Re: Odds of making a royal through throwing all five cards away on the flop.
This is not an easy calculation for me because of variables. And I'm not known for trying to come up with proper equations when I have no financial incentive. So I can ball park the thing pretty easy but won't attempt to zero in.
At 9/6 Jacks the game stats show 84,360 combinations out of 2,598,960 where you will throw away all five cards. Thats a frequency of 30.81 games.
With 47 cards left in the deck there are 1,533,939 possible combinations (47X46X45X44X43/5X4X3X2X1).
The problem from here on out is probably over 50% of the time the five card hand you throw away will have a ten in it. Which means there will be only 3 possible royals remaining in the deck. I'm going to go with 55%.
1,533,939/3 = 511,313
1,533,939/4 = 383,485
So 55% of the time it will be 30.81 X 511,313 = 15,753,553
And 45% of the time it will be 30.81 X 383,485 = 11,815,172
Averaging it together I come up with a frequency of 13,981,282. So you could say 1 in 14 million hands. No wonder it took me so long to hit one.
This is my take on it but I'm just an amateur mathematician. I'll leave it up to better mathematicians to zero in on the frequency.
Posted by: mickeycrimm@yahoo.com
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