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[QUOTE="BelFish, post: 6474797, member: 406001"]
The probability of getting a royal flush in Texas Hold'em if people didn't fold preflop and postflop some hands would be:

P = 4*C(5 of 5)*C(2 of 47)/C(7 of 52)=4324/133784560=0.0000323 or 0.00323%

Taking into account folds, we will roughly estimate this probability as a number of 0.00001, or 1 time for every 100,000 hands.

Then the probability of getting a 2 royal flush in the next 2 hands will be equal to 1 in 10 billion hands.

And here is that complex formula for calculating at a distance of N hands (for calculation in excel):

A1 is P
A2 is K
A3 is N
A6 is (p), or the probability of the event for the repeat series we are looking for.

A4=1+(1-A1)*A1^A2+(A2+1)*(1-A1)^2*A1^(2*A2)

A5=((1-A1*A4)/((A2+1-A2*A4)*(1-A1)))/A5^(A3+1)

A6=1-A5

Here is an example of calculating this formula for playing roulette: the probability that 11 or more times in a row will be one color, for example, red at a distance of 2000 games, is 47%, and for a distance of 5000 games this probability will be equal to 80%

Here we substitute K=11, P=18/37 into the formula and calculate for cases N=2000 and N=5000

K is the number of repetitions of the event in a row in a series of N games, and P is the probability of this event.

Similarly, using the same formula, you can calculate the probability of getting a royal flush 2 times in a row at any distance. To do this, you need to substitute K=2, P=0.00001 into the formula and see what happens for different values of N (1000, 10000, 100000, 10000000)
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