His Royal Hotness

[Buzz-cp]

K i've gotten 6 royals in 180K Hold'em hands. Please give me some kind of number that tells me how hot this is. FWIW some use 1 hole card & some use both.

Cheers,
Buzz

[BruceZ]

[ QUOTE ]
K i've gotten 6 royals in 180K Hold'em hands. Please give me some kind of number that tells me how hot this is. FWIW some use 1 hole card & some use both.

Cheers,
Buzz

[/ QUOTE ]

This is right in line with what you would expect if all of these hands went to the river. The probability of a royal using 1 or 2 hole cards is 1 in 32,487 hands that go to the river, or 6 in 194,922.

The probability of any royal can be computed as:

4*C(47,2) / C(52,7) =~ 1 in 30,940.

The total number of 7 card hands is C(52,7). There are 4 possible suits for the royal, and for each of these there are C(47,2) ways to choose the 2 cards that don't play. This includes the cases where neither hole card plays, but since these only account for 1 of the C(7,2) ways to choose the hole cards for each royal, we can exclude these by simply multiplying by [C(7,2)-1]/C(7,2) = 20/21. This gives the probability of 1 in 32,487.

Calling this probability P, the probability of getting 6 or more royals in 180,000 hands is given by the Excel function BINOMDIST as:

1 - BINOMDIST(5,180000,P,TRUE) =~ 47.8%.

Now if only half of these hands went to the river, then this probability would drop to about 6.3% which we get by changing 180000 to 90000. If 1/4 of the hands go to the river, then this becomes about 0.3%.

EDIT: Fixed typo 19/20 --> 20/21.

[bigpooch]

Just a typo to note here:

[ QUOTE ]
multiplying by [C(7,2)-1]/C(7,2) = 19/20.

[/ QUOTE ]

Here, BruceZ really means " = 20/21" since the probability
computed and stated in the following sentence is correct.