Comments - Dice throw: much less random than you think! - AnalyticBridge2020-07-02T20:29:10Zhttps://www.analyticbridge.datasciencecentral.com/profiles/comment/feed?attachedTo=2004291%3ABlogPost%3A56088&xn_auth=noInterestingly, Von Neumann ca…tag:www.analyticbridge.datasciencecentral.com,2009-10-22:2004291:Comment:561622009-10-22T18:11:25.410ZDominic Pouzinhttps://www.analyticbridge.datasciencecentral.com/profile/DominicPouzin
Interestingly, Von Neumann came up with a simple method to generate a fair coin toss from a biased coin.<br />
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Flip the coin twice. If it comes up heads followed by tails, then call the outcome head. If it comes up tails followed by heads, then call the outcome tail. Otherwise repeat the process. Assuming that flips are independent, the procedure simulates an unbiased coin, no matter what the coin's bias is. This is easy to verify using probability p for heads, and 1-p for tails: p * (1-p) = (1-p) *…
Interestingly, Von Neumann came up with a simple method to generate a fair coin toss from a biased coin.<br />
<br />
Flip the coin twice. If it comes up heads followed by tails, then call the outcome head. If it comes up tails followed by heads, then call the outcome tail. Otherwise repeat the process. Assuming that flips are independent, the procedure simulates an unbiased coin, no matter what the coin's bias is. This is easy to verify using probability p for heads, and 1-p for tails: p * (1-p) = (1-p) * p.<br />
<br />
By requiring that the starting position for all coin tosses be the same (ex: always heads), we should still be able to get fair NFL toss coins :) That's some cool stuff!! I ca…tag:www.analyticbridge.datasciencecentral.com,2009-10-21:2004291:Comment:561352009-10-21T09:36:05.239ZArunhttps://www.analyticbridge.datasciencecentral.com/profile/Arun
That's some cool stuff!! I can't believe it.. They're saying the which ever side you toss the coin, it has the bias created there itself! It does feel a little logical, since if we were to toss the coin from "Neither Heads Nor Tails" position, then maybe we could argue that the Expected Probablility could be 50:50.<br />
Atleast this is how I see it, since we're giving an initial bias i.e. here the position for the side tossed from, it is logical to say that that side might more probability of…
That's some cool stuff!! I can't believe it.. They're saying the which ever side you toss the coin, it has the bias created there itself! It does feel a little logical, since if we were to toss the coin from "Neither Heads Nor Tails" position, then maybe we could argue that the Expected Probablility could be 50:50.<br />
Atleast this is how I see it, since we're giving an initial bias i.e. here the position for the side tossed from, it is logical to say that that side might more probability of landing.<br />
<br />
But, even so, I'd still say, it's hardly a problem since the probability goes to about 55:45? That's not too significant to affect the outcome, and it can be safely considered random still right?? Only if the value can be predicted beforehand with a certain level of accuracy does the problem of affecting Randomness arise!<br />
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Is there someone who feels otherwise??