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        Arimaa >> Events >> Prediction contest anomoly
        
(Message started by: Fritzlein on Aug 13^th, 2005, 9:23pm)

Title: Prediction contest anomoly
Post by Fritzlein on Aug 13^th, 2005, 9:23pm

To pass the time, I was doing some calculations about the prediction contest for the upcoming World Championship tournament (Can you tell I'm eager for it to start?), and I noticed something strange.

The "how sure are you?" part of the prediction functioned just as I expected: the highest average points gleaned comes from predicting the true percentage of wins. For example, if someone is going to win 3 of 4 games, but you don't know which 3, your best bet is 3/4 = 75% on each game. That gets you 75 + 75 + 75 - 125 = 100 total points net. If you instead predict 100% on each game you get 100 + 100 + 100 - 300 = 0 total points net.

Now I naturally expected the game length prediction to work just the same. For example, suppose you know that someone will win in 30 moves one game and 60 moves the other, but you don't know which is which. My thought would be to guess 45 moves for each game. But it turns out that only gets you 100*(30/45 + 45/60) = 142 points, but guessing 30 both times or 60 both times gets you 100*(30/30 + 30/60) = 100*(30/60 + 60/60) = 150 points.

In fact, if you are going to guess the same number twice, any number between 30 and 60 does worse than the the endpoints, and the worst of the intermediates is the geometric mean!

I guess the lesson is that for the confidence bets it pays to hedge, but for the number of moves you might as well try to nail it. :-)

Title: Re: Prediction contest anomoly
Post by Janzert on Aug 14^th, 2005, 3:05am

http://www.arimaa.com/arimaa/wc/2005/predict/

It's a contest Omar setup that let's people try and make predictions about the championship tournament. The above link gives the details about the scoring as well as the results of last years contest.

Janzert