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    <p>Let me introduce you to my good friend Bayes... <a href="http://en.wikipedia.org/wiki/Bayesian_inference" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Bayesian_inference</a></p> <p>Edit: Part 1) Bayes will only work for non-independent trials. If winning one game somehow increases your probability of winning the next, you can carry on! Otherwise this isn't very helpful at all.</p> <p>Edit: Part 2) Regardless, the base is the following Bayes' Formula.</p> <pre><code>P(A|B) = P(B|A) P(A) ----------- P(B) </code></pre> <p>Which is read, "The probability of A given B is equal to Prob. B given A times Prob of A all over Prob. of B". To illustrate this, the car salesman with 3 doors problem is often given.</p> <blockquote> <p>You have 3 doors and behind one door there's a brand new car. The other two doors have absolutely nothing. The host then asks you to pick a door. Remember, there is door 'A', 'B' and 'C'. Therefore, you have a 1/3 probability of being correct.</p> <p>The host, being a generous guy, opens one of the other doors. He now gives you the option of either sticking with the same door or opening the other door.</p> </blockquote> <p>I realized that explaining this in a Stackoverflow reply would take forever and just googled it. This is the Monty Hall problem: <a href="http://en.wikipedia.org/wiki/Monty_Hall_problem" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Monty_Hall_problem</a>. <a href="http://en.wikipedia.org/wiki/Monty_Hall_problem#Bayesian_analysis" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Monty_Hall_problem#Bayesian_analysis</a> for the Bayes section.</p> <p>Edit: Part 3) You may want to look up 'Bayesian Networks' if you decide this sort of approach can work (but on a much grander scheme)</p>
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    1. POAI / inference problem
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    1. USMalaxeur
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    1. COCan you explain how it would apply to this particular problem ?
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      1. USJustin
    2. COThere are a lot of examples on the page, but the premise is that given certain probabilities you can 'infer' other probabilities given certain conditions. It's very vague, but it works. I'd reply in the comment however take a look at the edit for more information
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    3. CORe: Edit 1, What if he were modeling each individual match instead of the tournament as a whole?
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      1. USJoe Holloway
 

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