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Why oh why is Sheldon Adelson supporting Mitt Romney's campaign? Well, casino magnate Adelson knows a thing or two about gambling. Supporting Mitt is a gamble, to be sure. But if it pays off, it pays off big.

Let's take a look at the numbers. According to the Center for American Progress, Adelson stands to gain $2 billion in tax cuts if Romney is elected. If estate taxes are eliminated, Adelson and his family could gain more than $11 billion. That's a pretty good pile of money.

Where do they get these figures?

The potential return on investment is 11,000 percent. Yeah, you read that right. But he could LOSE $100 million, too. How does he know whether or not it's a bet worth taking? He needs to know the expected value of the bet, and the probabilities required to make the bet pay off.

What's the Expected Value of this Bet?

Still, $100 million dollars is big bucks to lose, and here at Daily Kos we agree Romney's chances of winning are smaller every day. Right now, Nate Silver says the probability of a Romney win is about 19%.

We can calculate the expected value of this type of bet. (See this page for a primer on calculating expected outcomes.)

Generally, the expected value is equal to the sum of the probabilities of the outcomes times the value of the possible outcomes. Huh??

In an election, there are two possible outcomes for the candidate: WIN and LOSE. Each outcome can be assigned a probability. In this case for simplicity let's use a 20% probability of a Romney win and an 80% probability of a Romney loss. The probabilities must sum to 100%, and they do here.

Each outcome has a value. In this case, if Romney wins, Adelson will GAIN at least $2,000,000,000, less the $100,000,000 investment. If Romney loses, Adelson will lose $100,000,000.

Simplify this by subtraction:
$2,000,000,000 - $100,000,000 = $1,900,000,000 if Romney wins
-$100,000,000 if Romney loses

Then the expected value of the bet is the probability of the win times the value of the win, PLUS the probability of the loss times the value of the loss.
Expected Value = (1.9 billion)x20% + (-.1 billion)x80% = .3 billion, or $300 million.

In words, the expected value of Adelson's bet, given the currently assigned probabilities, is $300 million, certainly enough to justify the gamble. (It is substantially higher if we include the potential savings in estate taxes.)

What's the Minimum Probability of a Romney Win Needed to Make this Bet?

Romney is a walking train wreck, the worst candidate of a major party in my lifetime. Every single day he says or does something to degrade his chances of winning. Adelson must see this, but as a casino owner, he can calculate the odds needed to make his bet worthwhile.

Any expected value that is negative is too small to take the bet. So what is the minimum probability of a Romney win needed to justify this gamble? It's infinitesimally higher than the probability that gives an expected value of zero. Huh??

Okay, so if Adelson is content with an expected value of ZERO on his investment (not losing), we can calculate the probabilities that would make this true.

Call the probability of a win "P" and the probability of a loss "1-P". Remember the probabilities must sum to 100%, or 1. They do.

Expected Value = 0 = (1.9 billion)xP + (-.1 billion)x(1-P)

Solve for P.  (Remember how?)

P = .05, or 5%. In words, a probability of 5% gives an expected value of zero. Any probability OVER 5% gives Adelson an expected win. Romney only needs just over a 5% probability of winning for this to be a reasonable risk for Adelson, from an expected value standpoint. (The required probability of a win is substantially lower if we include the potential savings in estate taxes.)

What About Risk Aversion?

I was explaining this to Jim and he reasonably balked. The notion of potentially losing $100 million was too daunting, especially given the outlook for Romney's campaign. It's true, these calculations are done without including any adjustments for risk aversion. A lot of financial and economic calculations assume no risk aversion, even though we know it exists.

But here's the thing: the more money a person has, the lower level of risk aversion they tend to have. After all, the loss of a dollar is relatively less important the wealthier you are. Remember Romney's offered bet to Rick Perry?

"Rick, I'll tell you what -- $10,000 bucks, $10,000 bet."
That's a perfect example. The vast majority of us couldn't imagine making a bet like that. But Romney can. And wealthier-than-god Adelson can. Their risk aversion is less intense than ours is.

Sheldon Adelson stands to make a ton of money if this gamble pays off. The other wealthy backers, many of whose names we'll never know, are making "investments" using the same type of calculus, though their individual variables differ.

The opportunity for WEALTH to carry an election, any election, is higher now than it has been in decades. The Citizens United decision, voter disenfranchisement, and the perversion of the political process through ALEC are just pieces to the whole.

I won't gain financially the way these people will, and 99.9% of Americans won't, either. But collectively we can defeat the individuals who look at politics as a roll of the dice, rather than as a matter for conscience.

Thanks to Son in IA for pointing out this story and spurring my thinking on it. As an engineer, he understood the notion of expected values quickly. I hope I didn't run through it too fast for most readers.

8:30 AM PT: I will be away from my computer until about 1:30 CT. I'll respond to comments when I return. Thanks to everyone who stops by to read and comment.

12:29 PM PT: Thanks to Rescue Rangers for the spotlight on this!

Originally posted to Melanie in IA on Thu Sep 13, 2012 at 06:20 AM PDT.

Also republished by Community Spotlight.

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