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Old 3rd March 2012, 02:41 PM   #15
ynot
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Join Date: Jan 2006
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Originally Posted by Ziggurat View Post
Let's do a simple example. Our contest is to pick a number between 1 and 100. If I pick once, my odds of winning are 0.01. If I pick two different numbers for the same contest, my odds of winning are 0.02, and my odds of losing are 0.98.

Now let's say I play the game twice, picking one number each time. The odds that I'll win any one of those contests is 0.01, and the odds I lose any one of those contest is 0.99. That means that the odds I win twice are 0.0001 (0.01*0.01). I could also win the first time and lose the second time with a probability of 0.0099 (0.01*0.99), or lose the first time and win the second time with a probability of 0.0099 (0.99*0.01), or never win with probability 0.9801 (0.99*0.99). So in this scenario, I have an 0.0198 chance of winning once (add the two different ways of doing it together), an 0.0001 chance of winning twice, and an 0.9801 chance of never winning. That's close to the odds of winning with two picks in one draw, but it's not quite the same. But the smaller my overall odds are, the less difference it will make how I arrange things. But does it make a difference? Yes, it makes a difference. Maybe not enough for you to care, but that's a different issue.
To demonstrate the point I think I have I would prefer a contest to pick a number between 1 and 100,000,000,000 rather than 1 and 100 as the likelihood of ever picking the correct number from 1 in 100 is far greater than from 1 in 100,000,000,000 (even thought the math is essentially the same).
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Last edited by ynot; 3rd March 2012 at 02:49 PM.
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