The math behind it is pretty straightforward. In a 52 card deck, the dealt royal cycle is fixed, at 649,740. The total royal cycle depends on the drawing strategy used, lets assume it's 40,000. So, in a dealt royal cycle on a single play, the total royals (on average) would be 649,740/40,000 = about 16. The standard deviation is the square root of the average, so sqrt(16) = 4. On a single play, the dealt royal represents one royal, and one is much less than the SD at 4, so it's basically lost in the noise. On a four play, you get four times as many royals per dealt royal cycle, so 64, and sqrt(64) = 8. The dealt royal represents four of those royals, or half the SD, now it's getting significant. On a 100 play, you get 100 times as many royals per dealt royal cycle, so 1600, and sqrt(1600) = 40. The dealt royal now represents 100 of those royals, or 2.5 times the SD. The dealt royal is now the more dominant noise factor over the standard deviation. This effect isn't limited to royals, but applies to all hands.
Posted by: nightoftheiguana2000@yahoo.com
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