EV = Probability X Payout = (1/(4.29 X 10^9)) X (5 X 10^8) = 0.11 cents per bet.

Assuming equivalence of payments and probability FTA.

EV cost with 10^7 possible entries: (1/(4.29 X 10^9)) X (5 X 10^8) X (10^7) = $1.1m

Ignoring secondary prizes and solvency costs.

I read some more details about the insurance policy here: http://www.latimes.com/business/la-fi-buffett-basketball-bet...

> Miller, the Duke professor, came up with his 1-in-1-billion probability through an equation that placed games into categories ranging from close games that could go either way to near locks. Based on his finding, Buffett would need to charge a premium of about $10 million to break even against his expected results, Miller said.

> "If I were Warren Buffett, anything over $10 million, I would probably do it," Miller said. "If $1 billion were going to ruin me, I wouldn't. But it's not going to ruin Warren Buffett."

> Buffett said his company is big enough to survive such a hit. "We've lost more money in a given event before," Buffett said. "Hurricane Katrina probably cost us $3 billion. "We will put more at risk in a given insurance transaction than anyone in the world. But we have more capital than anyone in the world."

> Berkshire Hathaway investors can take comfort in some news Buffett disclosed Tuesday. He said he would probably strike a deal — at significantly less than $1 billion — with anyone who gets deep into the tournament without missing a game.

> "If you get to the Final Four with a perfect bracket, I may buy you out of your position," Buffett said. "I'll make you an offer you can't refuse."

Buffett appears to be channelling Vito Corleone in that last statement right there: http://www.youtube.com/watch?v=SeldwfOwuL8

So assuming the new 1 in a 10^9 chance figure, we get:

EV cost: (1/(10^9)) X (5 X 10^8) X (10^7) = $5m

Now the previous time Buffett made this kind of a bet was here: http://en.wikipedia.org/wiki/Pepsi_Billion_Dollar_Sweepstake...

That had an EV cost of ~$1m as well (http://www.bloomberg.com/news/2014-01-21/buffett-makes-milli...), and he got paid a ~$10m premium from Pepsi for that risk.

So I'm guessing the same is true in this case. That is a 10x EV cost premium, with a range of ~$10m-$50m. I highly doubt that Quicken is willing to pay so much, so it'll be biased towards the lower end of the range. At the end of the day this is essentially a ~$10m-20m advertising project which uses free distribution through news/blogs/PR releases/forums/TV/radio/word of mouth/mind share, in addition to getting access to private consumer data when people sign up for the competition (email/address/name/age/etc).

Hopefully Quicken will have more luck and consumer buy in than Pepsi had in 2003 (http://www.psychologytoday.com/blog/the-decision-tree/201306...). I doubt it though. The more likely outcome here is that Buffett made himself a cool ~$10m-20m in one day for doing very little work, since he doesn't pay for any of the operational costs of the competition.

> Jay Farner, Quicken's president and marketing chief, said his company would benefit from the contest in two ways — news coverage and access to the email addresses of millions of potential customers. Anyone who enters the contest will have the option of receiving email offers from Quicken, he said.

Source: http://www.latimes.com/business/la-fi-buffett-basketball-bet...