My Math Forum Coin flipping game, approximation of one milion flips

 March 21st, 2011, 02:15 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: Coin flipping game, approximation of one milion flips The expected value is certainly correct - i.e. if you were to perform the million-coin-toss experiment a large number of times then the mean number of heads recorded would approach 500,000. As for the average difference between the recorded result and the 'perfect' 500k/500k split, from memory (you should check) it will be of the order of $\sqrt N$ or 1000. In other words, if you think of your experiment in the number line sense the average mean distance away from the origin would approach something on the order of 1000. However, since this is a simple binomial distribution with a very large N you will get a good approximation by the Normal approximation with mean 500000 and variance 250000. Using this to calculate the probability of returning a loss (no. of tails < 400000) gives a result more unlikely than finding Elvis riding the Loch Ness Monster.
 March 21st, 2011, 02:26 AM #3 Newbie   Joined: Mar 2011 Posts: 2 Thanks: 0 Re: Coin flipping game, approximation of one milion flips thanks man (bow) really appreciate
March 21st, 2011, 06:10 AM   #4
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Re: Coin flipping game, approximation of one milion flips

Quote:
 Originally Posted by mr_kaktus The absolute value (distance from 0 point) will become greater and greater, but ratio of number of flips and number of heads/tails will be closer and closer to 1/2.
It's worth mentioning that, if the coin is truly fair, you expect the distance from 0 to decrease to 0 or 1 infinitely often, even as the expected value of the absolute distance from 0 increases.

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