Now, what do we do?
- It was not my fault.
- I agree, but you were still late for the Go tournament!
- I know. That is why I could only play 3 instead of 5 games.
- You won 2 of the games. Sarah won 3 of her 5 games.
- Really! She has improved!
- So, what is best, 2 of 3 or 3 of 5?
- Why don’t you ask your readers?
- Good idea!
- You may like to add that a game of Go can not end in a draw.
- How come?
- We use a komi of 5.5.
- I don’t know what that means, but I will take your word for it.
Let a = games won and b = games played.
Is (2,3) better than (3,5)?
If the function used is a/b the answer is ‘yes’ since 2/3 = .67 and 3/5 is .6.
However if the function is a*a/b the answer is ‘no’ since 2*2/3 = 1.3 and 3*3/5 = 1.8.
To experiment with various functions there is a box below where you can enter the function before you press the Go button. Enter “a/b” (without the quotes) and press Go. All possible pairs of (a,b) with a less than six get their score calculated.
Now, edit the formula to a*a/b, and see what happens.
You can use more exciting formulas for a and b, like “Math.min(a,b)”, “a*Math.random()”. See Math functions in javascript for available functions. I have added the combin(a,b) function, so you could enter things like “combin(b,a)”.
So, the question is, is (2,3) better than (3,5)?
December 10th, 2007 at 12:40 am
Which person eats more pizza? The one who eats 2 of 3 pieces or the one who eats 3 of 5?
Depends on how you measure it, right?
…No it doesn’t. By definition, this is a simple division problem.
a/b is the only valid way to measure this problem so 2/3=.667 is better. 2/3 is the largest possible value in such a set because for a/b as b approaches ? and a is just enough to “win”, the result approaches .500.
December 10th, 2007 at 12:42 am
The last paragraph was supposed to have an infinity sign in it but this apparently doesn’t work on all OS platforms. It looked great on my computer so I did not catch it before submitting. That “?” is infinity. Sorry.
December 10th, 2007 at 6:52 am
As Michael so perspicaciously pointed out, a normal human being (and i use the term in its loosest sense) would figure 2/3 is marginally better than 3/5.
However, in my twisted universe, things are not as simple as that when it comes to gaming. Anything else, yeah just do straight division and be done with it. But gaming is serious business, dammit!
Consider a player’s gamesmanship. If you play 5 games, then you have a chance at losing 5 games. If you’re playing for a prize (say a nice cut of Kobe beef for the winner), then the steaks are considerably higher if you opt to play more games, since you have a greater chance of losing.
Also, if 5 games were indeed played in the tourney, then the “you” mentioned in the post only played 3 of those 5 (giving his/her opponent a walkover in the 2 games that he/she was late for), thus the actual win ratio is 2/5, not 2/3. At least, that’s how tourneys work.
Go Sarah Go!
December 10th, 2007 at 9:33 am
In a comment you can get the ∞ sign by typing
& # 8 7 3 4 ;
without the spaces between the characters. More.
December 11th, 2007 at 3:41 pm
It depends on what you mean by the question “what is best?” While the person winning 2 of 3 games has won a higher percentage of games, it does not indicate that they are the stronger player. It is more likely for a weaker player to win 2 of 3 games, than for them to win 3 of 5. Over longer tournaments, the person with greater skill (e.g. greater likelihood of winning an individual game) is increasingly likely to win.
So, I would congratulate Sarah, as it is more likely that she is the better player.