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imagineerThat
imagineerThat
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I think I intuitively see this more clearly now.

If one draws two parallel lines A and B with lengths equal to coin flips where heads adds a cm to A and tails adds a cm to B, then the more flips one takes, the larger the difference in lengths between A and B. This tends towards a positive value, much like the RMS distance from the origin.

However, if one takes the fraction of that difference (again AA-B)/(A+B) over expected difference, which is A/(A-B) or 0.5 for balanced flipping, then that fraction tends towards zero with more flips.

The excess tends to increase whereas the proportion of the excess over the total steps tends towards zero.

I think I intuitively see this more clearly now.

If one draws two parallel lines A and B with lengths equal to coin flips where heads adds a cm to A and tails adds a cm to B, then the more flips one takes, the larger the difference in lengths between A and B. This tends towards a positive value, much like the RMS distance from the origin.

However, if one takes the fraction of that difference (again A-B) over expected difference, which is A/(A-B) or 0.5 for balanced flipping, then that fraction tends towards zero with more flips.

I think I intuitively see this more clearly now.

If one draws two parallel lines A and B with lengths equal to coin flips where heads adds a cm to A and tails adds a cm to B, then the more flips one takes, the larger the difference in lengths between A and B. This tends towards a positive value, much like the RMS distance from the origin.

However, if one takes the fraction of that difference (A-B)/(A+B) over expected difference, which is 0.5 for balanced flipping, then that fraction tends towards zero with more flips.

The excess tends to increase whereas the proportion of the excess over the total steps tends towards zero.

Source Link
imagineerThat
imagineerThat
  • 150
  • 9

I think I intuitively see this more clearly now.

If one draws two parallel lines A and B with lengths equal to coin flips where heads adds a cm to A and tails adds a cm to B, then the more flips one takes, the larger the difference in lengths between A and B. This tends towards a positive value, much like the RMS distance from the origin.

However, if one takes the fraction of that difference (again A-B) over expected difference, which is A/(A-B) or 0.5 for balanced flipping, then that fraction tends towards zero with more flips.