OT: Game Theory/Statistics

[MrToxin]

I think I may have heard of it, but that's a bit simplistic to be an interesting game.

One of two things would happen: you would put ten in each box and break even every game, or put 20 in five boxes each and break even in every game.

[geoschmo]

It's simple rules, but the strategy comes in trying to anticipate your opponents moves. If you think he's the type to put ten in each box, then you can put 11 in 9 boxes and 1 in 1 box and win 9 out of 10. But there is no perfect strategy because a style that will beat one type of player might lose to another.

The discussion I read was more from a theoretical game science point of view than an "This is fun, let's play" perspective anyway. The game had a particular name and was used in discussing classifying other games. As in "This game is a "blank-type" game."

[MrToxin]

Ah, k. I never worry too much about the names of the games, just the statistics and whatever.

But, yeah...the problem comes from the fact that anybody that knows probability and game theory is going to, eventually, play the guaranteed draw instead of the possible win. Either that or a jerk that nobody will want to play with any more.

I understand the theory behind the game but, without randomness or a sense of what your opponent is doing, "safe" is better than "uncertain."

Of course, I'm probably over analyzing things, as I am often caught doing.

[geoschmo]

I think you aren't thinking it completely through actually. You can't really play to a draw in the way that you suggest. Putting ten in each box would only be a draw if your opponent also put ten in each box. And as I suggested before if you think your opponent likely to do that you could easily defeat them.

[capnq]

MrToxin said: anybody that knows probability and game theory is going to, eventually, play the guaranteed draw instead of the possible win.

People who know probability are a small minority, and game theorists are even rarer.

I'm not convinced that there is a guaranteed draw, but then I managed to fail three different probstat courses in college.

[Glyn]

Geoschmo - interesting little game. I don't know the name. Also, I don't think there is a guaranteed draw. Two really good players might get to the point where they are winning half the game and losing half the games.

[Suicide Junkie]

capnq said:

People who know probability are a small minority, and game theorists are even rarer.

I'm not convinced that there is a guaranteed draw, but then I managed to fail three different probstat courses in college.

There is quite a simple way to show that there is no guaranteed draw.

Put all your tokens down, and pretend I get lucky.

If your biggest pile of tokens is less than 9, I could have put 10 in every box and win 10 to zero.
If your biggest pile of tokens is 9 or more, I could have used the same distribution of tokens as you, except for zero against your biggest box, and +1 against all the other boxes. Meaning I win 9 to 1.

Therefore, no matter how many tokens your largest pile has, there is a possibility of me winning.

[geoschmo]

Suicide Junkie said:
There is quite a simple way to show that there is no guaranteed draw.

Put all your tokens down, and pretend I get lucky.

If your biggest pile of tokens is less than 9, I could have put 10 in every box and win 10 to zero.
If your biggest pile of tokens is 9 or more, I could have used the same distribution of tokens as you, except for zero against your biggest box, and +1 against all the other boxes. Meaning I win 9 to 1.

Therefore, no matter how many tokens your largest pile has, there is a possibility of me winning.

While I agree with your conclusion there are some problems with how you got there. First of all, each player has an 100 tokens and there are ten boxes. Simple division should show you the lowest possible number you can have for your biggest pile is 10, not 9. And that's if yo udivide them evenly. If any pile has less then ten then at least one other pile must have more than ten.

Secondly, each player has an equal numebr of tokens, so it's also impossible to outscore an opponent 10 to zip. The highest possible winning score would be 9 boxes to 1.

Geoschmo

[Suicide Junkie]

It is true that you couldn't have a maximum stack smaller than 10 unless you did not use all your tokens.

However, that is irrelevant to the proof.
The point being that if your maximum stack is any natural number at all, a random opponent will sometimes beat you no matter what you do.

In fact, if you allow a negative number of tokens in a box, it still works.