What do you get when you match up Pepsi, the WB, SCA Promotions, and Berkshire Hathaway? How about a monkey who could make someone a billionaire?

Through a somewhat complicated process of elimination, the thousand entrants will be pared down to a list of 10 finalists, who will then compete for a guaranteed $1 million prize.

Once the 10 finalists emerge, they will enter into successive, numbers-based Slot Gacor Hari Ini games of chance. Through a process of progressive elimination, the million-dollar winner will be picked.

That winner will hold a multi-digit number. In order for him to become a billionaire, the number must exactly match a number to be drawn at random on live TV.

“An unusually dexterous monkey” will do the picking, says executive producer Matti Leshem. “It’s the ultimate slap in the face to evolution: the fate of a billion dollars will be in the hands of a monkey.”

Link to the CNN article on it.

But what are the real odds of winning here — and more importantly, what is the expected value of a can of Pepsi in this promo? Pepsi is printing a billion numbers. In addition to the contest above, one million of those numbers will instantly win $15.

For a single can:

You have a 1,000,000/1,000,000,000=1/1,000 chance of winning $15 = 1.5 cents of E.V.

Pepsi thinks 15-20% of people will mail in their numbers to qualify for the TV show. From that, they’ll select 1,000 people. So you have about a 1,000/200,000,000=1/200,000 chance of making it onto the show. Let’s say only 80% of the 1,000 numbers chosen are from people who make it to the show, so assuming there’s no element of skill in the competition you have a 1/200,000*1/800=1/160,000,000 chance of making it to the big $1m prize. The article doesn’t say, but this is probably paid in a 30-year annuity ($33,333.33 per year), which gives it a present value of about $555k at 6% interest. So the expected value of the main million dollar prize = 0.35 cents

Once you make it to the big prize, it’s not as apparent what the odds are of this crazy monkey drawing your number for the one billion — the details are sparse in the article and online on how many numbers he draws from and how it will work.

The article does state that Berkshire Hathaway underwrote the billion dollar prize for seven figures. According to this excellent article on SCA Promotions and their big-bucks promotions, their profit margin on underwriting is typically well over 50%, but on straight-math and big-bucks promos their margin is much less. Let’s say Berkshire Hathaway took a 30% margin for a premium of $9m. So the “real” value of the bet is $6.3m, which for a $1b payoff represents a 1 in 159 shot (not too bad!). However, the real present value of $1b paid over 40 years at $25m a year is more like $417m assuming a 6% interest rate. That puts the chances at about 1/70. That’s close enough to 1/100 that I’m happy saying it’s 1/100, putting Berkshire’s margin at more like 54% which is probably reasonable. It could even be better than that, but I doubt that the premium cost $9m. I’d say more like $2-5m, in which case the chances are more likely to be slimmer than 1/100– maybe 1/200.

If these assumptions are correct, you’ll have a 1/160,000,000 shot of having a 1/100-1/200 shot of making a billion dollars over forty years. So your chances are 1/16,000,000,000 to 1/32,000,000,000, and the present value of that prize is $417m. That makes the expected value of the grand prize for a single can of Pepsi between 1.3 and 2.6 cents.

That makes the total value of this promotion, assuming Pepsi sells all their billion units of soda, and assuming you send in your can number, 3.15 to 4.45 cents per can.

Sound good? It’s not really that great. Coke’s recent Harry Potter Promo, for example, had a per-can E.V. of about 20 cents since you had a 1/24 chance of winning a $5 movie ticket (although the E.V. of the grand prize was just 0.11 cents).

But a billion dollar grand prize is just good TV.

Update 4/11/03: This article describes the determination of who wins from the final 10 players as “a game of chance and guts”. This could imply some element of calculated risk (aka skill), which means that for people who are good at analyzing risk situations, their chances could improve significantly at making it from the final 10 to the grand prize of $1m. If you were extremely good and the game was skill-based enough (and your opponents bad enough) that you had a 35% chance of winning a top 10 situation, your E.V. for the $1m prize increases to about 1.2 cents (from 0.35 cents) per can, and your E.V. for the $1b prize increases to 4.55-9.1 cents (from 1.3-2.6 cents) per can. So get practicing on your odds evaluation skills!

Update 4/11/03: Scott Leith of the Atlanta Journal-Constitution emailed me and pointed out that the $1b will not be a straight annuity, but will include a balloon payment of an unspecified amount. This makes a huge difference! It means basically they will screw you by making the balloon payment huge (thus greatly reducing the present value of the prize). I made a guess of $5m per year, with an $800m balloon payment after 40 years. This results in a present value of $161m for the $1b prize. This guess turns out to be pretty good based on past evidence; in 2000 SCA announced a $1b promo with a moving pay scale and a $620m balloon payment, and they gave it a present value of $170m.

Based on this, I think it very unlikely that Berkshire Hathaway’s premium is anywhere close to $9m. I think something like $2m is more like it, and still think the chances are likely somewhere around 1/100-1/200, which results in a margin of 15%-57.5% — a likely range. This also downgrades the E.V. of the grand billion dollar prize to 0.5-1 cent per can with no skill, and 1.9-3.7 cents per can with the 35% skill mentioned above.