The (Ugly) Math of 50-50 Fundraisers

One of the readers of the Freakonomics blog asked a question about 50/50 fundraisers. If you are unfamiliar, these are fundraisers where you buy raffle tickets and the organization keeps 50% of the money raised and gives away the other 50% to the winner of the raffle. Freakonomics reader Melissa Belvadi writes:

This strikes me as an incredibly bad deal, but a bit complicated to explain why, as it contains 2 components:

  1. As a gamble: poor expected value. I am not sure how to calculate this, but from my experience in Las Vegas where slot machines boast being set to 97% return ratios, a gamle where 50% goes to the “house” seems unlikely to be a good EV.
  2. As a charitable donation: poor “program ratio” - at most, 50% of my donation will go to the “program” (charitable cause) - this is considered a very poor ratio in the philanthropic world where typically 60% is the bare minimum acceptable - the BBB requires 65%

I completely agree with the above analysis. I think that 50-50 raffles are not great gambling or philanthropic decisions but they are obviously popular for a reason. To understand why I wonder if it helps to think about it from the perspective of the purchaser.

A person who purchases a lotto or traditional raffle ticket certainly hopes to win, but I don’t think there is any expectation that they will win. People might not be great with statistics but they understand that the odds are stacked against them. So win they think about their future they face two scenarios: the rare chance they win and become wealthy; the likely scenario though is that they will lose and be out their money.

In a 50-50 raffle the two outcomes are changed. There is still the rare chance that they will win but now if they lose they’ve still done something good with that money so it softens the blow some.

Does your organization do a 50-50 raffle? Do you participate in them? Tell me why or why not.

Game Theory

I love game theory. I think it’s a fascinating and dynamic way to understand the world and human behavior. At its essence, game theory is about competitive interactions between people and groups. It can explain small things like who moves when two people are walking towards each other on the sidewalk (could be viewed as a game of chicken or cooperation), as well as big things like how countries interact during war.

Unlike traditional economic theory which tends to produce more stable and linear results, game theory treats human interactions more dynamically and with several outcomes (equilibrium). For a long time game theory remained in the world of mathematics (think John Nash in A Beautiful Mind) but it has broken out into the social sciences and is making its way into the boardroom, the break room, and the bedroom (?).

If you are facing a strategic interaction; how much to ask in a settlement offer, how to break into a new market, or how much to price a new product, game theory can help and there are an increasing number of resources aimed at opening up game theory to the general public.

Gamestorming is probably the least rigorous (and least true to actual game theory) but is great at showing how to bring games into the boardroom. The Art of Strategy is a wonderful introduction to traditional game theory that shows how it applies to every day life. The Predictioneer’s Game is actually written by a former professor’s father and tells his wonderful story of applying game theory to foreign policy and outwitting the CIA. If you want to learn from the godfather of game theory, read Roger Myerson’s Game Theory: Analysis of Conflict, but warning, there’s a lot of math.

I love games. I love thinking that life is a little bit, or a lot, like a game. If you’re like me pick up some of these books and you’ll begin to see games everywhere.

Voter Math: Popular Vote vs Electoral College

If you’re interested in political science and the nuances of how campaign money is spent in our current electoral college system and why people like Al Gore, who won the popular vote in 2000, lose the election, check out this great post, Would Al Gore Have Won in 200o Without the Electoral College?, over on the FiveThirtyEight blog on the NYTimes.

My favorite line? “The optimal strategy for winning the Electoral College, of course, is probably sub-optimal for maximizing one’s popular vote.”

Enjoy!