Statistics Trick (why nobody played with me as a child)

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Statistics Trick (why nobody played with me as a child)

Post  Max on Fri Oct 15, 2010 1:28 am

Okay, okay, I'm a big nerd.

1) Take 2 quarters. Each quarter has heads or tails. Outcome of flipping both coins can be either two heads, two tails, or one head and one tail.

2) How much would it take for someone to accept a bet against you if you take 1 head and 1 tails and they take the other two possibilities? 2/3 odds in their favour and 1/3 odds in your favour means they should be willing to accept a wager of $0.67 vs. your wager of $ 0.33. 67% x $0.67 - 33% x $0.33 = expected value of $0.00.

3) Give them better odds. Offer to pay $0.40 each time the coins land with anything other than 1 head and 1 tail if they agreed to pay $0.60 each time the coins land with 1 head and one tail. 67% x $0.40 - 33% x -$0.60 = expected value of $0.10, therefore this is a good deal for your opponent and logically they should accept.

4) The catch. In fact your odds of landing 1 head and 1 tail are not 1/3. They are 2/4. Possible outcomes are actually A=heads, B=heads; A=heads, B=tails; A=tails, B=heads; A=tails, B=tails. 50% x $0.40 - 50% x $0.60 = expected value of -$0.20. A losing proposition for your opponent. You are relying on your opponent to use superficial logic without completely understanding the way the game works.

The lesson: you will find the stock markets (or at least the investors) work in the same way. We adhere to our own superficial understanding of the rules (assuming efficient markets, no collusion, no manipulation), and assume we can forecast what will happen in the future based on historical patterns. In my experience, reality is far more complicated and difficult to predict than any model is capable of. There are some things which are constants, and it is possible to have a theory and be right from time to time, but in my opinion your forecast should represent a range of probabilities and expected gain or loss with each outcome rather than predict a specific result. This approach is referred to in statistics as Expected Value and will provide a much clearer picture of the risk vs. reward tradeoff.

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