Framing matters: Pick a number

I wonder if fewer people would buy lottery tickets if instead of picking a set of numbers, you just had to pick a single number between 1 and 175 million.

Picking a set of numbers seems to disguise the true odds. This is very good for the lottery folks, because if people could more easily decipher their true odds of winning, they may not buy as many chances.

One might argue that the set of numbers easily allows for prizes other than the jackpot, like matching 3 or 4 numbers for a lower prize amount.

That’s easily corrected with range prizes. For example, in the Powerball, if you match 5 numbers, you win $1 million. In my ‘Pick Your Number’ lottery, you would have to guess the winning number to within 17.

That means if you picked 10,134,210 in my lottery, you would win the $1 million prize if the winning number falls anywhere between 10,134,193 to 10,134,227.

In the Powerball, you win $4 if you pick the Powerball. To win that in my lottery, you only have to get within about 1.5 million of the winning number. So, with your pick of 10,134,210, you could win $4 if the lottery draws anywhere from about 8.6 million and 11.6 million, again out of 175 million.

The genius of the picking the set of numbers format in most lotteries is how it frames the game to mask the odds. Even when you tell folks their chance of winning is 1 in 175 million, they don’t easily translate that back to picking a set of numbers.

Disclosure: I do occasionally buy lottery tickets.

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Putting my money where my mouth is

Inspired by Bryan Caplan’s Bettor’s Oath, I offered to put my money where my mouth is in the comments of this Marginal Revolution post.

A group calling itself the Intelligence Advanced Research Projects Agency (IARPA) conducted a test project last year of inviting folks to make forecasts on major trends around the world. Their forecasts beat the forecast of a control group by 60%.

Now, they are skimming the best forecasters from the project to see if they can get better.

I doubt they can and said I would put money on it. Another commenter, “DK”, has taken me up on my offer. We have traded emails and established this bet:

I bet $20 that using the same weighting algorithm that the super-forecasters do not outperform the control group by 60% or more. If they outperform by less than 60% or do not outperform, I win. If they outperform by 60% or more, DK wins. If we find out the algorithm changed, either of us can use that to call off the bet.

DK offered $200 originally. I turned it down for these reasons:

I do realize that a) I could be wrong, b) the super forecasters could get lucky, c) Tetlock could change the weighting-algorithm without telling us to rig his results and/or d) the control group contains some crazy guesses (and may even be selected, unknowingly, to contain crazy guesses).

I offered $20 because I have a corollary to Caplan’s oath: Never bet more than you are willing to lose.

I’m not sure if my ‘weighting algorithm’ condition means anything or matters.

My memory is bad, so I’m counting on DK to update me when the second year of results are released. And, I’m rather confident that he or she will. I’d be willing to bet on that.