re: PowerBall just short of $ 1 billion, Mega Millions at $20 million

quote:

---

Lol. Are you legitimately taking that deal if you’re the one holding 200 mil and I’m selling the 85% chance to make 40 more?

---

There is a mathematical expected value (EV) and an individual's risk tolerance. You are addressing risk tolerance.

Mathematically speaking, the EV of that decision node is $204m. The alternative is worth $5m ($5m x 100%). Total EV is $209m. You SHOULD take the $204m option. It's mathematically worth 40x more.

If losing $204m leaves you broke, you probably won't take it.

If you're a fund worth billions, then you'd take that expected value for the 85% probability and negotiate off of it. As long as you don't pay > $203.99m, you'd take it.

If it's a one-time deal, you'd probably negotiate it down quite a bit from the EV of $204m because your single event could catch an outlier.

If it's a recurring opportunity - meaning if you lose this one you have another crack at it later - then you'd be willing to get closer to the $204m because the law of large numbers says the greater the number of iterations, the closer to the expected value the outcomes will cluster. Meaning over time, it's going to hit 85% of the time.

5.1 wins to cover 1 loss. 5.1 in 6 attempts is ... 85%. If you pay exactly the EV and do it enough times, you'll always break even. The value to you is the difference you negotiate ($204m less whatever you pay...that's what you're capturing over time).