by Guest » Sun Nov 07, 2021 10:01 pm
I don't consider that a very good approximation!
You state that there are 2,598,960 possible poker hands. I will accept that. It would be very tedious to calculate it! And there are 4 "royal flushes"- that's easy, they are "A, K, Q, J, 10 of spades", "A, K, Q, J, 10 of hearts", "A, K, Q, J, 10 of diamonds", and "A, K, Q, J, 10 of clubs". So the probability of any given poker hand be a royal flush is 4/2598960= 1/649840= 0.00000153908 approximately. We can write that as 1.53908/1000000 (we moved the decimal point 6 places to the right which is equivalent to multiplying by 10 six so we have to divide by 10 times to correct that).
But rather rounding up to 0.000002 is would round instead to 0.0000015. Since 1.5= 3/2 that converts to 1.5/100000= 3/2000000. Rather than "2 chances in a million" that gives the much more accurate "3 chances in 2 million".