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Old 08-28-2005, 05:03 PM
alThor alThor is offline
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Join Date: Mar 2004
Posts: 6
Default Re: Theory: 11.7447%, Excel Simulation: 10.4%, Mathematica Sim 11.3%

I reran the Excel simulation with your corrections. Among the 200,000 virtual deals there were 20,789 deals that had 14 pairs or more in a window. That simulation gives a 10.4% estimate of the probability.

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Just so we are clear, does 200k deals mean 200 million hands?

In any case, I also wrote a sim from scratch in Python. After 20k trials (i.e. up to 20 million "hands"), I got around 10.3%, which has a conf. interval size around +/- half a percent, so I believe it is below 11%.

I wrote a simulator in Mathematica and got 22,545 deals with 14 pairs or more. That's 11.3%. Given the size of the simulations, either there is a bug one of the simulation programs and the theoretical derivation, or these random generators are not good enough. Hmm.

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It is not a problem with the random generators (though with something that big, I wouldn't trust Excel completely). Perhaps we both made the same sim mistake, whatever it is. I also checked some of your numbers; I agree with your "r" values, etc. We are missing something. Oh well.

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