This question is asked at a time when the Powerball jackpot is at a record high and in the news a lot.
Big jackpot games advertise their jackpot in terms of the amount that would be paid out in total if the winner chose an annuity option. If the winner chooses a lump-sum-cash option, the amount used to be about half the advertised jackpot, but now seems to be closer to the advertised jackpot (e.g. the ad is now $1.3B / $806M cash). Is there a predictable mathematical relationship between these two numbers? If so, what is it?
If the same answer applies to other big jackpot games, please feel free to note that in your answer.
Also, I realize that both numbers are estimates and that the actual value depends on ticket sales volume, but they are both published and likely to be related by some formula.