your stock, you pay no taxes, you can continue to invest all your money which will earn more than the interest payments will cost on the loan. 4b, you take out loans to pay for your other loans, it's basically always more profitable to keep your money invested and you never pay full tax on investment income if you need to use it.

Say you earn 7% interest in the stock market and loans charge 3.5% interest, a loan to buy the house, you take out 2 lines of credit (loans), you use the lines of credit to pay for the mortgage payments and each line of credit to make minimum payments on the other, and your investments appreciate. Averaged out, you "earn" 7M from your investments you didn't sell, and accrue only about 3.5M or so additional debt, and pay no taxes on any of it. Each year, this repeats with larger numbers and profit growing faster than debt, you bought a house, you actually paid nothing, people will keep giving you loans so long as you keep having much more holdings than debt, ad infinum. This works until the stock market cracks in half and you earn less interest than debt accrued, but even then you just need to sell enough stock to max minimum payments, and only pay lower taxes on the profits until the market turns around. That's more or less the extreme example.