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#1
08-28-2005, 02:41 PM
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Theory: 11.7447%, Excel Simulation: 10.4%, Mathematica Sim 11.3%
I agree, there are 901 windows. That changes the theoretical answer to 11.7447%.
For the Excel simulation, I agree that cell E1 should be =D1. In the other E cells I had max of cells D(i-1) and E(i-1) which I think works as well as your formula. 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. 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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#2
08-28-2005, 05:03 PM
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Re: Theory: 11.7447%, Excel Simulation: 10.4%, Mathematica Sim 11.3%
[ QUOTE ]
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. [/ QUOTE ] 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%. [ QUOTE ] 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. [/ QUOTE ] 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. alThor
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