## an argument about a logic question

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I've had an argument with someone and I would like to know for sure if I'm right. I don't know if you have heard of the board game "Catan", it's not really important. Well, long story short, at the start of the game, when you place the resources - I said that if you plant the resources in a random order - throw them around the table then put them in place, while faced down, and turn them around face up, is the same thing as pulling each card from the resources, also face down, and put them in a "snake trail". - He says -> No that is not the same thing because I've read the rules and they say we have to put them in a "snake trail".

It's the same random, because RANDOM IS RANDOM. This is like saying, in a "who has the highest card game", we have 2 cards faced down and we have to decide who draws the first card, because it matters who draws the first card.

He simply did not understand and used the game rules as an argument for his "no" answer, which had obviously no connection with the fact that he failed in logic.

My question is, how do I explain to him that his logic is wrong, how do I make him see he's using a wrong argument for his answer, and how do you deal in general with people like him?

"The Same Thing" here is a little vague. Cards in a pile have a linear structure, while picking cards up from arbitrary elements in an array has no such structure. The question is whether this linear structure serves any purpose in the game other than simply being the source of your draw (I don't know anything about Catan). If it does serve such a purpose, then the fact that we're dealing with the same sort of imperfect information when we're drawing cards is actually a smoke-screen. – Paul Ross – 2012-03-02T01:43:05.083

The goal of that stage is to randomly place the cards across the map, and whether you place them in snake trail or all at once and turn them around is the same thing, randomly speaking. – Andrei Cristian Prodan – 2012-03-21T06:04:51.910

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It's a statistical question. You have X cards which are spread among X slots.

Every card has the same probability to fit into the first place, the second, the third and so on.

You can simplify the board to fit only 2x2 cards, and then exhaustively enumerate all possibilities:

4*3*2*1=24


You can write the possibilities down, in a systematical manner:

1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 ...
2 ...
3 ...
4 ...


The digits are combined, building a 4-digit number in increasing order. Every number would symbolize one of the specific cards (Wood, Sheep, ...), even if they are repeated.

Every number represents one different way, how the cards can be placed, which all occur with the same probability. For the gameplay, it wouldn't matter which of the wood-cards comes first - they are all equal. But to compare the distributions - spreading all cards over the table or mixing them, and playing them sequentially, leads to the same result and is more easy to understand.

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Sorry, but your friend is correct-- it's not the same thing.

It gives the same result, but that's not the point; when playing a game, one plays by the rules, and if the rules say to lay out the cards in a snake pattern, that's the way you are supposed to do it. If the rules say you have to be standing up when you lay out the cards, facing east, and wearing a silk hat, that's the way you are supposed to do it. You can argue that the cards will show the same values even if you face west, or wear polyester-- but that's irrelevant.

From a logic perspective, your friend is using an Appeal to Authority, which in this case is not a fallacy, because the rules of a game constitute the definitive authority on the matter.

I totally agree with that, I never went against the rules. I will quote myself 'He simply did not understand and used the game rules as an argument for his "no" answer, which had obviously no connection with ....' That's actually a logical fallacy, what he did. The argument was whether or not it's random when you throw them on the board and turn them face up, and he said no, using the rules(which had nothing to do with anything in the world being random or not) as an argument. It's possible he did not get that I was generally speaking about randomization.Hmm.. Thanks for your answer anyway. – Andrei Cristian Prodan – 2012-03-21T06:14:42.163