Fritzlein
Forum Guru
Arimaa player #706
Gender: 
Posts: 5928
|
 |
Prediction contest anomoly
« on: Aug 13th, 2005, 9:23pm » |
 Quote  Modify
|
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. 
|
Home
Help
Search
Members
Login
Register
Reply
Notify of replies
Send Topic
Print
Author
IP Logged