Originally Posted by
ynot
I understand your point but wonder if it’s actually applicable in practice when the odds of any individual attempt ever winning are so incredibly unlikely. Would 1 attempt in 100 billion draws really make it any more likely you would ever win against 100 billion to 1 odds?
No amount of previous draws has any effect on current or future draws (the balls don’t have a memory).
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.