Proability of occurance of a split hand in stud with the same straight?

Question

In 7 card stud, what is the probability that two people will split the pot with the same straight?

Answer 1

The odds depend on the number of players.

According to wizardofodd.com

http://wizardofodds.com/poker

there are 6,180,020 combinations resulting in a straight in seven card stud, making the odds of a straight in a given hand

0.04619382 = 4.6% or roughly 22 to 1.

Since there are ten different straights possible (5 high through ace high) the number of combinations resulting in a straight with a particular card high is

6,180,020 / 10 = 618,002

if all 52 cards are in play. However, when you are calculating the odds of matching another straight not all 52 cards are available. To calculate the impact, use the fact that 3/4 of cards of each rank is still in the deck, So for each of the five cards in the straight, you have to multiply the number of combinations by 0.75.

0.75 to the fifth power is 0.2373046875

and

0.2373046875 x 618,002 = 146,655

That makes the odds of having another specific hand have the same straight

146,655 / 133,784,560 = 0.0010962 = 0.11% = 912 to 1

Now you need to factor in number of players. Call the number of players n.

The odds of any player having a straight =

n x 0.04619382

and the odds of a second player having the same straight =

(n-1) x 0.0010962

then, finally, you have to multiply the two results together.

So, for a five player game, the odds would be

5 x 0.04619382 x 4 x 0.0010962 = 0.00101 = 0.1% = 1,000 to 1

Please note that there are several simplifying assumptions made in this calculation which will have increased the odds slightly. For example, the possibility of the second straight being a straight flush was not factored in, nor was the possibility that the pot would not be split because a third hand beat the straights.

Answer 2

the odds of getting a straight are one in 132. which is any straight. the odds of two people getting the same straight is probably more rare. If there are 10 possible straights (A-5, 2-6, 3-7, etc) , I would multiply 132 by 10 and get one in 1320. Not sure if that's right, but it might be close...sorry I'm not a statistician. another question you could ask is the odds of 4 people having the same straight....that's probably even more rare.

Answer 3

Hard question. I have no tools to calculate that but its occur more often than a split hand with a flush, which is extremely rare.